arXiv subjects

Keiji Saito

Publications and source records attributed to Keiji Saito.

At least 37 records · Page 2Linked to original sources

arXiv2024

Effective light cone and digital quantum simulation of interacting bosons

The speed limit of information propagation is one of the most fundamental features in non-equilibrium physics. The region of information propagation by finite-time dynamics is approximately restricted inside the effective light cone that is formulated by the Lieb-Robinson bound. To date, extensive studies have been conducted to identify the shape of effective light cones in most experimentally relevant many-body systems. However, the Lieb-Robinson bound in the interacting boson systems, one of the most ubiquitous quantum systems in nature, has remained a critical open problem for a long time. This study reveals a tight effective light cone to limit the information propagation in interacting bosons, where the shape of the effective light cone depends on the spatial dimension. To achieve it, we prove that the speed for bosons to clump together is finite, which in turn leads to the error guarantee of the boson number truncation at each site. Furthermore, we applied the method to provide a provably efficient algorithm for simulating the interacting boson systems. The results of this study settle the notoriously challenging problem and provide the foundation for elucidating the complexity of many-body boson systems.

quant-ph↗

arXiv2024

Dissipation, quantum coherence, and asymmetry of finite-time cross-correlations

Recent studies have revealed a deep connection between the asymmetry of cross-correlations and thermodynamic quantities in the short-time limit. In this study, we address the finite-time domain of the asymmetry for both open classical and quantum systems. Focusing on Markovian dynamics, we show that the asymmetry observed in finite-time cross-correlations is upper bounded by dissipation. We prove that, for classical systems in a steady state with arbitrary operational durations, the asymmetry exhibits, at most, linear growth over time, with the growth speed determined by the rates of entropy production and dynamical activity. In the long-time regime, the asymmetry exhibits exponential decay, with the decay rate determined by the spectral gap of the transition matrix. Remarkably, for quantum cases, quantum coherence is equally important as dissipation in constraining the asymmetry of correlations. We demonstrate an example where only quantum coherence bounds the asymmetry while the entropy production rate vanishes. Furthermore, we generalize the short-time bounds on correlation asymmetry, as reported by Shiraishi [Phys. Rev. E 108, L042103 (2023)] and Ohga et al. [Phys. Rev. Lett. 131, 077101 (2023)], to encompass finite-time scenarios. These findings offer novel insights into the thermodynamic aspects of correlation asymmetry.

cond-mat.stat-mech↗

arXiv2023

Universal bounds on the performance of information-thermodynamic engine

We investigate fundamental limits on the performance of information processing systems from the perspective of information thermodynamics. We first extend the thermodynamic uncertainty relation (TUR) to a subsystem. Specifically, for a bipartite composite system consisting of a system of interest X and an auxiliary system Y, we show that the relative fluctuation of an arbitrary current for X is lower bounded not only by the entropy production associated with X but also by the information flow between X and Y. As a direct consequence of this bipartite TUR, we prove universal trade-off relations between the output power and efficiency of an information-thermodynamic engine in the fast relaxation limit of the auxiliary system. In this limit, we further show that the Gallavotti-Cohen symmetry is satisfied even in the presence of information flow. This symmetry leads to universal relations between the fluctuations of information flow and entropy production in the linear response regime. We illustrate these results with simple examples: coupled quantum dots and coupled linear overdamped Langevin equations. Interestingly, in the latter case, the equality of the bipartite TUR is achieved even far from equilibrium, which is a very different property from the standard TUR. Our results will be applicable to a wide range of systems, including biological systems, and thus provide insight into the design principles of biological systems.

cond-mat.stat-mech↗

arXiv2023

Thermodynamic Unification of Optimal Transport: Thermodynamic Uncertainty Relation, Minimum Dissipation, and Thermodynamic Speed Limits

Thermodynamics serves as a universal means for studying physical systems from an energy perspective. In recent years, with the establishment of the field of stochastic and quantum thermodynamics, the ideas of thermodynamics have been generalized to small fluctuating systems. Independently developed in mathematics and statistics, the optimal transport theory concerns the means by which one can optimally transport a source distribution to a target distribution, deriving a useful metric between probability distributions, called the Wasserstein distance. Despite their seemingly unrelated nature, an intimate connection between these fields has been unveiled in the context of continuous-state Langevin dynamics, providing several important implications for nonequilibrium systems. In this study, we elucidate an analogous connection for discrete cases by developing a thermodynamic framework for discrete optimal transport. We first introduce a novel quantity called dynamical state mobility, which significantly improves the thermodynamic uncertainty relation and provides insights into the precision of currents in nonequilibrium Markov jump processes. We then derive variational formulas that connect the discrete Wasserstein distances to stochastic and quantum thermodynamics of discrete Markovian dynamics described by master equations. Specifically, we rigorously prove that the Wasserstein distance equals the minimum product of irreversible entropy production and dynamical state mobility over all admissible Markovian dynamics. These formulas not only unify the relationship between thermodynamics and the optimal transport theory for discrete and continuous cases but also generalize it to the quantum case. In addition, we demonstrate that the obtained variational formulas lead to remarkable applications in stochastic and quantum thermodynamics.

cond-mat.stat-mech↗

arXiv2022

Thermodynamic geometry of ideal quantum gases: a general framework and a geometric picture of BEC-enhanced heat engines

Thermodynamic geometry provides a physically transparent framework to describe thermodynamic processes in meso- and micro-scale systems that are driven by slow variations of external control parameters. Focusing on periodic driving for thermal machines, we extend this framework to ideal quantum gases. To this end, we show that the standard approach of equilibrium physics, where a grand-canonical ensemble is used to model a canonical one by fixing the mean particle number through the chemical potential, can be extended to the slow driving regime in a thermodynamically consistent way. As a key application of our theory, we use a Lindblad-type quantum master equation to work out a dynamical model of a quantum many-body engine using a harmonically trapped Bose gas. Our results provide a geometric picture of the BEC-induced power enhancement that was previously predicted for this type of engine on the basis of an endoreversible model [New J. Phys. 24, 025001 (2022)]. Using an earlier derived universal trade-off relation between power and efficiency as a benchmark, we further show that the Bose-gas engine can deliver significantly more power at given efficiency than an equally large collection of single-body engines. Our work paves the way for a more general thermodynamic framework that makes it possible to systematically assess the impact of quantum many-body effects on the performance of thermal machines.

cond-mat.quant-gas↗

arXiv2022

Topological Speed Limit

Any physical system evolves at a finite speed that is constrained not only by the energetic cost but also by the topological structure of the underlying dynamics. In this Letter, by considering such structural information, we derive a unified topological speed limit for the evolution of physical states using an optimal transport approach. We prove that the minimum time required for changing states is lower bounded by the discrete Wasserstein distance, which encodes the topological information of the system, and the time-averaged velocity. The bound obtained is tight and applicable to a wide range of dynamics, from deterministic to stochastic, and classical to quantum systems. In addition, the bound provides insight into the design principles of the optimal process that attains the maximum speed. We demonstrate the application of our results to chemical reaction networks and interacting many-body quantum systems.

quant-ph↗

arXiv2022

Universal limitation of quantum information recovery: symmetry versus coherence

Quantum information is scrambled via chaotic time evolution in many-body systems. The recovery of initial information embedded locally in the system from the scrambled quantum state is a fundamental concern in many contexts. From a dynamical perspective, information recovery can measure dynamical instability in quantum chaos, fault-tolerant quantum computing, and the black hole information paradox. This article considers general aspects of quantum information recovery when the scrambling dynamics have conservation laws due to Lie group symmetries. Here, we establish fundamental limitations on the information recovery from scrambling dynamics with arbitrary Lie group symmetries. We show universal relations between information recovery, symmetry, and quantum coherence, which apply to many physical situations. The relations predict that the behavior of the Hayden-Preskill black hole model changes qualitatively under the assumption of the energy conservation law. Consequently, we can rigorously prove that under the energy conservation law, the error of the information recovery from a small black hole remains unignorably large until it completely evaporates. Moreover, even when the black hole is very large, the recovery of information thrown into the black hole is not completed until most of the black hole evaporates. The relations also provide a unified view of the symmetry restrictions on quantum information processing, such as the approximate Eastin-Knill theorem and the Wigner-Araki-Yanase theorem for unitary gates.

quant-ph↗

arXiv2022

Exponential clustering of bipartite quantum entanglement at arbitrary temperatures

Macroscopic quantum effects play central roles in the appearance of inexplicable phenomena in low-temperature quantum many-body physics. Such macroscopic quantumness is often evaluated using long-range entanglement, i.e., entanglement in the macroscopic length scale. The long-range entanglement not only characterizes the novel quantum phases but also serves as a critical resource for quantum computation. Thus, the problem that arises is under which conditions can the long-range entanglement be stable even at room temperatures. Here, we show that bi-partite long-range entanglement is unstable at arbitrary temperatures and exponentially decays with distance. Our theorem provides a no-go theorem on the existence of the long-range entanglement. The obtained results are consistent with the existing observations that long-range entanglement at non-zero temperatures can exist in topologically ordered phases, where tripartite correlations are dominant. In the derivation of our result, we introduce a quantum correlation defined by the convex roof of the standard correlation function. We establish an exponential clustering theorem for generic quantum many-body systems for such a quantum correlation at arbitrary temperatures, which yields our main result by relating quantum correlation to quantum entanglement. As a simple application of our analytical techniques, we derived a general limit on the Wigner-Yanase-Dyson skew information and the quantum Fisher information, which will attract significant attention in the field of quantum metrology. Our work reveals novel general aspects of low-temperature quantum physics and sheds light on the characterization of long-range entanglement.

quant-ph↗

arXiv2022

Thermodynamics of Precision in Markovian Open Quantum Dynamics

The thermodynamic and kinetic uncertainty relations indicate trade-offs between the relative fluctuation of observables and thermodynamic quantities such as dissipation and dynamical activity. Although these relations have been well studied for classical systems, they remain largely unexplored in the quantum regime. In this paper, we investigate such trade-off relations for Markovian open quantum systems whose underlying dynamics are quantum jumps, such as thermal processes and quantum measurement processes. Specifically, we derive finite-time lower bounds on the relative fluctuation of both dynamical observables and their first passage times for arbitrary initial states. The bounds imply that the precision of observables is constrained not only by thermodynamic quantities but also by quantum coherence. We find that the product of the relative fluctuation and entropy production or dynamical activity is enhanced by quantum coherence in a generic class of dissipative processes of systems with nondegenerate energy levels. Our findings provide insights into the survival of the classical uncertainty relations in quantum cases.

cond-mat.stat-mech↗

arXiv2022

Is there any upper bound on current fluctuation in cross-transport beyond linear response regime?

Input and output current fluctuations in stationary cross-transport systems with two kinds of currents are investigated. In Saryal {\it et al.} [Phys. Rev. Lett. 127, 190603 (2021)], upper bounds on input and output current fluctuations are proven in the linear response regime and suggested the validity beyond the linear response regime. We examine these bounds beyond the linear response regime and find that these bounds are violated in general nonequilibrium stationary conditions. We show two examples to demonstrate the violation. Through these examples, we argue that no upper bound on input and output current fluctuations exist beyond the linear response regime.

cond-mat.stat-mech↗

arXiv2022

Fate of measurement-induced phase transition in long-range interactions

We consider quantum many-body dynamics under quantum measurements, where the measurement-induced phase transitions (MIPs) occur when changing the frequency of the measurement. In this work, we consider the robustness of the MIP for long-range interaction that decays as $r^{-α}$ with distance $r$. The effects of long-range interactions are classified into two regimes: (i) the MIP is observed $(α> α_c)$, and (ii) the MIP is absent even for arbitrarily strong measurements $(α<α_c)$. Using fermion models, we demonstrate both regimes in integrable and non-integrable cases. We identify the underlying mechanism and propose sufficient conditions to observe the MIP, that is, $α> d/2+1$ for general bilinear systems and $α> d+1$ for general non-integrable systems ($d$: spatial dimension). Numerical calculation indicates that these conditions are optimal.

quant-ph↗

arXiv2021

Finite-Time Quantum Landauer Principle and Quantum Coherence

The Landauer principle states that any logically irreversible information processing must be accompanied by dissipation into the environment. In this study, we investigate the heat dissipation associated with finite-time information erasure and the effect of quantum coherence in such processes. By considering a scenario wherein information is encoded in an open quantum system whose dynamics are described by the Markovian Lindblad equation, we show that the dissipated heat is lower-bounded by the conventional Landauer cost, as well as a correction term inversely proportional to the operational time. To clarify the relation between quantum coherence and dissipation, we derive a lower bound for heat dissipation in terms of quantum coherence. This bound quantitatively implies that the creation of quantum coherence in the energy eigenbasis during the erasure process inevitably leads to additional heat costs. The obtained bounds hold for arbitrary operational time and control protocol. By following an optimal control theory, we numerically present an optimal protocol and illustrate our findings by using a single-qubit system.

cond-mat.stat-mech↗

arXiv2021

Kondo Effect in a Quantum Dot under Continuous Quantum Measurement

The backaction of quantum measurement on the Kondo effect in a quantum dot system is investigated by considering continuous projective measurement of singly occupied states of a quantum dot. We elucidate the qualitative feature of the Kondo effect under quantum measurement and determine effective Kondo temperature affected by the measurement. The Kondo resonance in the spectral function is suppressed when the measurement strength reaches the energy scale of the Kondo temperature without measurement. Through the spin susceptibility, we identify the generalized Kondo temperature under continuous quantum measurement. The measurement backaction changes the singularity in the spin susceptibility into a highly non-monotonic temperature dependence around the generalized Kondo temperature. The dependence of the generalized Kondo temperature on the measurement strength is quantitatively discussed.

cond-mat.mes-hall↗

arXiv2021

Lieb-Robinson bound and almost-linear light-cone in interacting boson systems

In this work, we investigate how quickly local perturbations propagate in interacting boson systems with Bose-Hubbard-type Hamiltonians. In general, these systems have unbounded local energies, and arbitrarily fast information propagation may occur. We focus on a specific but experimentally natural situation in which the number of bosons at any one site in the unperturbed initial state is approximately limited. We rigorously prove the existence of an almost-linear information-propagation light-cone, thus establishing a Lieb--Robinson bound: the wave-front grows at most as $t\log^2 (t)$. We prove the clustering theorem for gapped ground states and study the time complexity of classically simulating one-dimensional quench dynamics, a topic of great practical interest.

quant-ph↗

arXiv2021

Anisotropic heat conduction of coherently transported phonons in InGaO3(ZnO)m single crystal films with superlattice structures

Superlattices provide a great platform for studying coherent transportation of low-frequency phonons, which are the main issues in mastering the manipulation of heat conduction. Studies have shown that the dominating characteristics in the thermal conductivity of superlattice can be adjusted between wave-like and particle-like phonon properties depending on the superlattice period. However, the phonon coherence length and the phonon mean free path from Umklapp processes have not been defined in one superlattice system, and the transition from wave-like and particle-like behavior is not clear to date despite the extensive research efforts. In this study, we use InGaO3(ZnO)m (m = integer) single crystal films with superlattice structure to experimentally characterize the phonon coherence length as well as the Umklapp mean free path in one system. According to the results, the nature of heat conduction in superlattice can change in three different ways depending on the ratio between the phonon coherence length and the superlattice period. We also discuss the role of the phonon characteristic lengths in the heat conduction of superlattices and its anisotropy.

cond-mat.mtrl-sci↗

arXiv2021

Microscopic theory of the fluctuating hydrodynamics in nonlinear lattices

The theory of fluctuating hydrodynamics has been an important tool for analyzing macroscopic behavior in nonlinear lattices. However, despite its practical success, its microscopic derivation is still incomplete. In this work, we provide the microscopic derivation of fluctuating hydrodynamics, using the coarse-graining and projection technique; the equivalence of ensembles turns out to be critical. The Green-Kubo (GK) like formula for the bare transport coefficients is presented in a numerically computable form. Our numerical simulations show that the bare transport coefficients exist for a sufficiently large but finite coarse-graining length in the infinite lattice within the framework of the GK like formula. This demonstrates that the bare transport coefficients uniquely exist for each physical system.

cond-mat.stat-mech↗

arXiv2021

Information-theoretical bound of the irreversibility in thermal relaxation processes

We establish that entropy production, which is crucial to the characterization of thermodynamic irreversibility, is obtained through a variational principle involving the Kulback-Leibler divergence. A simple application of this representation leads to an information-theoretical bound on entropy production in thermal relaxation processes; this is a stronger inequality than the conventional second law of thermodynamics. This bound is also interpreted as a constraint on the possible path of a thermal relaxation process in terms of information geometry. Our results reveal a hidden universal law inherent to general thermal relaxation processes.

cond-mat.stat-mech↗

arXiv2021

Absence of fast scrambling in thermodynamically stable long-range interacting systems

In this study, we investigate out-of-time-order correlators (OTOCs) in systems with power-law decaying interactions such as $R^{-α}$, where $R$ is the distance. In such systems, the fast scrambling of quantum information or the exponential growth of information propagation can potentially occur according to the decay rate $α$. In this regard, a crucial open challenge is to identify the optimal condition for $α$ such that fast scrambling cannot occur. In this study, we disprove fast scrambling in generic long-range interacting systems with $α>D$ ($D$: spatial dimension), where the total energy is extensive in terms of system size and the thermodynamic limit is well-defined. We rigorously demonstrate that the OTOC shows a polynomial growth over time as long as $α>D$ and the necessary scrambling time over a distance $R$ is larger than $t\gtrsim R^{\frac{2α-2D}{2α-D+1}}$.

quant-ph↗