arXiv subjects

Akira Shimizu

Publications and source records attributed to Akira Shimizu.

At least 19 recordsLinked to original sources

arXiv2026

Second law of thermodynamics in closed quantum many-body systems

The second law of thermodynamics for adiabatic operations -- constraints on state transitions in closed systems under external control -- is one of the fundamental principles of thermodynamics. On the other hand, it is recently established that even pure quantum states can represent thermal equilibrium. However, pure quantum states do not satisfy the second law in that they are not passive, i.e., work can be extracted from them if arbitrary unitary operations are allowed. It therefore remains unresolved how quantum mechanics can be reconciled with thermodynamics. Here, based on our key quantum-mechanical notions of thermal equilibrium and adiabatic operations, we address the emergence of the second law for adiabatic operations in the thermodynamics limit. We first introduce infinite-observable macroscopic thermal equilibrium (iMATE); a quantum state, including pure states, is in iMATE if the expectation values of all additive observables agree with their equilibrium values. We also introduce a macroscopic operation as unitary evolution generated by a time-dependent additive Hamiltonian, which is regarded as corresponding to adiabatic operations. Employing these concepts, we show that no extensive work can be extracted from any quantum state in iMATE through any macroscopic operations. Furthermore, we introduce a quantum-mechanical form of entropy density such that it agrees with thermodynamic entropy density for any quantum state in iMATE. We then prove that for any initial state in iMATE, this entropy density cannot be decreased by any macroscopic operations, followed by a time-independent relaxation process. Our theory thus proves two different forms of the second law, by adopting macroscopically reasonable classes of observables, equilibrium states, and operations. We also discuss the time scales of macroscopic operations in these results.

cond-mat.stat-mech↗

arXiv2026

Characterization and generation of a SQL-beating catlike state through repetitive measurements

Sensitivity in metrology without entanglement is limited by the standard quantum limit (SQL). Recent studies have found that the Heisenberg-limited scaling, the ultimate sensitivity in quantum metrology, can be achieved by generalized cat states, which are characterized by an index that indicates coherence among macroscopically distinct states and are associated with additive observables. Although generalized cat states include diverse states, encompassing classical mixtures of exponentially large numbers of states, the preparation of large generalized cat states has not been demonstrated yet. Here we characterize SQL-beating catlike states using the index $q$ indicating macroscopic coherence and prove that any state with $q>1.5$ has a potential to surpass the SQL when used as a sensor. We propose a protocol to generate them through repetitive measurements on a quantum spin system of $N$ spins, which we call a spin ensemble. Starting from a thermal equilibrium state of the spin ensemble, we demonstrate that we can increase the coherence among the spin ensemble via repetitive weak measurements of its total magnetization, which is indirectly measured through an ancillary qubit collectively coupled to the ensemble. Notably, our method for creating the SQL-beating catlike states requires no dynamical control over the spin ensemble. As a potential experimental realization, we discuss a hybrid system composed of a superconducting flux qubit and donor spins in silicon. Our results pave the way for the realization of entanglement-enhanced quantum metrology in state-of-the-art technology.

quant-ph↗

arXiv2025

Demonstration of a quantum comparator on an ion-trap quantum device

Quantum computers are believed to solve a class of computational problems that are based on modular arithmetic faster than classical computers. Among the arithmetic building blocks, comparison of integer pairs is a primitive. Here we report its demonstration in the Reimei quantum computer at RIKEN, whose trapped-ion architecture provides all-to-all qubit connectivity together with high gate fidelities. We observe high success probabilities for bit widths n = 3, 5, 7, and 9: Under a conventional output-only success criterion we obtain 95% at n=9; under a stricter criterion additionally requiring the ancilla to be correct, the success is 69% at n=9. These results demonstrate reliable quantum comparison at scales far beyond those previously achieved experimentally, not only for comparators but also in the broader context of quantum arithmetic circuits.

quant-ph↗

arXiv2023

Key Observable for Linear Thermalization

For studies on thermalization of an isolated quantum many-body system, the fundamental issue is to determine whether a given system thermalizes or not. However, most studies tested only a small number of observables, and it was unclear whether other observables thermalize. Here, we study whether `linear thermalization' occurs for all additive observables: We consider a quantum many-body system prepared in an equilibrium state and its unitary time evolution induced by a small change $Δf$ of a physical parameter $f$ of the Hamiltonian, and examine whether \emph{all} additive observables relax to the equilibrium values in a manner fully consistent with thermodynamics up to the linear order in $Δf$. We find that the additive observable conjugate to $f$ is key for linear thermalization in that its linear thermalization guarantees, under physically reasonable conditions, linear thermalization of all additive observables. Such a linear thermalization occurs in the timescale of $\mathcal{O}(|Δf|^0)$, and lasts at least for a period of $o(1/\sqrt{|Δf|})$. We also consider linear thermalization against the change of other parameters, and find that linear thermalization of the key observable against $Δf$ guarantees its linear thermalization against small changes of any other parameters. Furthermore, we discuss the generalized susceptibilities for cross responses and their consistency between quantum mechanics and thermodynamics. We demonstrate our main result by performing numerical calculations for spin models. The present paper offers an efficient way of judging linear thermalization because it guarantees that examination of the single key observable is sufficient.

cond-mat.stat-mech↗

arXiv2023

Statistical ensembles for phase coexistence states specified by noncommutative additive observables

A phase coexistence state cannot be specified uniquely by any intensive parameters, such as the temperature and the magnetic field, because they take the same values over all coexisting phases. It can be specified uniquely only by an appropriate set of additive observables. Hence, to analyze phase coexistence states the statistical ensembles that are specified by additive observables have been employed, such as the microcanonical and restricted ensembles. However, such ensembles are ill-defined or ill-behaved when some of the additive observables do not commute with each other. Here, we solve this fundamental problem by extending a generalized ensemble in such a way that it is applicable to phase coexistence states which are specified by noncommutative additive observables. We prove that this ensemble correctly gives the density matrix corresponding to phase coexistence states of general quantum systems as well as the thermodynamic functions. Furthermore, these ensembles are convenient for practical calculations because of good analytic properties and useful formulas by which temperature and other intensive parameters are directly obtained from the expectation values of the additive observables. As a demonstration, we apply our formulation to a two-dimensional system whose phase coexistence states are specified by an additive observable (order parameter) that does not commute with the Hamiltonian.

cond-mat.stat-mech↗

arXiv2021

Robustness of equilibrium off-diagonal current fluctuation against localization of electron states in macroscopic two-dimensional systems

We study the off-diagonal current fluctuation in a macroscopic quantum system measured in an ideal manner that is as close as possible to the classical ideal measurement. We show rigorously that not only extended but also localized states contribute to the off-diagonal current fluctuation. This result contrasts with the fact that only the extended states affect the off-diagonal (Hall) conductivity and apparently contradicts the naive expectation from the fluctuation-dissipation theorem that might directly connect these two quantities. More specifically, we study the off-diagonal current fluctuation in a disordered two-dimensional electron system in a strong magnetic field at low temperatures. The fluctuation is almost unchanged from that of the pure system reflecting the property mentioned above, being approximately proportional to the Landau level filling factor with high accuracy. Our finding paves the way to estimate the filling factor and the electron density from the off-diagonal current fluctuation observed in macroscopic systems.

cond-mat.mes-hall↗

arXiv2021

Thermal Pure Quantum Matrix Product States Recovering a Volume Law Entanglement

We propose a way to construct a thermal pure quantum matrix product state (TPQ-MPS) that can simulate finite temperature quantum many-body systems with a minimal numerical cost comparable to the matrix product algorithm for the ground state. The MPS was originally designed for the wave function with area-law entanglement. However, by attaching the auxiliary sites to the edges of the random matrix product state, we find that the degree of entanglement is automatically tuned so as to recover the volume law of the entanglement entropy that characterizes the TPQ state. The finite temperature physical quantities of the transverse Ising and the spin-1/2 Heisenberg chains evaluated by a TPQ-MPS show excellent agreement even for bond dimension $\sim 10$-$20$ with those of the exact results.

cond-mat.str-el↗

arXiv2020

Entropic Quantum Machine

We study nanomachines whose relevant (effective) degrees of freedom f >> 1 but smaller than f of proteins. In these machines, both the entropic and the quantum effects over the whole system play the essential roles in producing nontrivial functions. We therefore call them entropic quantum machines (EQMs). We propose a systematic protocol for designing the EQMs, which enables a rough sketch, accurate design of equilibrium states, and accurate estimate of response time. As an illustration, we design a novel EQM, which shows two characteristic shapes. One can switch from one shape to the other by changing temperature or by applying a pulsed external field. We discuss two potential applications of this example of an EQM.

cond-mat.mes-hall↗

arXiv2020

Anomalous Behavior of Magnetic Susceptibility Obtained by Quench Experiments in Isolated Quantum Systems

We examine how the magnetic susceptibility obtained by the quench experiment on isolated quantum systems is related to the isothermal and adiabatic susceptibilities defined in thermodynamics. Under the conditions similar to the eigenstate thermalization hypothesis, together with some additional natural ones, we prove that for translationally invariant systems the quench susceptibility as a function of wave vector k is discontinuous at k=0. Moreover, its values at k=0 and the k to 0 limit coincide with the adiabatic and the isothermal susceptibilities, respectively. We give numerical predictions on how these particular behaviors can be observed in experiments on the XYZ spin chain with tunable parameters, and how they deviate when the conditions are not fully satisfied.

cond-mat.stat-mech↗

arXiv2019

Quantum metrology with generalized cat states

We show a general relationship between a superposition of macroscopically distinct states and sensitivity in quantum metrology. Generalized cat states are defined by using an index which extracts the coherence between macroscopically distinct states, and a wide variety of states, including a classical mixture of an exponentially large number of states, has been identified as the generalized cat state with this criterion. We find that, if we use the generalized cat states for magnetic field sensing without noise, we achieve the Heisenberg limited sensitivity. Moreover, we even show that sensitivity of generalized cat states achieves the ultimate scaling sensitivity beyond the standard quantum limit under the effect of dephasing. As an example, we investigate the sensitivity of a generalized cat state that is attainable through a single global manipulation on a thermal equilibrium state and find an improvement of a few orders of magnitude from the previous sensors. Clarifying a wide class that includes such a peculiar state as metrologically useful, our results significantly broaden the potential of quantum metrology.

quant-ph↗

arXiv2019

Squeezed ensemble for systems with first-order phase transitions

All ensembles of statistical mechanics are equivalent in the sense that they give the equivalent thermodynamic functions in the thermodynamic limit. However, when investigating microscopic structures in the first-order phase transition region, one must choose an appropriate statistical ensemble. The appropriate choice is particularly important when one investigates finite systems, for which even the equivalence of ensembles does not hold. We propose a class of statistical ensembles, which always give the correct equilibrium state even in the first-order phase transition region. We derive various formulas for this class of ensembles, including the one by which temperature is obtained directly from energy without knowing entropy. Moreover, these ensembles are convenient for practical calculations because of good analytic properties. We also derive formulas which relate statistical-mechanical quantities of different ensembles, including the conventional ones, for finite systems. The formulas are useful for obtaining results with smaller finite-size effects, and for improving the computational efficiency. The advantages of the squeezed ensembles are confirmed by applying them to the Heisenberg model and the frustrated Ising model.

cond-mat.stat-mech↗

arXiv2019

Anomalous Enhancement of Entanglement Entropy in Nonequilibrium Steady States Driven by Zero-Temperature Reservoirs

We investigate the size scaling of the entanglement entropy (EE) in nonequilibrium steady states (NESSs) of a one-dimensional open quantum system with a random potential. It models a mesoscopic conductor, composed of a long quantum wire (QWR) with impurities and two electron reservoirs at zero temperature. The EE at equilibrium obeys the logarithmic law. However, in NESSs far from equilibrium the EE grows anomalously fast, obeying the `quasi volume law,' although the conductor is driven by the zero-temperature reservoirs. This anomalous behavior arises from both the far from equilibrium condition and multiple scatterings due to impurities.

quant-ph↗

arXiv2018

From Linear to Nonlinear Responses of Thermal Pure Quantum States

We propose a self-validating scheme to calculate the unbiased responses of quantum many-body systems to external fields of arbibraty strength at any temperature. By switching on a specified field to a thermal pure quantum state of an isolated system, and tracking its time evolution, one can observe an intrinsic thermalization process driven solely by many-body effects. The transient behavior before thermalization contains rich information on excited states, giving the linear and nonlinear response functions at all frequencies. We uncover the necessary conditions to clarify the applicability of this formalism, supported by a proper definition of the nonlinear response function. The accuracy of the protocol is guaranteed by a rigorous upper bound of error exponentially decreasing with system size, and is well implemented in the simple ferromagnetic Heisenberg chain, whose response at high fields exhibits a nonlinear band deformation. We further extract the characteristic features of excitation of the spin-1/2 kagome antiferromagnet; the wavenumber-insensitive linear responses from the possible spin liquid ground state, and the significantly broad nonlinear peaks which should be generated from numerous collisions of quasi-particles, that are beyond the perturbative description.

cond-mat.stat-mech↗

arXiv2018

Macroscopic Quantum Violation of Fluctuation-Dissipation Theorem in Equilibrium

We examine the Hall conductivity of macroscopic two-dimensional quantum system, and show that the observed quantities can sometimes violate the fluctuation dissipation theorem (FDT), even in the linear response (LR) regime infinitesimally close to equilibrium. The violation can be an order of magnitude larger than the Hall conductivity itself at low temperature and in strong magnetic field, which are accessible in experiments. We further extend the results to general systems and give a necessary condition for such large-scale violation to happen. This violation is a genuine quantum phenomenon that appears on a macroscopic scale. Our results are not only bound to the development of the fundamental issues of nonequilibrium physics, but the idea is also meaningful for practical applications, since the FDT is widely used for the estimation of noises from the LRs.

cond-mat.stat-mech↗

arXiv2018

Conversion of Thermal Equilibrium States into Superpositions of Macroscopically Distinct States

A simple procedure for obtaining superpositions of macroscopically distinct states is proposed and analyzed. We find that a thermal equilibrium state can be converted into such a state when a single global measurement of a macroscopic observable, such as the total magnetization, is made. This method is valid for systems with macroscopic degrees of freedom and finite (including zero) temperature. The superposition state is obtained with a high (low) probability when the measurement is made with a high (low) resolution. We find that this method is feasible in an experiment.

quant-ph↗

arXiv2017

Quantum Violation of Fluctuation-Dissipation Theorem

We study quantum measurements of temporal equilibrium fluctuations in macroscopic quantum systems. It is shown that the fluctuation-dissipation theorem, as a relation between observed quantities, is partially violated in quantum systems, even if measurements are made in an ideal way that emulates classical ideal measurements as closely as possible. This is a genuine quantum effect that survives on a macroscopic scale. We also show that the state realized during measurements of temporal equilibrium fluctuations is a `squeezed equilibrium state,' which is macroscopically identical to the pre-measurement equilibrium state but is squeezed by the measurement. It is a time-evolving state, in which macrovariables fluctuate and relax. We also explain some of subtle but important points, careless treatments of which often lead to unphysical results, of the linear response theory.

cond-mat.stat-mech↗

arXiv2016

Detection of Macroscopic Entanglement by Correlation of Local Observables

We propose a correlation of local observables on many sites in macroscopic quantum systems. By measuring the correlation one can detect, if any, superposition of macroscopically distinct states, which we call macroscopic entanglement, in arbitrary quantum states that are (effectively) homogeneous. Using this property, we also propose an index of macroscopic entanglement.

quant-ph↗

arXiv2016

Universal Property of Quantum Measurements of Equilibrium Fluctuations and Violation of Fluctuation-Dissipation Theorem

For macroscopic quantum systems, we study what are measured when equilibrium fluctuations of macrovariables are measured in an ideal way that mimics classical ideal measurements as closely as possible. We find that the symmetrized time correlation (symTC) is always obtained for such measurements. As an important consequence, we show that the fluctuation-dissipation theorem (FDT) is partially violated as a relation between observed quantities in macroscopic quantum systems even if measurements are made in such an ideal way.

cond-mat.stat-mech↗