We propose a design of a quantum battery exploiting the non-Hermitian Hamiltonian as a charger. In particular, starting with the ground or the thermal state of the interacting (noninteracting) Hamiltonian as the battery, the charging of the battery is performed via parity-time ($\mathcal{PT}$)- and rotational-time ($\mathcal{RT}$)-symmetric Hamiltonians to store energy. We report that such a quenching with a non-Hermitian Hamiltonian leads to an enhanced power output compared to a battery with a Hermitian charger. We identify the region in the parameter space which provides the gain in performance. We also demonstrate that the improvements persist with the increase of system size for batteries with both $\mathcal{PT}$- and $\mathcal{RT}$-symmetric chargers. In the $\mathcal{PT}$-symmetric case, although the anisotropy of the $\mathrm{XY}$ model does not help in the performance, we show that the $\mathrm{XXZ}$ model as a battery with a non-Hermitian charger performs better than that of the $\mathrm{XX}$ model having certain interaction strengths. We also exhibit that the advantage of non-Hermiticity remains valid even at finite temperatures in the initial states.

Quantum error correction (QEC) is theoretically capable of achieving the ultimate estimation limits in noisy quantum metrology. However, existing quantum error-correcting codes designed for noisy quantum metrology generally exploit entanglement between one probe and one noiseless ancilla of the same dimension, and the requirement of noiseless ancillas is one of the major obstacles to implementing the QEC metrological protocol in practice. Here we successfully lift this requirement by explicitly constructing two types of multiprobe quantum error-correcting codes, where the first one utilizes a negligible amount of ancillas and the second one is ancilla free. Specifically, we consider Hamiltonian estimation under Markovian noise and show that (i) when the Heisenberg limit (HL) is achievable our codes can achieve the HL and its optimal asymptotic coefficient and (ii) when only the standard quantum limit (SQL) is achievable (even with arbitrary adaptive quantum strategies) the optimal asymptotic coefficient of the SQL is also achievable by our codes under slight modifications.

In a quantum change point problem, a source emitting particles in a fixed quantum state (default) switches to a different state at some stage, and the objective is to identify when the change happened by measuring a sequence of particles emitted from such a source. Motivated by entanglement-sharing protocols in quantum information, we study this problem within the paradigm of local operations and classical communication (LOCC). Here, we consider a source that emits entangled pairs in a default state, but starts producing another entangled state (mutation) at a later stage. Then, a sequence of entangled pairs prepared from such a source and shared between distant observers cannot be used for quantum information processing tasks as the identity of each entangled pair remains unknown. We show that identifying the change point using LOCC leads to the distillation of free entangled pairs. In particular, if the default and the mutation are mutually orthogonal, there exists an efficient LOCC protocol that identifies the change point without fail and distills a sufficiently large number of pairs. However, if they are nonorthogonal, there is a probability of failure. In this case, we compute the number of entangled pairs that may be obtained on average. We also consider a relaxation of the two-state problem where the mutation is not known a priori, but instead belongs to a known set. Here we show that local distinguishability plays a crucial role: if the default and the possible mutations are locally distinguishable, the problem reduces to the two-state problem with orthogonal states, but if not, one may still identify the mutation, the change point, and distill entanglement, as we illustrate with a concrete example.

When creating a quantum system whose natural dynamics provide useful computational operations, designers have two key tools at their disposal: the (constrained) choice of both the Hamiltonian and the the initial state of the system (an encoding). Typically, we fix the design and utilize encodings post factum to tolerate experimental imperfections. In this paper we describe a vital insight that incorporates encoding into the design process, with radical consequences. This transforms the study of perfect state transfer from the unrealistic scenario of specifying the Hamiltonian of an entire system to the far more realistic situation of being given a Hamiltonian over which we had no choice in the design, and designing time control of just two parameters to still achieve perfect transfer.

The equilibrium charge state distribution of laser-accelerated carbon ions traversing a tri-cellulose-acetate (TCA, ${\mathrm{C}}_9{\mathrm{H}}_{16}{\mathrm{O}}_8$) foam target was measured experimentally. The ions were generated through the target normal sheath acceleration mechanism. This allowed us to obtain the equilibrium charge state for a wide energy range near the maximum energy loss within a single laser shot. The foam had a porous structure with 2 mg/${\mathrm{cm}}^3$ volume density, which is between the typical density of gas- and solid-state matter. We found that the measured average equilibrium charge states were significantly underestimated by theoretical models applicable for gas targets, while were in close agreement with both semiempirical formulas and rate equation predictions based on ion-solid interactions. The solid-density fiber filaments in the current foam structure were attributed and demonstrated. The target density effects, which increase the ionization probability through frequent collisions and decrease the electron capture probability, were proven to play an important role in the foam target. Since the foam targets are widely used in laser plasma interaction experiments, our findings are relevant for a broad range of applications.

We study the quench dynamics of two bosons possessing on-site repulsive interaction on a two-leg ladder and show that the presence of uniform flux piercing through the plaquettes of the ladder favors the localization of the bound states in the dynamics. We find that, when the two bosons are symmetrically initialized on the edge rung of the ladder, they tend to edge-localize in their quantum walk, a phenomenon which is not possible in the absence of flux. However, when the bosons are initialized on the bulk rung they never localize and exhibit linear spreading in their quantum walk. Interestingly, however, we find that, in the later case, a finite flux favors localization of the bulk bound states in the presence of sufficiently weak quasiperiodic disorder, which is otherwise insufficient to localize the particles in the absence of flux. In both cases, we obtain that the localization in the dynamics strongly depends on the combined effect of the flux and interaction strengths, as a result of which we obtain a signature of reentrant delocalization as a function of flux (interaction) for fixed interaction (flux) strengths.

We concentrate on the skin effects and topological edge states in the nonreciprocal non-Hermitian Su-Schrieffer-Heeger (SSH) chain, by taking into account the presence of $\mathcal{PT}$-symmetric imaginary potentials. Following a detailed demonstration of the theoretical method, we find that, regardless of the application manner of $\mathcal{PT}$-symmetric imaginary potentials, they take weak impacts from the skin effect of bulk states, but efficiently modulate the topological edge states. On the other hand, if such potentials are applied according to two domains, the skin effect and new edge states can be induced along the domain wall, which are also dependent on the structural parameters. Therefore, the findings in this paper promote understanding of the independent modulations of the skin effects and topological edge states via the interplay between the imaginary potentials and nonreciprocal couplings in the SSH lattices.

Metastability in open system dynamics describes the phenomena of initial relaxation to long-lived metastable states before decaying to the asymptotic stable states. It has been found in continuous-time stochastic dynamics of both classical and quantum systems. However, many cases of open quantum system dynamics are intrinsically discrete, and the evolution within each discrete time interval is described by an arbitrary quantum channel, which often cannot be generated by continuous-time master equations. Here we develop a general theory of metastability in discrete-time open quantum dynamics, described by sequential repetitive quantum channels. We apply the general metastability theory to a typical class of quantum channels on a target system, induced by an ancilla qubit with a pure-dephasing coupling to the target system and under Ramsey sequences. Interesting metastable behaviors are predicted and numerically demonstrated by decomposing the average dynamics of sequential quantum channels into stochastic trajectories. We also present examples of applications in quantum state and dynamics engineering of a target quantum system with an ancilla qubit.

The Leggett-Garg inequality (LGI) delineates a boundary between quantum and classical systems. While the temporal quantum correlations represented by LGIs have been extensively investigated in the Hermitian domain, the exploration of LGIs under non-Hermitian conditions remains scarce. Theoretical conjectures posit that nonunitary dynamics could transcend the boundary of LGIs set by Hermitian quantum mechanics, yet its empirical validation is lacking. Here, we demonstrate the enhanced violation of LGIs in a non-Hermitian system of a parity-time ($\mathcal{PT}$)-symmetric trapped-ion qubit. The upper bounds of both the third-order parameter $K_3$ and fourth-order parameter $K_4$ increase with dissipation and can reach the maximum value when the system approaches the exceptional point, where $K_3=C_{21}+C_{32}-C_{31}$ is comprising three two-time correlations and $K_4=C_{21}+C_{32}+C_{43}-C_{41}$ is comprising four correlations. We also find that the lower bounds of $K_3$ and $K_4$ exhibit distinctive behaviors, where the lower bound of $K_3$ remains constant, but that of $K_4$ depends on the target states and measurement operators. These findings reveal a pronounced correlation between the dissipative nature of a quantum system and its temporal correlations.

As with a Bell inequality, Hardy's paradox manifests a contradiction between the prediction given by quantum theory and local hidden-variable theories. In this work, we give two generalizations of Hardy's arguments for manifesting such a paradox to an arbitrary, but symmetric, Bell scenario involving two observers. Our constructions recover that of Meng et al. [Phys. Rev. A 98, 062103 (2018)] and that first discussed by Cabello [Phys. Rev. A 65, 032108 (2002)] as special cases. Among the two constructions, one can be naturally interpreted as a demonstration of the failure of the transitivity of implications (FTI). Moreover, one of their special cases is equivalent to a ladder-proof-type argument for Hardy's paradox. Through a suitably generalized notion of success probability called degree of success, we provide evidence showing that the FTI-based formulation exhibits a higher degree of success compared with all other existing proposals. Moreover, this advantage seems to persist even if we allow imperfections in realizing the zero-probability constraints in such paradoxes. Explicit quantum strategies realizing several of these proofs of nonlocality without inequalities are provided.

Quantum resource theories (QRTs) provide a unified framework to analyze quantum properties as resources for achieving advantages in quantum information processing. The generalized robustness and the weight of resource have been gaining increasing attention as useful resource quantifiers. However, the existing analyses of these measures were restricted to the cases where convexity of the set of free states is assumed, and physically motivated resources do not necessarily satisfy this restriction. In this paper, we give characterizations of robustness- and weight-based measures in general QRTs without convexity restriction through two different yet related approaches. On the one hand, we characterize the generalized robustness and the weight of resource by introducing a nonlinear witness. We show a general construction of new witness observables that detect the resourcefulness of a given state from multiple copies of the state and, using these witnesses, we provide operational interpretations of the above resource measures even without any convexity assumption. On the other hand, we find that the generalized robustness and the weight of resource can also be interpreted as the worst-case maximum advantage in variants of channel-discrimination and channel-exclusion tasks, respectively, where the set of free states consists of several convex subsets corresponding to multiple restrictions. We further extend these results to QRTs for quantum channels and quantum instruments. These characterizations show that every quantum resource exhibits an advantage for the corresponding tasks, even in general QRTs without convexity assumption. Thus, we establish the usefulness of robustness-based and weight-based techniques beyond the conventional scope of convex QRTs, leading to a better understanding of the general structure of QRTs.

We prove rigorous bounds on the growth of $\alpha$-Rényi entropies $S_{\alpha }\left(t\right)$ (the von Neumann entropy being the special case $\alpha =1$) associated with any subsystem $A$ of a general lattice quantum many-body system with finite on-site Hilbert space dimension. For completely nonlocal Hamiltonians, we show that the instantaneous growth rates $|S_{\alpha }^{\prime }\left(t\right)|$ (with $\alpha \ne 1$) can be exponentially larger than $|S_1^{\prime }\left(t\right)|$ as a function of the subsystem size $\left|A\right|$. For $D$-dimensional systems with geometric locality, we prove bounds on $|S_{\alpha }^{\prime }\left(t\right)|$ that depend on the decay rate of interactions with distance. When $\alpha =1$, the bound is $\left|A\right|$ independent for all power-law decaying interactions $V\left(r\right)\sim r^{-w}$ with $w>2D+1$. However, for $\alpha >1$, the bound is $\left|A\right|$ independent only when the interactions are finite-range or decay faster than $V\left(r\right)\sim e^{-c{r}^D}$ for some $c$ depending on the local Hilbert space dimension. Using similar arguments, we also prove bounds on $k$-local systems with or without geometric locality. A central theme of this work is that the value of $\alpha$ strongly influences the interplay between locality and instantaneous entanglement growth. In other words, the von Neumann entropy and the $\alpha$-Rényi entropies cannot be regarded as proxies for each other in studies of entanglement dynamics. We compare these bounds with analytic and numerical results on Hamiltonians with varying degrees of locality and find concrete examples that almost saturate the bound for nonlocal dynamics.

In a quantum unitary system, an initial state may have different paths to evolve to a target state, and the only requirement is that the initial and target states share the same eigenvalue spectrum. We focus on the evolution between two nondegenerate mixed states in this paper, and investigate the shortest evolution path between them. By minimizing the path distance contained in the unitary operator connecting the initial and target states over a series of phases, the shortest evolution path could be figured out. This minimum path distance has an analytical form in the single-qubit dynamical system, and its solution in the three- or higher-dimensional dynamical system could be obtained numerically. Based on the unitary operator associated with the shortest evolution path, a general form for the Hamiltonian to realize it is presented. Here we present another way to study quantum optimal control, which is based on the path distance between the initial state and its evolution state, rather than the state distance between them.

Quantum simulation is one of the major applications of quantum devices. In the noisy intermediate-scale quantum era, however, the general quantum simulation is not yet feasible, such as that of lattice gauge theories, which is likely limited due to the violation of the Gauss law constraint and the complexity of the real-time dynamics, especially in the deconfined phase. Inspired by the recent works of Ashkenazi and Zohar [Phys. Rev. A 105, 022431 (2022)] and of Tantivasadakarn, Thorngren, Vishwanath, and Verresen [arXiv:2112.01519], we propose to simulate dynamics of lattice gauge theories by using the Kramers-Wannier transformation via cluster-state-like entanglers, mid-circuit measurements, and feedforwarded corrections, which altogether is a constant-depth deterministic operation. In our scheme, specifically, we first quantum simulate the time evolution under a corresponding symmetric Hamiltonian from an initial symmetric state, and then apply the Kramers-Wannier procedure. This results in a wave function that has time evolved under the corresponding lattice gauge theory from a corresponding initial, gauged wave function. In the presence of noises in time evolution, the procedure succeeds when we are able to pair up magnetic monopoles represented by nontrivial measurement outcomes. Furthermore, given a noise-free Kramers-Wannier transformation, the resulting wave function from a noisy time evolution satisfies the Gauss law constraint. We give explicit examples with the low dimensional pure gauge theories and gauge theories coupled to bosonic or fermionic matters such as the Fradkin-Shenker model.

Quantum kernel methods leverage a kernel function computed by embedding input information into the Hilbert space of a quantum system. However, large Hilbert spaces can hinder generalization capability, and the scalability of quantum kernels becomes an issue. To overcome these challenges, various strategies under the concept of inductive bias have been proposed. Bandwidth optimization is a promising approach that can be implemented using quantum simulation platforms. We propose trapped-ion simulation platforms as a means to compute quantum kernels, filling a gap in the previous literature and demonstrating their effectiveness for binary classification tasks. We compare the performance of the proposed method with an optimized classical kernel and evaluate the robustness of the quantum kernel against noise. The results show that ion trap platforms are well-suited for quantum kernel computation and can achieve high accuracy with only a few qubits.

Boson sampling is a specialized algorithm native to the quantum photonic platform developed for near-term demonstrations of quantum advantage over classical computers. While clear useful applications for such near-term pre-fault-tolerance devices are not currently known, reaching a quantum advantage regime serves as a useful benchmark for the hardware. Here, we analyze and detail hardware requirements needed to reach quantum advantage with deterministic quantum emitters, a promising platform for photonic quantum computing. We elucidate key steps that can be taken in experiments to overcome practical constraints and establish quantitative hardware-level requirements. We find that quantum advantage is within reach using quantum emitters with an efficiency of $60\%\text{–}70\%$ and interferometers constructed according to a hybrid-mode-encoding architecture, constituted of Mach-Zehnder interferometers with an insertion loss of $0.0035\mathrm{dB}$ (a transmittance of $99.92\%$) per component.

Quantum metrology is recognized for its capability to offer high-precision estimation by utilizing quantum resources, such as quantum entanglement. Here, we propose a generalized Tavis-Cummings model by introducing the $XY$ spin interaction to explore the impact of the many-body effect on estimation precision, quantified by the quantum Fisher information (QFI). By deriving the effective description of our model, we establish a closed relationship between the QFI and the spin fluctuation induced by the $XY$ spin interaction. Based on this exact relation, we emphasize the indispensable role of the spin anisotropy in achieving Heisenberg-scaling precision for estimating a weak magnetic field. Furthermore, we observe that the estimation precision can be enhanced by increasing the strength of the spin anisotropy. We also reveal a clear scaling transition of the QFI in the Tavis-Cummings model with a reduced Ising interaction. Our results contribute to the enrichment of metrology theory by considering many-body effects, and they also present an alternative approach to improving the estimation precision by harnessing the power provided by many-body quantum phases.