## Quantum Physics (quant-ph) updates on the arXiv.org e-print archive



The low energy physics of interacting quantum systems is typically understood through the identification of the relevant quasiparticles or low energy excitations and their quantum numbers. We present a quantum information framework that goes beyond this to examine the nature of the entanglement in the corresponding quantum states. We argue that the salient features of the quasiparticles, including their quantum numbers, locality and fractionalization are reflected in the entanglement spectrum and in the mutual information. We illustrate these ideas in the specific context of the $d=1$ transverse field Ising model with an integrability breaking perturbation.

The study of dissipation and decoherence in generic open quantum systems recently led to the investigation of spectral and steady-state properties of random Lindbladian dynamics. A natural question is then how realistic and universal those properties are. Here, we address these issues by considering a different description of dissipative quantum systems, namely the discrete-time Kraus map representation of completely positive quantum dynamics. Through random matrix theory (RMT) techniques and numerical exact diagonalization, we study random Kraus maps, allowing for a varying dissipation strength, and their local circuit counterpart. We find the spectrum of the random Kraus map to be either an annulus or a disk inside the unit circle in the complex plane, with a transition between the two cases taking place at a critical value of dissipation strength. The eigenvalue distribution and the spectral transition are well described by a simplified RMT model that we can solve exactly in the thermodynamic limit, by means of non-Hermitian RMT and quaternionic free probability. The steady-state, on the contrary, is not affected by the spectral transition. It has, however, a perturbative crossover regime at small dissipation, inside which the steady-state is characterized by uncorrelated eigenvalues. At large dissipation (or for any dissipation for a large-enough system) the steady-state is well described by a random Wishart matrix. The steady-state properties thus coincide with those already observed for random Lindbladian dynamics, indicating their universality. Quite remarkably, the statistical properties of the local Kraus circuit are qualitatively the same as those of the nonlocal Kraus map, indicating that the latter, which is more tractable, already captures the realistic and universal physical properties of generic open quantum systems.

We establish the appearance of a qualitatively new type of spin liquid with emergent exceptional points when coupling to the environment. We consider an open system of the Kitaev honeycomb model generically coupled to an external environment. In extended parameter regimes, the Dirac points of the emergent Majorana fermions from the original model are split into exceptional points with Fermi arcs connecting them. In glaring contrast to the original gapless phase of the honeycomb model which requires time-reversal symmetry, this new phase is stable against all perturbations. The system also displays a large sensitivity to boundary conditions resulting from the non-Hermitian skin effect with telltale experimental consequences. Our results point to the emergence of new classes of spin liquids in open systems which might be generically realized due to unavoidable couplings with the environment.

Semiconductor quantum dots in cavities are high-performance single-photon sources. Thus far the most efficient sources utilise resonant excitation of an unpolarized quantum emitter coupled to a highly birefringent cavity. However, this demands very high polarization extinction, and challenging experimental operation. Here, we remove these requirements by using off-resonant phonon-assisted excitation of a linear exciton dipole, exploiting the quantum dot's vibrational environment and natural asymmetry. This allows the collection of single photons that are spectrally separated from the excitation laser, and intrinsically present a very high degree of linear polarization up to 0.994 $\pm$ 0.007. This phonon-assisted excitation scheme enables very high single-photon purity and indistinguishability, and only reduces the emitter population by (15 $\pm$ 1) %, as compared to resonant excitation. Overall, we simultaneously demonstrate a polarized first lens brightness of 0.51 $\pm$ 0.01, with a single-photon purity of 0.939 $\pm$ 0.001 and corrected single-photon indistinguishability of 0.915 $\pm$ 0.003.

The Gottesman-Knill theorem states that a Clifford circuit acting on stabilizer states can be simulated efficiently on a classical computer. Recently, this result has been generalized to cover inputs that are close to a coherent superposition of logarithmically many stabilizer states. The runtime of the classical simulation is governed by the stabilizer extent, which roughly measures how many stabilizer states are needed to approximate the state. An important open problem is to decide whether the extent is multiplicative under tensor products. An affirmative answer would yield an efficient algorithm for computing the extent of product inputs, while a negative result implies the existence of more efficient classical algorithms for simulating largescale quantum circuits. Here, we answer this question in the negative. Our result follows from very general properties of the set of stabilizer states, such as having a size that scales subexponentially in the dimension, and can thus be readily adapted to similar constructions for other resource theories.

Variational quantum eigensolver (VQE) emerged as a first practical algorithm for near-term quantum computers. Its success largely relies on the chosen variational ansatz, corresponding to a quantum circuit that prepares an approximate ground state of a Hamiltonian. Typically, it either aims to achieve high representation accuracy (at the expense of circuit depth), or uses a shallow circuit sacrificing the convergence to the exact ground state energy. Here, we propose the approach which can combine both low depth and improved precision, capitalizing on a genetically-improved ansatz for hardware-efficient VQE. Our solution, the multiobjective genetic variational quantum eigensolver (MoG-VQE), relies on multiobjective Pareto optimization, where topology of the variational ansatz is optimized using the non-dominated sorting genetic algorithm (NSGA-II). For each circuit topology, we optimize angles of single-qubit rotations using covariance matrix adaptation evolution strategy (CMA-ES) -- a derivative-free approach known to perform well for noisy black-box optimization. Our protocol allows preparing circuits that simultaneously offer high performance in terms of obtained energy precision and the number of two-qubit gates, thus trying to reach Pareto-optimal solutions. Tested for various molecules (H$_2$, H$_4$, H$_6$, BeH$_2$, LiH), we observe nearly ten-fold reduction in the two-qubit gate counts as compared to the standard hardware-efficient ansatz. For 12-qubit LiH Hamiltonian this allows reaching chemical precision already at 12 CNOTs. Consequently, the algorithm shall lead to significant growth of the ground state fidelity for near-term devices.

The concept of an embodied intelligent agent is a key concept in modern AI and robotics. Physically, an agent---like a Turing machine---is an open system embedded in an environment which it interacts with through sensors and actuators. It contains a learning algorithm that correlates the sensor and actuator results by learning features about its environment. The sensor-actuator system is similar to a measurement based control system. Quantum mechanics enables new measurement and control protocols capable of exceeding what can be achieved classically. We demonstrate how quantum optical sensors and actuators can dramatically improve an agent's ability to learn in a thermal environment. Furthermore we use the Jarzynski equality to show that learning maximises the exchange in free energy $\Delta F$ between the agent's sensor and actuator when considered as a stochastic feedback cycle.

All three motional modes of a charged dielectric nanoparticle in a Paul trap are cooled by direct feedback to temperatures of a few mK. We test two methods, one based on electrical forces and the other on optical forces; for both methods, we find similar cooling efficiencies. Cooling is characterized for both feedback forces as a function of feedback parameters, background pressure, and the particle's position.

A quantum algorithm is developed to calculate decay rates and cross sections using quantum resources that scale polynomially in the system size assuming similar scaling for state preparation and time evolution. This is done by computing finite-volume one- and two-particle Green's functions on the quantum hardware. Particle decay rates and two particle scattering cross sections are extracted from the imaginary parts of the Green's function. A $0+1$ dimensional implementation of this method is demonstrated on IBM's superconducting quantum hardware for the decay of a heavy scalar particle to a pair of light scalars.

When a quantum system is subject to a thermal gradient it may sustain a steady non-equilibrium heat current, by entering into a so-called non equilibrium steady state (NESS). Here we show that NESS constitute a thermodynamic resource that can be exploited to fuel a quantum heat engine. This adds to the list of recently reported sources available at the nano-scale, such as coherence, entanglement and quantum measurements. We elucidate this concept by showing analytic and numerical studies of a two-qubits quantum battery that is alternatively charged by a thermal gradient and discharged by application of a properly chosen unitary gate. The presence of a NESS for the charging step guarantees steady operation with positive power output. Decreasing the duration of the charging step results in a time periodic steady state accompanied by increased efficiency and output power. The device is amenable to implementation with different nanotechnology platforms.

Quantum mechanics in the Wigner-von Neumann interpretation is presented. This is characterized by 1) a quantum dualism between matter and consciousness unified within an informational neutral monism, 2) a quantum perspectivism which is extended to a complementarity between the Copenhagen interpretation and the many-worlds formalism, 3) a psychophysical causal closure akin to Leibniz parallelism and 4) a quantum solipsism, i.e. a reality in which classical states are only potentially-existing until a conscious observation is made.

The monogamy of quantum entanglement captures the property of limitation in the distribution of entanglement. Various monogamy relations exist for different entanglement measures that are important in quantum information processing. Our goal in this work is to propose a general monogamy inequality for all entanglement measures on entangled qubit systems. The present result provide a unified model for various entanglement measures including the concurrence, the negativity, the entanglement of formation, Tsallis-q entropy, Renyi-q entropy, and Unified-(q,s) entropy. We then proposed tightened monogamy inequalities for multipartite systems. We finally prove a generic result for the tangle of high-dimensional entangled states to show the distinct feature going beyond qubit systems. These results are useful for exploring the entanglement theory, quantum information processing and secure quantum communication.

We designed a nanoscale light extractor (NLE) for the efficient outcoupling and beaming of broadband light emitted by shallow, negatively charged nitrogen-vacancy (NV) centers in bulk diamond. The NLE consists of a patterned silicon layer on diamond and requires no etching of the diamond surface. Our design process is based on adjoint optimization using broadband time-domain simulations, and yields structures that are inherently robust to positioning and fabrication errors. Our NLE functions like a transmission antenna for the NV center, enhancing the optical power extracted from an NV center positioned 10 nm below the diamond surface by a factor of more than 35, and beaming the light into a 30{\deg} cone in the far field. This approach to light extraction can be readily adapted to other solid-state color centers.

Estimation of the coin parameter(s) is an important part of the problem of implementing more robust schemes for quantum simulation using quantum walks. We present the estimation of the quantum coin parameter used for one-dimensional discrete-time quantum walk evolution using machine learning algorithms on their probability distributions. We show that the models we have implemented are able to estimate these evolution parameters to a good accuracy level. We also implement a deep learning model that is able to predict multiple parameters simultaneously. Since discrete-time quantum walks can be used as quantum simulators, these models become important when extrapolating the quantum walk parameters from the probability distributions of the quantum system that is being simulated.

We study the effect of strain on the band engineering in gapped graphene subject to external sources. By applying the Floquet theory, we determine the effective Hamiltonian of electron dressed by a linearly, circularly and an elliptically polarized dressing field in the presence of strain along armchair and zigzag directions. Our results show that the energy spectrum exhibits different symmetries and still isotropic for the strainless case, whereas it is linear as in the case of pristine graphene. It decreases slowly when strain is applied along the armchair direction but increases rapidly for the zigzag case. Moreover, it is found that the renormalized band gap changes along different strain magnitudes and does not change for the polarization phase $\theta$ compared to linear and circular polarizations where its values change oppositely.

Exceptional points, the spectral degeneracy points in the complex parameter space, are fundamental to non-Hermitian quantum systems. The dynamics of non-Hermitian systems in the presence of exceptional points differ significantly from those of Hermitian ones. Here we investigate non-adiabatic transitions in non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric systems, in which the exceptional points are driven through at finite speed which are quadratic or cubic functions of time. We identity different transmission dynamics separated by exceptional points, and derive analytical approximate formulas for the non-adiabatic transmission probabilities. We discuss possible experimental realizations with a $\mathcal{P}\mathcal{T}$-symmetric non-Hermitian one-dimensional tight-binding optical waveguide lattice.

We identify a (pseudo) relativistic spin-dependent analogue of the celebrated quantum phase transition driven by the formation of a bright soliton in attractive one-dimensional bosonic gases. In this new scenario, due to the simultaneous existence of the linear dispersion and the bosonic nature of the system, special care must be taken with the choice of energy region where the transition takes place. Still, due to a crucial adiabatic separation of scales, and identified through extensive numerical diagonalization, a suitable effective model describing the transition is found. The corresponding mean-field analysis based on this effective model provides accurate predictions for the location of the quantum phase transition when compared against extensive numerical simulations. Furthermore, we numerically investigate the dynamical exponents characterizing the approach from its finite-size precursors to the sharp quantum phase transition in the thermodynamic limit.

Quantum teleportation is a method for utilizing quantum measurements and the maximally entangled Einstein-Podolsky-Rosen (EPR) pair to transmit an unknown quantum state. It is well known that all entangled states demonstrate so-called "nonclassical teleportation" that cannot be simulated by the seminal classical measure-prepare strategy. Herein, we propose a new benchmark which reveals that not all nonclassical teleportations are truly quantum-mechanical. Rather, there exists a more robust classical-teleportation model, which includes the measure-prepare mimicry as a special case, that can describe certain nonclassical teleportations. Invalidating such a general classical model indicates genuine quantum teleportation wherein both the pair state and the measurement are truly quantum-mechanical. We prove that EPR steering empowers genuine quantum teleportations, rather than entanglement. The new benchmark can be readily used in practical experiments for ensuring that genuine quantum teleportation is implemented. The results presented herein provide strict criteria for implementing quantum-information processing where genuine quantum teleportation is indispensable.

This paper presents a proof of the existence of novel bound states of the two-photon quantum Rabi model at the collapse point. The two-photon Rabi model is interesting not only for its important role on non-linear light-matter interaction, but also for the exhibition of many-energy-levels degenerating process called the "spectral collapse". The squeezing property of the two-photon annihilation and creation operators is the origin for this phenomenon which is well studied without the energy-slitting term $\omega_0$. However, many numerical studies have pointed out that with the presence of $\omega_0$ , some low-level isolated states exist while other high energy states collapse to $E=-\frac{\omega}{2}$, which known as incomplete spectral collapse. From the eigenvalue equation in real space, pair of second order differential equations, which are similarly to the Schrodinger equation, are derived at the collapse point. These differential equations provide explanation to the existence of isolated bound states below $E=-\frac{\omega}{2}$ with the presence of the spin slitting $\omega_0$ and better numerical method to generate those bound states.

Decoherence-induced leakage errors can potentially damage physical or logical qubits by coupling them to other system levels. Here we report the first experimental implementation of Leakage Elimination Operators (LEOs) that aims to reduce this undermining, and that can be applied alongside universal quantum computing. Using IBM's cloud quantum computer, we have studied three potentially applicable examples of subspaces in two- and three-qubit Hilbert spaces and found that the LEOs significantly suppress leakage.

Oblivious transfer is an important primitive in modern cryptography. Applications include secure multiparty computation, oblivious sampling, e-voting, and signatures.

Information-theoretically secure perfect 1-out-of 2 oblivious transfer is impossible to achieve. Imperfect variants, where both participants' ability to cheat is still limited, are possible using quantum means while remaining classically impossible. Precisely what security parameters are attainable remains unknown.

We introduce a theoretical framework for studying semi-random quantum oblivious transfer, which is shown equivalent to regular oblivious transfer in terms of cheating probabilities. We then use it to derive bounds on cheating. We also present a protocol with lower cheating probabilities than previous schemes, together with its optical realisation.

We investigate the heat flow transport properties of a parallel-coupled double quantum-dot system connected to two reservoirs with a temperature bias in the Coulomb blockade regime. We demonstrate that the effects of thermal rectification and negative differential thermal conductance (NDTC) exist in this system and analyze the influences of energy level difference and Coulomb interaction on the thermal rectification and NDTC. We find that this system can achieve a high thermal rectification ratio and NDTC when the asymmetry factor of the system is enhanced.

Photonic de Broglie waves (PBWs) via two-mode entangled photon pair interactions on a beam splitter show a pure quantum feature which cannot be obtained by classical means1-4. Although PBWs have been intensively studied for quantum metrology5-13 and quantum sensing14-25 over the last several decades, their implementation has been limited due to difficulties of high-order NOON state generation4. Recently a coherence version of PBWs, the so-called coherence de Broglie waves (CBWs), has been proposed in a pure classical regime of an asymmetrically coupled Mach-Zehnder interferometer (MZI)26. Unlike PBWs, the quantumness of CBWs originates from the cascaded quantum superposition of the coupled MZI. Here, the first CBWs observation is presented in a pure classical regime and discussed for its potential applications in coherence quantum metrology to overcome conventional PBWs limited by higher-order entangled photons. To understand the quantum superposition-based nonclassical features in CBWs, various violation tests are also performed, where asymmetrical phase coupling is the key parameter for CBWs.

The phenomenon of Many-Body Stark Localization of bosons in tilted optical lattice is studied. Despite the fact that no disorder is necessary for Stark localization to occur, it is very similar to well known many body localization (MBL) in sufficiently strong disorder. Not only the mean gap ratio reaches poissonian value as characteristic for localized situations but also the eigenstates reveal multifractal character as in standard MBL. Stark localization enables a coexistence of spacially separated thermal and localized phases in the harmonic trap similarly to fermions. Stark localization may also lead to spectacular trapping of particles in a reversed harmonic field which naively might be considered as an unstable configuration.

We provide a detailed examination of a thermal out-of-time-order correlator (OTOC) growing exponentially in time in systems without chaos. The system is a one-dimensional quantum mechanics with a potential whose part is an inverted harmonic oscillator. We numerically observe the exponential growth of the OTOC when the temperature is higher than a certain threshold. The Lyapunov exponent is found to be of the order of the classical Lyapunov exponent generated at the hilltop, and it remains non-vanishing even at high temperature. We adopt various shape of the potential and find these features universal. The study confirms that the exponential growth of the thermal OTOC does not necessarily mean chaos when the potential includes a local maximum. We also provide a bound for the Lyapunov exponent of the thermal OTOC in generic quantum mechanics in one dimension, which is of the same form as the chaos bound obtained by Maldacena, Shenker and Stanford.

We have revisited the Dirac theory in 1+1 and 2+1 dimensions by using the covariant representation of the parity-extended Poincar\'e group in their native dimensions. The parity operator plays a crucial role in deriving wave equations in both theories. We studied two position operators, a canonical one and a covariant one that becomes the particle position operator projected onto the particle subspace. In 1+1 dimensions the particle position operator, not the canonical position operator, provides the conserved Lorentz generator. The mass moment defined by the canonical position operator needs an additional unphysical spin-like operator to become the conserved Lorentz generator in 1+1 dimensions. In 2+1 dimensions, the sum of the orbital angular momentum given by the canonical position operator and the spin angular momentum becomes a constant of motion. However, orbital and spin angular momentum do not conserve separately. On the other hand the orbital angular momentum given by the particle position operator and its corresponding spin angular momentum become a constant of motion separately.

Using the language of differential geometry, I derive a form of the Bayesian Cram\'er-Rao bound that remains invariant under reparametrization. By assuming that the prior probability density is the square of a wavefunction, I also express the bound in terms of functionals that are quadratic with respect to the wavefunction and its gradient. The problem of finding an unfavorable prior to tighten the bound for minimax estimation is shown, in a special case, to be equivalent to finding the ground-state energy with the Schr\"odinger equation, with the Fisher information playing the role of the potential.

Thermodynamic principles are often deceptively simple and yet surprisingly powerful. We show how a simple rule, such as the net flow of energy in and out of a moving atom under nonequilibrium steady state condition, can expose the shortcomings of many popular theories of quantum friction. Our thermodynamic approach provides a conceptual framework in guiding atom-optical experiments, thereby highlighting the importance of fluctuation-dissipation relations and long-time correlations between subsystems. Our results introduce consistency conditions for (numerical) models of nonequilibrium dynamics of open quantum systems.

We consider using optomechanical accelerometers as resonant detectors for ultralight dark matter. As a concrete example, we describe a detector based on a silicon nitride membrane fixed to a beryllium mirror, forming an optical cavity. The use of different materials gives access to forces proportional to baryon (B) and lepton (L) charge, which are believed to be coupling channels for vector dark matter particles ("dark photons"). The cavity meanwhile provides access to quantum-limited displacement measurements. For a centimeter-scale membrane pre-cooled to 10 mK, we argue that sensitivity to vector B-L dark matter can exceed that of the E\"{o}t-Wash experiment in integration times of minutes, over a fractional bandwidth of $\sim 0.1\%$ near 10 kHz (corresponding to a particle mass of $10^{-10}$eV/c$^2$). Our analysis can be translated to alternative systems such as levitated particles, and suggests the possibility of a new generation of table-top experiments.

The No-Free-Lunch (NFL) theorem is a celebrated result in learning theory that limits one's ability to learn a function with a training data set. With the recent rise of quantum machine learning, it is natural to ask whether there is a quantum analog of the NFL theorem, which would restrict a quantum computer's ability to learn a unitary process (the quantum analog of a function) with quantum training data. However, in the quantum setting, the training data can possess entanglement, a strong correlation with no classical analog. In this work, we show that entangled data sets lead to an apparent violation of the (classical) NFL theorem. This motivates a reformulation that accounts for the degree of entanglement in the training set. As our main result, we prove a quantum NFL theorem whereby the fundamental limit on the learnability of a unitary is reduced by entanglement. We employ Rigetti's quantum computer to test both the classical and quantum NFL theorems. Our work establishes that entanglement is a commodity in quantum machine learning.

Avalanche photodiodes (APDs) are well-suited for single-photon detection on quantum communication satellites as they are a mature technology with high detection efficiency without requiring cryogenic cooling. They are, however, prone to significantly increased thermal noise caused by in-orbit radiation damage. Previous work demonstrated that a one-time application of thermal annealing reduces radiation-damage-induced APD thermal noise. Here we examine the effect of cyclical proton irradiation and thermal annealing, emulating the realistic operating profile of a satellite in low-Earth-orbit over a two-year life span. We show that repeated thermal annealing is effective in maintaining thermal noise of silicon APDs within a range suitable for quantum key distribution throughout the nominal mission life, and beyond. We examine two strategies---annealing at a fixed period of time, and annealing only when the thermal noise exceeds a pre-defined limit---and find that the latter exhibits lower thermal noise at end-of-life for most samples. We also observe that afterpulsing probability of the detector increases with cumulative proton irradiation. This knowledge helps guide design and tasking decisions for future space-borne quantum communication applications.

We study the quantum motion of an impurity atom immersed in a Bose Einstein condensate in arbitrary dimension. The Bogoliubov excitations of the Bose Einstein condensate act as a bosonic bath for the impurity. We present a detailed derivation of the $d$-dimensional Langevin equations that describe the quantum dynamics of the system, and of the associated generalized tensor that describes the spectral density in the full generality. When the impurity is not trapped, we calculate the mean square displacement, showing that the motion is super diffusive. We obtain also explicit expressions for the super diffusive coefficient in the small and large temperature limits. We find that, in the latter case, the maximal value of this coefficient is the same in all dimensions. We study also the behaviour of the average energy and compare the results for various dimensions. In the trapped case, we study squeezing and find that the stronger position squeezing can be obtained in lower dimensions. We quantify the non-Markovianity of the particle's motion, and find that it increases with dimensionality.

Acoustic devices play an important role in classical information processing. The slower speed and lower losses of mechanical waves enable compact and efficient elements for delaying, filtering, and storing of electric signals at radio and microwave frequencies. Discovering ways of better controlling the propagation of phonons on a chip is an important step towards enabling larger scale phononic circuits and systems. We present a platform, inspired by decades of advances in integrated photonics, that utilizes the strong piezoelectric effect in a thin film of lithium niobate on sapphire to excite guided acoustic waves immune from leakage into the bulk due to the phononic analogue of index-guiding. We demonstrate an efficient transducer matched to 50 ohm and guiding within a 1-micron wide mechanical waveguide as key building blocks of this platform. Putting these components together, we realize acoustic delay lines, racetrack resonators, and meander line waveguides for sensing applications. To evaluate the promise of this platform for emerging quantum technologies, we characterize losses at low temperature and measure quality factors on the order of 50,000 at 4 kelvin. Finally, we demonstrate phononic four-wave mixing in these circuits and measure the nonlinear coefficients to provide estimates of the power needed for relevant parametric processes.

Logical inference leads to one of the major interpretations of probability theory called logical interpretation, in which the probability is seen as a measure of the plausibility of a logical statement under incomplete information. In this paper, assuming that our usual inference procedure makes sense for every set of logical propositions represented in terms of commuting projectors on a given Hilbert space, we extend the logical interpretation to quantum mechanics and derive the Born rule. Our result implies that, from the epistemological viewpoints, we can regard quantum mechanics as a natural extension of the classical probability.

A fundamental pursuit in complexity theory concerns reducing worst-case problems to average-case problems. There exist complexity classes such as PSPACE that admit worst-case to average-case reductions. However, for many other classes such as NP, the evidence so far is typically negative, in the sense that the existence of such reductions would cause collapses of the polynomial hierarchy(PH). Basing cryptographic primitives, e.g., the average-case hardness of inverting one-way permutations, on NP-completeness is a particularly intriguing instance. As there is evidence showing that classical reductions from NP-hard problems to breaking these primitives result in PH collapses, it seems unlikely to base cryptographic primitives on NP-hard problems. Nevertheless, these results do not rule out the possibilities of the existence of quantum reductions. In this work, we initiate a study of the quantum analogues of these questions. Aside from formalizing basic notions of quantum reductions and demonstrating powers of quantum reductions by examples of separations, our main result shows that if NP-complete problems reduce to inverting one-way permutations using certain types of quantum reductions, then coNP $\subseteq$ QIP(2).

Large-scale multisource networks have been employed to overcome the practical constraints that entangled systems are difficult to faithfully transmit over large distance or store in long time. However, a full characterization of the multipartite nonlocality of these networks remains out of reach, mainly due to the complexity of multipartite causal models. In this paper, we propose a general framework of Bayesian networks to reveal connections among different causal structures. The present model implies a special star-convex set of non-signaling correlations from multisource networks that allows constructing polynomial-time algorithm for solving the compatibility problem of a given correlation distribution and a fixed causal network. It is then used to classify the nonlocality originated from the standard entanglement swapping of tripartite networks. Our model provides a unified device-independent information processing method for exploring the practical security against non-signaling eavesdroppers on multisource quantum networks.

The generalized amplitude damping channel (GADC) is one of the sources of noise in superconducting-circuit-based quantum computing. It can be viewed as the qubit analogue of the bosonic thermal channel, and it thus can be used to model lossy processes in the presence of background noise for low-temperature systems. In this work, we provide an information-theoretic study of the GADC. We first determine the parameter range for which the GADC is entanglement breaking and the range for which it is anti-degradable. We then establish several upper bounds on its classical, quantum, and private capacities. These bounds are based on data-processing inequalities and the uniform continuity of information-theoretic quantities, as well as other techniques. Our upper bounds on the quantum capacity of the GADC are tighter than the known upper bound reported recently in [Rosati et al., Nat. Commun. 9, 4339 (2018)] for the entire parameter range of the GADC, thus reducing the gap between the lower and upper bounds. We also establish upper bounds on the two-way assisted quantum and private capacities of the GADC. These bounds are based on the squashed entanglement, and they are established by constructing particular squashing channels. We compare these bounds with the max-Rains information bound, the mutual information bound, and another bound based on approximate covariance. For all capacities considered, we find that a large variety of techniques are useful in establishing bounds.

Number-resolving single-photon detectors represent a key technology for a host of quantum optics protocols, but despite significant efforts, state-of-the-art devices are limited to few photons. In contrast, state-dependent atom counting in arrays can be done with extremely high fidelity up to hundreds of atoms. We show that in waveguide QED, the problem of photon counting can be reduced to atom counting, by entangling the photonic state with an atomic array in the collective number basis. This is possible as the incoming photons couple to collective atomic states and can be achieved by engineering a second decay channel of an excited atom to a metastable state. Our scheme is robust to disorder and finite Purcell factors, and its fidelity increases with atom number. Analyzing the state of the re-emitted photons, we further show that if the initial atomic state is a symmetric Dicke state, dissipation engineering can be used to implement a nondestructive photon-number measurement, in which the incident state is scattered into the waveguide unchanged. Our results generalize to related platforms, including superconducting qubits.

We propose a novel one-way quantum repeater architecture based on photonic tree-cluster states. Encoding a qubit in a photonic tree-cluster protects the information from transmission loss and enables long-range quantum communication through a chain of repeater stations. As opposed to conventional approaches that are limited by the two-way communication time, the overall transmission rate of the current quantum repeater protocol is determined by the local processing time enabling very high communication rates. We further show that such a repeater can be constructed with as little as two stationary qubits and one quantum emitter per repeater station, which significantly increases the experimental feasibility. We discuss potential implementations with diamond defect centers and semiconductor quantum dots efficiently coupled to photonic nanostructures and outline how such systems may be integrated into repeater stations.

Mixing (or quasirandom) properties of the natural transition matrix associated to a graph can be quantified by its distance to the complete graph. Different mixing properties correspond to different norms to measure this distance. For dense graphs, two such properties known as spectral expansion and uniformity were shown to be equivalent in seminal 1989 work of Chung, Graham and Wilson. Recently, Conlon and Zhao extended this equivalence to the case of sparse vertex transitive graphs using the famous Grothendieck inequality. Here we generalize these results to the non-commutative, or quantum', case, where a transition matrix becomes a quantum channel. In particular, we show that for irreducibly covariant quantum channels, expansion is equivalent to a natural analog of uniformity for graphs, generalizing the result of Conlon and Zhao. Moreover, we show that in these results, the non-commutative and commutative (resp.) Grothendieck inequalities yield the best-possible constants.

Aharonov-Bohm cages correspond to an extreme confinement for two-dimensional tight-binding electrons in a transverse magnetic field. When the dimensionless magnetic flux per plaquette $f$ equals a critical value $f_c=1/2$, a destructive interference forbids the particle to diffuse away from a small cluster. The corresponding energy levels pinch into a set of highly degenerate discrete levels as $f\to f_c$. We show here that cages also occur for discrete-time quantum walks on either the diamond chain or the $\mathcal{T}_3$ tiling but require specific coin operators. The corresponding quasi-energies versus $f$ result in a Floquet-Hofstadter butterfly displaying pinching near a critical flux $f_c$ and that may be tuned away from 1/2. The spatial extension of the associated cages can also be engineered.

We solve rigorously the time dependent Schr\"odinger equation describing electron emission from a metal surface by a laser field perpendicular to the surface. We consider the system to be one-dimensional, with the half-line $x<0$ corresponding to the bulk of the metal and $x>0$ to the vacuum. The laser field is modeled as a classical electric field oscillating with frequency $\omega$, acting only at $x>0$. We consider an initial condition which is a stationary state of the system without a field, and, at time $t=0$, the field is switched on. We prove the existence of a solution $\psi(x,t)$ of the Schr\"odinger equation for $t>0$, and compute the surface current. The current exhibits a complex oscillatory behavior, which is not captured by the "simple" three step scenario. As $t\to\infty$, $\psi(x,t)$ converges with a rate $t^{-\frac32}$ to a time periodic function with period $\frac{2\pi}{\omega}$ which coincides with that found by Faisal, Kami\'nski and Saczuk (Phys Rev A 72, 023412, 2015). However, for realistic values of the parameters, we have found that it can take quite a long time (over 50 laser periods) for the system to converge to its asymptote. Of particular physical importance is the current averaged over a laser period $\frac{2\pi}\omega$, which exhibits a dramatic increase when $\hbar\omega$ becomes larger than the work function of the metal, which is consistent with the original photoelectric effect.

A relativistic version of the effective charge model for computation of observable characteristics of multi-electron atoms and ions is developed. A complete and orthogonal Dirac hydrogen basis set, depending on one parameter -- effective nuclear charge $Z^{*}$ -- identical for all single-electron wave functions of a given atom or ion, is employed for the construction of the secondary-quantized representation. The effective charge is uniquely determined by the charge of the nucleus and a set of electron occupation numbers for a given state. We thoroughly study the accuracy of the leading-order approximation for the total binding energy and demonstrate that it is independent of the number of electrons of a multi-electron atom. In addition, it is shown that the fully analytical leading-order approximation is especially suited for the description of highly charged ions since our wave functions are almost coincident with the Dirac-Hartree-Fock ones for the complete spectrum. Finally, we evaluate various atomic characteristics, such as scattering factors and photoionization cross-sections, and thus envisage that the effective charge model can replace other models of comparable complexity, such as the Thomas-Fermi-Dirac model for all applications where it is still utilized.

Every renormalization group flow in $d$ spacetime dimensions can be equivalently described as spectral deformations of a generalized free CFT in $(d-1)$ spacetime dimensions. This can be achieved by studying the effective action of the Nambu-Goldstone boson of broken conformal symmetry in anti-de Sitter space and then taking the flat space limit. This approach is particularly useful in even spacetime dimension where the change in the Euler anomaly $a_{UV}-a_{IR}$ can be related to anomalous dimensions of lowest twist multi-trace operators in the dual CFT. As an application, we provide a simple proof of the 4d $a$-theorem using the dual description. Furthermore, we reinterpret the statement of the $a$-theorem in 6d as a conformal bootstrap problem in 5d.

Manipulating quantum computing hardware in the presence of imperfect devices and control systems is a central challenge in realizing useful quantum computers. Susceptibility to noise limits the performance and capabilities of noisy intermediate-scale quantum (NISQ) devices, as well as any future quantum computing technologies. Fortunately quantum control enables efficient execution of quantum logic operations and algorithms with built-in robustness to errors, without the need for complex logical encoding. In this manuscript we introduce software tools for the application and integration of quantum control in quantum computing research, serving the needs of hardware R&D teams, algorithm developers, and end users. We provide an overview of a set of python-based classical software tools for creating and deploying optimized quantum control solutions at various layers of the quantum computing software stack. We describe a software architecture leveraging both high-performance distributed cloud computation and local custom integration into hardware systems, and explain how key functionality is integrable with other software packages and quantum programming languages. Our presentation includes a detailed mathematical overview of central product features including a flexible optimization toolkit, filter functions for analyzing noise susceptibility in high-dimensional Hilbert spaces, and new approaches to noise and hardware characterization. Pseudocode is presented in order to elucidate common programming workflows for these tasks, and performance benchmarking is reported for numerically intensive tasks, highlighting the benefits of the selected cloud-compute architecture. Finally, we present a series of case studies demonstrating the application of quantum control solutions using these tools in real experimental settings for both trapped-ion and superconducting quantum computer hardware.

We show that the states generated by a three-mode spontaneous parametric downconversion (SPDC) interaction Hamiltonian possess tripartite entanglement of a different nature to other paradigmatic three-mode entangled states generated by the combination of two-mode SPDCs interactions. While two-mode SPDC generates gaussian states whose entanglement can be characterized by standard criteria based on two-mode quantum correlations, these criteria fail to capture the entanglement generated by three-mode SPDC. We use criteria built from three-mode correlation functions to show that the class of states recently generated in a superconducting-circuit implementation of three-mode SPDC ideally have tripartite entanglement, contrary to recent claims in the literature. These criteria are suitable for triple SPDC but we show that they fail to detect tripartite entanglement in other states which are known to possess it, which illustrates the existence of two fundamentally different notions of tripartite entanglement in three-mode continuous variable systems.

Correlators of unitary quantum field theories in Lorentzian signature obey certain analyticity and positivity properties. For interacting unitary CFTs in more than two dimensions, we show that these properties impose general constraints on families of minimal twist operators that appear in the OPEs of primary operators. In particular, we rederive and extend the convexity theorem which states that for the family of minimal twist operators with even spins appearing in the reflection-symmetric OPE of any scalar primary, twist must be a monotonically increasing convex function of the spin. Our argument is completely non-perturbative and it also applies to the OPE of nonidentical scalar primaries in unitary CFTs, constraining the twist of spinning operators appearing in the OPE. Finally, we argue that the same methods also impose constraints on the Regge behavior of certain CFT correlators.

It is shown that the carrier of a bounded localized free Dirac wavefunction shrinks from infinity and subsequently expands to infinity again. The motion occurs isotropicly at the speed of light. In between there is the phase of rebound, which is limited in time and space in the order of the diameter of the carrier at its minimal extension. This motion proceeds anisotropicly and abruptly as for every direction in space there is a specific time, at which the change from shrinking to expanding happens instantaneously. Asymptotically, regarding the past and the future as well, the probability of position concentrates up to 1 within any spherical shell whose outer radius increases at light speed.

Recently, it was established that there exists a direct relation between the non-Hermitian skin effects, -strong dependence of spectra on boundary conditions for non-Hermitian Hamiltonians-, and boundary zero modes for Hermitian topological insulators. On the other hand, in terms of the spectral theory, the skin effects can also be interpreted as instability of spectra for nonnormal (non-Hermitian) Hamiltonians. Applying the latter interpretation to the former relation, we develop a theory of zero modes with quantum anomaly for general Hermitian lattice systems. Our theory is applicable to a wide range of systems: Majorana chains, non-periodic lattices, and long-range hopping systems. We relate exact zero modes and quasi-zero modes of a Hermitian system to spectra and pseudospectra of a non-Hermitian system, respectively. These zero and quasi-zero modes of a Hermitian system are robust against a class of perturbations even if there is no topological protection. The robustness is measured by nonnormality of the corresponding non-Hermitian system. We also present explicit construction of such zero modes by using a graphical representation of lattice systems. Our theory reveals the presence of nonnormality-protected zero modes, as well as the usefulness of the nonnormality and pseudospectra as tools for topological and/or non-Hermitian physics.

We show that two-time, second-order correlations of scattered photons from planar arrays and chains of atoms display nonclassical features that can be described by a superatom picture of the canonical single-atom $g_2(\tau)$ resonance fluorescence result. For the superatom, the single-atom linewidth is replaced by the linewidth of the underlying collective low light-intensity eigenmode. Strong light-induced dipole-dipole interactions lead to a correlated response, suppressed joint photon detection events, and dipole blockade that inhibits multiple excitations of the collective atomic state. For targeted subradiant modes, nonclassical nature of emitted light can be dramatically enhanced even compared with that of a single atom.

The Hartmann-Hahn technique allows sensitivity enhancement of magnetic resonance imaging and spectroscopy by coupling the spins under study to another spin species that is externally driven. Here we theoretically study the coupled spins' dynamics, and find that for a certain region of driving parameters the system becomes unstable. The required conditions for making this region of instability becoming experimentally accessible are discussed.

We experimentally demonstrate that electrically neutral particles, neutrons, can be used to directly visualize the electrostatic field inside a target volume that can be isolated or occupied. Electric-field images were obtained using a polychromatic, spin-polarized neutron beam with a sensitive polarimetry scheme. This work may enable new diagnostic power of the structure of electric potential, electric polarization, charge distribution, and dielectric constant by imaging spatially dependent electric fields in objects that cannot be accessed by other conventional probes.

Time-reversal-invariant topological superconductor (TRITOPS) wires host Majorana Kramers pairs that have been predicted to mediate a fractional Josephson effect with $4\pi$ periodicity in the superconducting phase difference. We explore the TRITOPS fractional Josephson effect in the presence of time-dependent local mixing' perturbations that instantaneously preserve time-reversal symmetry. Specifically, we show that just as such couplings render braiding of Majorana Kramers pairs non-universal, the Josephson current becomes either aperiodic or $2\pi$-periodic (depending on conditions that we quantify) unless the phase difference is swept sufficiently quickly. We further analyze topological superconductors with $\mathcal{T}^2 = +1$ time-reversal symmetry and reveal a rich interplay between interactions and local mixing that can be experimentally probed in nanowire arrays.

We consider a homogeneous mixture of bosons and polarized fermions. We find that long-range and attractive fermion-mediated interactions between bosons have dramatic effects on the properties of the bosons. We construct the phase diagram spanned by boson-fermion mass ratio and boson-fermion scattering parameter. It consists of stable region of mixing and unstable region toward phase separation. In stable mixing phase, the collective long-wavelength excitations can either be well-behaved with infinite lifetime or be finite in lifetime suffered from the Landau damping. We examine the effects of the induced interaction on the properties of weakly interacting bosons. It turns out that the induced interaction not only enhances the repulsion between the bosons against collapse but also enhances the stability of the superfluid state by suppressing quantum depletion.

Information is physical but information is also processed in finite time. Where computing protocols are concerned, finite-time processing in the quantum regime can dynamically generate coherence. Here we show that this can have significant thermodynamic implications. We demonstrate that quantum coherence generated in the energy eigenbasis of a system undergoing a finite-time information erasure protocol yields rare events with extreme dissipation. These fluctuations are of purely quantum origin. By studying the full statistics of the dissipated heat in the slow driving limit, we prove that coherence provides a non-negative contribution to all statistical cumulants. Using the simple and paradigmatic example of single bit erasure, we show that these extreme dissipation events yield distinct, experimentally distinguishable signatures.

In this paper, we analytically study the critical exponents and universal amplitudes of the thermodynamic curvatures such as the intrinsic and extrinsic curvature at the critical point of the small-large black hole phase transition for the charged AdS black holes. At the critical point, it is found that the normalized intrinsic curvature $R_N$ and extrinsic curvature $K_N$ has critical exponents 2 and 1, respectively. Based on them, the universal amplitudes $R_Nt^2$ and $K_Nt$ are calculated with the temperature parameter $t=T/T_c-1$ where $T_c$ the critical value of the temperature. Near the critical point, we find that the critical amplitude of $R_Nt^2$ and $K_Nt$ is $-\frac{1}{2}$ when $t\rightarrow0^+$, whereas $R_Nt^2\approx -\frac{1}{8}$ and $K_Nt\approx-\frac{1}{4}$ in the limit $t\rightarrow0^-$. These results not only hold for the four dimensional charged AdS black hole, but also for the higher dimensional cases. Therefore, such universal properties will cast new insight into the thermodynamic geometries and black hole phase transitions.

We study the quantum query complexity of two problems.

First, we consider the problem of determining if a sequence of parentheses is a properly balanced one (a Dyck word), with a depth of at most $k$. We call this the $Dyck_{k,n}$ problem. We prove a lower bound of $\Omega(c^k \sqrt{n})$, showing that the complexity of this problem increases exponentially in $k$. Here $n$ is the length of the word. When $k$ is a constant, this is interesting as a representative example of star-free languages for which a surprising $\tilde{O}(\sqrt{n})$ query quantum algorithm was recently constructed by Aaronson et al. Their proof does not give rise to a general algorithm. When $k$ is not a constant, $Dyck_{k,n}$ is not context-free. We give an algorithm with $O\left(\sqrt{n}(\log{n})^{0.5k}\right)$ quantum queries for $Dyck_{k,n}$ for all $k$. This is better than the trival upper bound $n$ for $k=o\left(\frac{\log(n)}{\log\log n}\right)$.

Second, we consider connectivity problems on grid graphs in 2 dimensions, if some of the edges of the grid may be missing. By embedding the "balanced parentheses" problem into the grid, we show a lower bound of $\Omega(n^{1.5-\epsilon})$ for the directed 2D grid and $\Omega(n^{2-\epsilon})$ for the undirected 2D grid. The directed problem is interesting as a black-box model for a class of classical dynamic programming strategies including the one that is usually used for the well-known edit distance problem. We also show a generalization of this result to more than 2 dimensions.

We study stabilizer quantum error-correcting codes (QECC) generated under hybrid dynamics of local Clifford unitaries and local Pauli measurements in one dimension. Building upon 1) a general formula relating the error-susceptibility of a subregion to its entanglement properties, and 2) a previously established mapping between entanglement entropies and domain wall free energies of an underlying spin model, we propose a statistical mechanical description of the QECC in terms of "entanglement domain walls". Free energies of such domain walls generically feature a leading volume law term coming from its "surface energy", and a sub-volume law correction coming from thermodynamic entropies of its transverse fluctuations. These are most easily accounted for by capillary-wave theory of liquid-gas interfaces, which we use as an illustrative tool. We show that the information-theoretic decoupling criterion corresponds to a geometric decoupling of domain walls, which further leads to the identification of the "contiguous code distance" of the QECC as the crossover length scale at which the energy and entropy of the domain wall are comparable. The contiguous code distance thus diverges with the system size as the subleading entropic term of the free energy, protecting a finite code rate against local undetectable errors. We support these correspondences with numerical evidence, where we find capillary-wave theory describes many qualitative features of the QECC; we also discuss when and why it fails to do so.