What is measured when fluctuation of macrovariables is measured in quantum systems

Kyota Fujikura, Akira Shimizu

Published Aug 2, 2015• 0 citations

Abstract

For equilibrium states of macroscopic quantum systems, we study what are measured when fluctuations of macrovariables are measured. To mimic classical ideal measurements, we consider `quasi-classical measurements' which are minimally-disturbing, homogeneous, and unbiased quantum measurements with moderate magnitudes of errors. For all such measurements, we find that the symmetrized time correlation is obtained among many quantum correlations that reduce, in the classical limit, to the same classical time correlation. As an important consequence of this universal result, we show that the fluctuation-dissipation theorem (FDT) and Onsager's hypothesis are partially violated in macroscopic quantum systems. The post-measurement state is squeezed by backactions of the measurements, but is macroscopically identical to the pre-measurement equilibrium state. This state evolves with time, in which macrovariables fluctuate and relax, unlike other microstates (such as the Gibbs state) that represent the same equilibrium state.

Related papers

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

Kyota Fujikura, Akira Shimizu

For macroscopic quantum systems, we study what is 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 is always obtained for such measurements. As an important consequence, we show that the fluctuation-dissipation theorem is partially violated as a relation between observed quantities in macroscopic quantum systems even if measurements are made in such an ideal way.

arXiv:1508.00221Physical Review LettersJun 28, 20167 citations

Quantum violation of fluctuation-dissipation theorem

Akira Shimizu, Kyota Fujikura

Abstract 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.

arXiv:1610.03161Journal of Statistical Mechanics Theory and ExperimentFeb 1, 201716 citations

Fluctuation-dissipation theorem for non-equilibrium quantum systems

Mohammad Mehboudi, Anna Sanpera, Juan M. R. Parrondo

The fluctuation-dissipation theorem (FDT) is a central result in statistical physics, both for classical and quantum systems. It establishes a relationship between the linear response of a system under a time-dependent perturbation and time correlations of certain observables in equilibrium. Here we derive a generalization of the theorem which can be applied to any Markov quantum system and makes use of the symmetric logarithmic derivative (SLD). There are several important benefits from our approach. First, such a formulation clarifies the relation between classical and quantum versions of the equilibrium FDT. Second, and more important, it facilitates the extension of the FDT to arbitrary quantum Markovian evolution, as given by quantum maps. Third, it clarifies the connection between the FDT and quantum metrology in systems with a non-equilibrium steady state.

arXiv:1705.03968QuantumMay 24, 201819 citations

Quantum stochastic thermodynamics of macroscopic systems: an algebraic approach

Antoine Rignon-Bret, Cyril Elouard

We build a framework for the thermodynamics of macroscopic quantum systems. In contrast with approaches requiring access to the full density matrix, our framework relies on a coarse-grained description, based on measurement statistics of a few observables. When these observables commute, the outcomes define classical macrostates whose entropy is quantified by observational entropy, accounting for uncertainty about both the macrostate and the microstate within it. We extend this notion to non-commuting observables forming a subalgebra of the operator space, and use Jaynes' principle to define an algebra-dependent entropy interpolating between von Neumann and observational entropies. Given initial and final measurement sets, connected by internal and/or environment-induced dynamics, we derive a second law for the coarse-grained dynamics. Unlike formulations based on von Neumann entropy, our inequality captures irreversibility from both non-unitary environment-induced dynamics and internal equilibration. It takes the usual form of a positive entropy production when the system is initially at internal equilibrium, while correction terms capture nonequilibrium resources ignored by the coarse-graining. We also derive fluctuation theorems for coarse-grained thermodynamic quantities. Along a quasi-static path of measurement schemes, we identify quantum macroscopic notions of work and heat fulfilling the first and second laws, including an additional work contribution from manipulating the algebra to which the system is confined, through external constraints or quantum measurement backaction. Finally, we apply our framework to examples illustrating the impact of varying the coarse-graining scheme. Our approach unifies macroscopic and stochastic thermodynamics in a genuinely quantum framework, laying the basis for a versatile, experimentally friendly toolbox to analyze complex quantum dynamics.

quant-pharXiv:2607.09242Jul 13, 20260 citations

There is No Quantum Regression Theorem

G. W. Ford, Robert F. O’Connell

The Onsager regression hypothesis states that the regression of fluctuations is governed by macroscopic equations describing the approach to equilibrium. It is here asserted that this hypothesis fails in the quantum case. This is shown first by explicit calculation for the example of quantum Brownian motion of an oscillator and then in general from the fluctuation-dissipation theorem. It is asserted that the correct generalization of the Onsager hypothesis is the fluctuation-dissipation theorem.

Physical Review LettersJul 29, 1996107 citations

Generalized fluctuation-dissipation relation for quantum Markovian systems

Mohammad Mehboudi, Anna Sanpera, Juan M. R. Parrondo

The fluctuation-dissipation theorem (FDT) is a central result in statistical physics, both for classical and quantum systems. It establishes a relationship between the linear response of a system under a time-dependent perturbation and time correlations of certain observables in equilibrium. Here we derive a generalization of the theorem which can be applied to any Markov quantum system and makes use of the symmetric logarithmic derivative (SLD). There are several important benefits from our approach. First, such a formulation clarifies the relation between classical and quantum versions of the equilibrium FDT. Second, and more important, it facilitates the extension of the FDT to arbitrary quantum Markovian evolutions, as given by quantum maps. Third, it brings out the full connection between the FDT and the Quantum Fisher information, the figure of merit in quantum metrology.

May 10, 20170 citations