Kirkwood-Dirac representations of quantum states are increasingly finding use in many areas within quantum theory. Usually, representations of this sort are only applied to provide a representation of quantum states (as complex functions over some set). We show how standard Kirkwood-Dirac representations can be extended to a fully compositional representation of all of quantum theory (including channels, measurements, and so on), and prove that this extension satisfies the essential features of functoriality (namely, that the representation commutes with composition of channels), linearity, and quasistochasticity. Interestingly, the representation of a positive operator-valued measure (POVM) element is uniquely picked out to be the collection of weak values for it relative to the bases defining the representation. We then prove that if one can find any Kirkwood-Dirac representation that is everywhere real and non-negative for a given experimental scenario or fragment of quantum theory, then the scenario or fragment is consistent with the principle of generalized noncontextuality, a key notion of classicality in quantum foundations. We also show that the converse does not hold: even if one verifies that all Kirkwood-Dirac representations (as defined herein) of an experiment require negativity or imaginarity, one cannot generally conclude that the experiment witnesses contextuality.

The Grover mixer operator is a variational version of Grover's diffusion operator, introduced as a mixing operator for the quantum alternating operator ansatz (QAOA) and used in a variant known as Grover mixer QAOA (GM-QAOA). An important property of the QAOA with Grover mixer is that its expectation value is invariant over any permutation of states. As a consequence, the algorithm is independent of the structure of the problem. If, on the one hand, this characteristic raises serious doubts about the capacity of the algorithm to overcome the bound of the unstructured search problem, on the other hand, it can pave the way to its analytical study. In this sense, a prior work introduced a statistical approach to analyze GM-QAOA that results in an analytical expression for the expectation value depending on the probability distribution associated with the problem Hamiltonian spectrum. Although the method provides surprising simplifications in calculations, the expression depends exponentially on the number of layers, which makes direct analytical treatment unfeasible. In this work, we extend the analysis to the more simple context of Grover mixer threshold QAOA, a variant that replaces the phase separation operator of GM-QAOA to encode a threshold function. As a result, we obtain an expression for the expectation value independent of the number of layers and, with it, we provide bounds for different performance metrics. Furthermore, we extend the analysis to a more general context of QAOA with Grover mixer, which we called Grover-based QAOA. In that framework, which allows the phase separation operator to encode any compilation of the cost function, we generalize all the bounds by using an argument by contradiction with the optimality of Grover's algorithm on the unstructured search problem. As a result, we get the main contribution of this work, an asymptotic lower bound on the quantile achieved by the expectation value that formalizes the notion that the Grover mixer, at most, reflects a quadratic Grover-style speed-up over classical brute force. We apply that bound on the max-cut problem to the particular class of complete bipartite graphs and argue that the number of rounds required to achieve guarantees for any approximation ratio must grow exponentially with the number of vertices or edges, a severe limitation on the performance of the algorithm.

Parity-time ($\mathcal{P}\mathcal{T}$) symmetry is extensively studied within non-Hermitian physical systems as it has the capability to ensure the presence of real eigenenergies of the systems characterized by non-Hermitian Hamiltonians. Previous studies have been mostly based on the Bloch band theory. Recent developments have unveiled intriguing phenomena which can only be explained by non-Bloch band theory. In this paper, we observe the $\mathcal{P}\mathcal{T}$ phase transition in photonic quantum walks, which can only be explained by the non-Bloch band theory, which relies on the open boundary condition. Furthermore, we explore the impact of disorder on $\mathcal{P}\mathcal{T}$ symmetry and demonstrate disorder-induced $\mathcal{P}\mathcal{T}$ phase transitions. Our work provides a valuable perspective for further explorations on non-Hermitian physics.

Spaceborne optical clocks will play a significant role in the tests of fundamental physics. However, orbital motion and gravitational potential lead to the relativistic redshift (RRS), which introduces systematic errors in frequency measurements. Based on perturbation force models and orbital ephemeris data, we calculated the trajectory of the China Space Station (CSS), and evaluated the RRS of a strontium optical lattice clock aboard. The uncertainty of the RRS is estimated to be $3.3\times {10}^{-17}$, and the instability reaches $3.57\times {10}^{-19}$ at ${10}^4$ s, which is comparable to the overall uncertainty and instability of the state-of-the-art ground-based optical clock. Therefore, according to our assessment, the evaluating method for the RRS of the optical clock in the CSS is feasible and effective, and the results can serve as a reference for dynamic frequency correction of spaceborne optical clocks.

Quantum imaginarity and quantum nonlocality capture the essence of quantumness of a physical system from different aspects. We establish a connection between the imaginarity and quantum nonlocality in any two-qubit states. Based on the imaginarity $l_1$-norm and relative entropy, we derive complementary relations among the quantum imaginarities with respect to any set of mutually unbiased bases for arbitrary qubit states. Based on these complementary relations, we introduce the nonlocal advantage of quantum imaginarity (NAQI). We show that any two-qubit state with NAQI is quantum steerable, but not vice versa. In addition, we investigate the exclusion property of NAQI in three-qubit pure states.

The geometric properties of quantum states are fully encoded by the quantum geometric tensor. The real and imaginary parts of the quantum geometric tensor are the quantum metric and Berry curvature, which characterize the distance and phase difference between two nearby quantum states in Hilbert space, respectively. For conventional Hermitian quantum systems, the quantum metric corresponds to the fidelity susceptibility and has already been used to specify quantum phase transitions from the geometric perspective. In this paper, we extend this wisdom to the non-Hermitian systems for revealing non-Hermitian critical points. To be concrete, by employing numerical exact diagonalization and analytical methods, we calculate the quantum metric and corresponding order parameters in various non-Hermitian models, which include two non-Hermitian generalized Aubry-André models and non-Hermitian cluster and mixed-field Ising models. We demonstrate that the quantum metric of eigenstates in these non-Hermitian models exactly identifies the localization transitions, mobility edges, and many-body quantum phase transitions with gap closings, respectively. We further show that this strategy is robust against the finite-size effect and different boundary conditions.

There are few explicit examples of two-player nonlocal games with a large gap between classical and quantum value. One of the reasons is that estimating the classical value is usually a hard computational task. This paper is devoted to analyzing classical values of the so-called linear games (generalization of XOR games to a larger number of outputs). We employ nontrivial results from graph theory and combine them with number theoretic results used earlier in the context of harmonic analysis to obtain a tool—the girth method—allowing to provide explicit examples of linear games with prescribed low classical value. In particular, we provide games with minimal possible classical value. We then speculate on the potential unbounded violation, by comparing the obtained classical values with a known upper bound for the quantum value. If this bound can be even asymptotically saturated, our games would have the best ratio of quantum to classical value as a function of the product of the number of inputs and outputs when compared with other explicit (i.e., nonrandom) constructions.

In a conventional circuit for quantum machine learning, the quantum gates used to encode the input parameters and the variational parameters are constructed with a fixed order. The resulting output function, which can be expressed in the form of a restricted Fourier series, has limited flexibility in the distributions of its Fourier coefficients. This indicates that a fixed order of quantum gates can limit the performance of quantum machine learning. Building on this key insight (also elaborated with examples), we introduce indefinite causal order to quantum machine learning. Because the indefinite causal order of quantum gates allows for the superposition of different orders, the performance of quantum machine learning can be significantly enhanced. Considering that the current accessible quantum platforms only allow one to simulate a learning structure with a fixed order of quantum gates, we reform the existing simulation protocol to implement indefinite causal order and further demonstrate the positive impact of indefinite causal order on specific learning tasks. Our results offer useful insights into possible quantum effects in quantum machine learning.

Excited-state properties of highly correlated systems are key to understanding photosynthesis, luminescence, and the development of novel optical materials, but accurately capturing their interactions is computationally costly. We present an algorithm that combines classical shadow tomography with physical constraints on the two-electron reduced density matrix (2RDM) to treat excited states. The method reduces the number of measurements of the many-electron 2RDM on quantum computers by (i) approximating the quantum state through a random sampling technique called shadow tomography and (ii) ensuring that the 2RDM represents an $N$-electron system through imposing $N$-representability constraints by semidefinite programming. This generalizes recent work on the $N$-representability-enhanced shadow tomography of ground-state 2RDMs. We compute excited-state energies and 2RDMs of the ${\mathrm{H}}_4$ chain and analyze the critical points along the photoexcited reaction pathway from gauche-1,3-butadiene to bicyclobutane via a conical intersection. The results show that the generalized shadow tomography retains critical multireference correlation effects while significantly reducing the number of required measurements, offering a promising avenue for the efficient treatment of electronically excited states on quantum devices.

Two-level systems (TLSs) are the major source of dephasing of spin qubits in numerous quantum computing platforms. In spite of much effort, it has been difficult to substantially mitigate the effects of this noise or, in many cases, to fully understand its physical origin. We propose a method to make progress on both of these issues. When an oscillating field is applied to a TLS, stochastic resonance can occur and the noise spectrum is moved to higher frequencies. This shift in the TLS noise spectrum will increase the dephasing times of the qubits that they influence. Furthermore, the details of this effect depend on the physical properties of the noise sources. Thus one can use qubit spectroscopy to investigate their physical properties, specifically the extent to which the TLSs themselves possess quantum coherence. We find that it should be possible to determine the dephasing rate and the energy-level separation of the TLS themselves in this way.

Entanglement between distant parties is a key resource in quantum networks. However, photon losses in quantum channels significantly reduce the success probability of entanglement sharing, which scales quadratically with the channel transmittivity. Quantum repeaters using entanglement swapping can mitigate this effect, but usually require high-performance photonic quantum memories to synchronize photonic qubits. In this work, we theoretically and experimentally investigate an entanglement swapping protocol using photon-number-encoded states that can effectively alleviate quantum channel losses without requiring photonic quantum memories. We demonstrate that the protocol exhibits a success probability scaling linearly with the channel transmittivity. Furthermore, we show that while unbalanced channel losses can degrade the shared entanglement, this effect can be compensated by optimally adjusting the initial entangled states. Our results highlight the potential of photon-number encoding for realizing robust entanglement distribution in lossy quantum networks.

One of quantum physics' fundamental, but largely unsolved, problems is the computation of the correlation functions in many-body systems. We address this problem in the case of one-dimensional spinor gases with repulsive contact interactions in the presence of a confining potential. We take advantage of the fact that in the strong-coupling limit, the wave function factorizes with the charge degrees of freedom expressed as a Slater determinant of spinless fermions and the spin sector described by a spin chain of Sutherland type with exchange coefficients that depend only on the trapping potential. This factorization is also present in the expressions for the correlation functions. Still, analytical and numerical investigations were hindered by the fact that the local exchange coefficients and the charge component of the correlators are expressed as $N-1$ multidimensional integrals, with $N$ the number of particles, which are notoriously hard to compute using conventional methods. We introduce a different approach to calculating these integrals that is extremely simple, scales polynomially with the number of particles, and is several orders of magnitude faster than the previous methods reported in the literature. This allows us to investigate the static and dynamic properties, temperature dependence, and nonequilibrium dynamics for systems with a larger number of particles than previously considered and discover new phenomena. We show that contrary to natural expectations, the momentum distribution of strongly interacting trapped spinor gases becomes narrower as we increase the temperature and derive simple determinant representations for the correlators in the spin incoherent regime that is valid for both equilibrium and nonequilibrium situations. For homogeneous systems of impenetrable particles at zero temperature, we analytically compute the large distance asymptotics of the correlators, finding that the leading term of the asymptotic expansion is proportional to $e^{-x{k}_{F}ln\kappa /\pi }$, with $\kappa$ the number of components of the system, which precludes any singularity of the momentum distribution.

In this paper, the photon-pair blockade effect in a three-wave mixing system with Kerr nonlinearity has been studied. By analytical calculation and numerical analysis, we find that the conventional photon blockade and unconventional photon blockade of the photon pair could be realized simultaneously in the strong-coupling regime in this system, and the photon-pair blockade effect could be enhanced strongly by the combination of them. The combination could also lead to a much stronger photon-pair blockade effect in this hybrid system than in a three-wave mixing system, which may contribute to construction of single photon-pair sources with much higher purity without the loss of brightness. In addition, both the same-frequency and different-frequency photon-pair blockades could be realized in this scheme, which may contribute to construction of the same-frequency or different-frequency photon-pair sources or devices. All the results may provide useful theoretical references for the design of correlated photon-pair sources or devices in future experiments and applications.

We propose an approach based on stochastic differential equations to describe superfluorescence in compact ensembles of multilevel emitters in the presence of various incoherent processes. This approach has a numerical complexity that does not depend on the number of emitters. The stochastic differential equations are derived directly from the quantum master equation. In this study, we present a series of numerical examples, comparing our solution to exact calculations and discussing the limits of applicability. For many relevant cases, the proposed stochastic differential equations provide accurate results and correctly capture quantum many-body correlation effects.

Cavity magnomechanics using mechanical degrees of freedom in ferromagnetic crystals provides a powerful platform for observing many interesting classical and quantum nonlinear phenomena in the emerging field of magnon spintronics. However, to date, the generation and control of chaotic motion in a cavity magnomechanical system remain an outstanding challenge due to the inherently weak nonlinear interaction of magnons. Here, we present an efficient mechanism for achieving magnomechanical chaos, in which the magnomechanical system is coherently driven by a two-tone microwave field consisting of a pump field and a probe field. Numerical simulations show that the relative phase of the two input fields plays an important role in controlling the appearance of chaotic motion and, more importantly, the threshold power of chaos is reduced by 6 orders of magnitude from watts to microwatts. In addition to providing insight into the nonlinear interaction of magnons, cavity magnomechanical chaos will always be of interest because of its significance in both fundamental physics and potential applications ranging from ultralow threshold chaotic motion to chaos-based secret information processing.

In their recent paper, Ramezani et al. [Phys. Rev. A 108, 052405 (2023)] presented a quantum multiplication algorithm with $O(\sqrt{N}{log}^2\left(N\right))$ operations, while the best classical algorithm [Harvey and van der Hoeven, Ann. Math. 193, 563 (2021)] needs $O(Nlog\left(N\right))$ operations. This Comment corrects the incompleteness of the quantum complexity, showing that the classical method performs better.

Synchronization and asynchronization are ubiquitous occurrences in a wide range of natural and artificial systems. The underlying mechanisms responsible for these events are typically complex, presenting a considerable difficulty to grasp the crucial elements that cause synchronization or asynchronization. Moreover, real-world systems frequently encounter energy exchanges with their surrounding environment; synchronization and asynchronization in such non-Hermitian systems have not been fully understood. In this work, we study the synchronization and asynchronization phenomena in a simple non-Hermitian system that involves two coupled bosonic modes. We find that such an open system evolves towards a state of lower dissipation as it synchronizes, whereby the existence of particular symmetries, such as anti-parity-time (anti-$\mathcal{PT}$) symmetry and $\mathcal{PT}$ symmetry, impact synchronization. Peculiarly, we show that when the anti-$\mathcal{PT}$ symmetry is broken or the $\mathcal{PT}$ symmetry is unbroken, a state of asynchronization occurs as the result of the degeneracy of imaginary parts of the eigenvalues. We designate this occurrence as “degeneracy-induced asynchronization.” Our findings shed light on generating and controlling synchronization and asynchronization in non-Hermitian systems.

We study information scrambling (a spread of initially localized quantum information into the system's many degree of freedom) in discrete-time quantum walks. We consider out-of-time-ordered correlators (OTOC) and K complexity as a probe of information scrambling. The OTOC for local spin operators in all directions has a light-cone structure which is “shell-like.” As the wavefront passes, the OTOC approaches to zero in the long-time limit, showing no signature of scrambling. The introduction of spatial or temporal disorder changes the shape of the light-cone akin to localization of wavefuction. We formulate the K complexity in system with discrete-time evolution, and show that it grows linearly in discrete-time quantum walk. The presence of disorder modifies this growth to sublinear. Our study present interesting case to explore many-body phenomenon in a discrete-time quantum walk using scrambling.

We consider the problem of maximizing the stored energy for a given charging duration in a quantum battery composed of a pair of spins-$1/2$ with Ising coupling starting from the spin-down state, using bounded transverse field control. We map this problem to an optimal control problem on a single qubit and by using optimal control theory we show that, although a single bang pulse can quickly achieve considerable charging levels for relatively large upper control bounds, higher levels of stored energy including complete charging are accomplished by a bang-singular-bang pulse sequence, where the intermediate singular pulse is an off pulse. If the control is restricted between zero and a maximum value, the initial and final bang pulses attain the maximum bound but have different durations, while if it is restricted between symmetric negative and positive boundaries, the bang pulses have the same duration but opposite boundary values. For both cases we provide transcendental equations from which the durations of the individual pulses in the optimal pulse-sequence can be calculated. For the case of full charging we surprisingly find that the three “switching” functions for the equivalent qubit problem become zero while the adjoint ket does not, consistent with optimal control theory.

Detecting the presence of multiple incoherent sources is a fundamental and challenging task for quantum imaging, especially within sub-Rayleigh region. In this paper, the discrimination of one-versus-two point-like incoherent sources in symmetric and asymmetric scenarios is studied. We calculate the quantum lower bounds on error probabilities of making a decision after one-shot and multishot tests. The results are compared with the error probability of prior-based direct guess, and the minimal number of tests required to make a decision outperforming direct guess is discussed. We also show the asymptotic quantum lower bound for a large number of tests. For practical purposes, we propose a specific strategy along with decision rule of which can work without any prior knowledge. With respect to each of two scenarios, the error probability can approach the quantum lower bound in one-shot tests as well as multishot tests. In addition, the potential challenges and solutions in a realistic scenario are analyzed. Our results may contribute to real-world quantum imaging such as microscopy and astronomy.