Quantum chaotic fluctuation-dissipation theorem: Effective Brownian motion in closed quantum systems

Nation, Charlie; Porras, Diego

doi:10.1103/physreve.99.052139

Cited by 32 publications

(83 citation statements)

References 43 publications

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“…Results similar to Eq. (8) have been obtained even in the nonperturbative regime in the context of thermalization [31,32], giving evidence of the broad validity of the predicted behavior for δ(A, t).…”

Section: A Evolution Under Weak Random Perturbationsmentioning

confidence: 72%

Quantifying the Sensitivity to Errors in Analog Quantum Simulation

et al. 2020

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Quantum simulators are widely seen as one of the most promising near-term applications of quantum technologies. However, it remains unclear to what extent a noisy device can output reliable results in the presence of unavoidable imperfections. Here we propose a framework to characterize the performance of quantum simulators by linking the robustness of measured quantum expectation values to the spectral properties of the output observable, which in turn can be associated with its macroscopic or microscopic character. We show that, under general assumptions and on average over all states, imperfect devices are able to reproduce the dynamics of macroscopic observables accurately, while the relative error in the expectation value of microscopic observables is much larger on average. We experimentally demonstrate the universality of these features in a state-of-the-art quantum simulator and show that the predicted behavior is generic for a highly accurate device, without assuming any detailed knowledge about the nature of the imperfections.

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Section: A Evolution Under Weak Random Perturbationsmentioning

confidence: 72%

Quantifying the Sensitivity to Errors in Analog Quantum Simulation

et al. 2020

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“…Our results may be of particular importance in setups allowing environmental monitoring and feedback control [50,51,[62][63][64][65][66][67], and for quantum thermal devices working in nonequilibrium steady-state conditions [68][69][70][71][72][73][74][75]. It would be also interesting to explore connections with path-integral approaches [76], one-shot quantum thermodynamics [77][78][79][80], and quantum information [81][82][83][84][85]. Finally, we remark that some of our results could be applied to classical systems where knowledge of system's state is incomplete e.g.…”

mentioning

confidence: 71%

Quantum Martingale Theory and Entropy Production

2019

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We employ martingale theory to describe fluctuations of entropy production for open quantum systems in nonequilbrium steady states. Using the formalism of quantum jump trajectories, we identify a decomposition of entropy production into an exponential martingale and a purely quantum term, both obeying integral fluctuation theorems. An important consequence of this approach is the derivation of a set of genuine universal results for stopping-time and infimum statistics of stochastic entropy production. Finally we complement the general formalism with numerical simulations of a qubit system. PACS numbers: 05.70.Ln, 05.40.-a 05.30.-d 03.67.-a 42.50.DvThe development of stochastic thermodynamics in the last decades allowed the description of work, heat and entropy production at the level of single trajectories in nonequilibrium processes [1,2]. This framework has successfully provided several genuine insights on the second law, such as the discovery of universal relations constraining the statistics of fluctuating thermodynamic quantities, usually known as fluctuation theorems [3][4][5]. The fundamental interest in refining our understanding of irreversibility and their microscopic imprints has been brought to its ultimate consequences by extending stochastic thermodynamics to the quantum realm [6], where fluctuation theorems have been derived [7][8][9][10][11][12][13], and experimentally tested in the last years [14,15].When information about entropy production in single trajectories of a process is available, a natural question to ask is until what extend this information can be useful. For instance whether or not it is possible to implement strategies leading to a reduction in entropy which might be eventually used as a fuel, like in the celebrated Maxwell's demon [16,17]. In the same context, one may ask whether the second law of thermodynamics will manifest as fundamental constraints limiting such strategies. A powerful method to handle these general questions, is to employ a set of particularly interesting stochastic processes, namely Martingales [18]. Martingales are well known in mathematics [19] and quantitative finance as models of fair financial markets [20]. However, martingale theory has been only little exploited until now both in stochastic thermodynamics [21][22][23][24][25][26][27] and quantum physics [28,29].Applying concepts of martingale theory in stochastic thermodynamics, it has been shown that the exponential of minus the entropy production ∆S tot (t) associated with classical trajectories γ {0,t} −single paths in phase space− in generic non-equilibrium steady-state conditions is an exponential martingale, i.e. e −∆Stot(t) | γ {0,τ } = * gmanzano@ictp.it † edgar@ictp.it e −∆Stot(τ ) , for any t ≥ τ ≥ 0, where X(t)|γ {0,τ } denotes the conditional expectation of a functional X(t) given γ {0,τ } [19]. It has been shown that the martingality of e −∆Stot(t) implies a series of universal equalities and inequalities concerning the statistics of infima and stopping times (e.g. first-passage, escape ti...

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“…Continuing, we assume that the initial state for the quantum quench is an eigenstate of H 0 , |ψ (0) = |φ α 0 , with eigenenergy E α 0 , though the formalism is easily extended to more general cases [32]. We focus local observables that are diagonal in the free basis, O αβ ∝ δ αβ .…”

Section: Chaotic Wave Functions and Random Matrix Theorymentioning

confidence: 99%

“…The study of quantum nonequilibrium dynamics has only recently become experimentally feasible [8][9][10][11][12][13], raising questions surrounding the process and conditions in which isolated many-body quantum systems equilibrate to a thermal state [14][15][16][17][18][19][20][21][22], a process known as quantum thermalization [23][24][25][26][27]. Important related questions remain surrounding relaxation timescales and the route to equilibrium of complex quantum systems [28][29][30][31][32][33][34][35][36], as well as the emergence of thermodynamical laws [37][38][39][40]. A useful approach to the description of generic nonintegrable quantum systems can be developed from quantum chaos [41,42] and the eigenstate thermalization hypothesis (ETH), which in turn can be derived from an underlying random matrix theory (RMT) [32,33,[43][44][45][46].…”

Section: Introductionmentioning

confidence: 99%

“…Important related questions remain surrounding relaxation timescales and the route to equilibrium of complex quantum systems [28][29][30][31][32][33][34][35][36], as well as the emergence of thermodynamical laws [37][38][39][40]. A useful approach to the description of generic nonintegrable quantum systems can be developed from quantum chaos [41,42] and the eigenstate thermalization hypothesis (ETH), which in turn can be derived from an underlying random matrix theory (RMT) [32,33,[43][44][45][46].…”

Section: Introductionmentioning

confidence: 99%

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Taking snapshots of a quantum thermalization process: Emergent classicality in quantum jump trajectories

Nation

Porras

2020

Phys. Rev. E

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We investigate theoretically the emergence of classical statistical physics in a finite quantum system that is either totally isolated or otherwise subjected to a quantum measurement process. We show via a random matrix theory approach to nonintegrable quantum systems that the set of outcomes of the measurement of a macroscopic observable evolve in time like stochastic variables, whose variance satisfies the celebrated Einstein relation for Brownian diffusion. Our results show how to extend the framework of eigenstate thermalization to the prediction of properties of quantum measurements on an otherwise closed quantum system. We show numerically the validity of the random matrix approach in quantum chain models.

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Quantum chaotic fluctuation-dissipation theorem: Effective Brownian motion in closed quantum systems

Cited by 32 publications

References 43 publications

Quantifying the Sensitivity to Errors in Analog Quantum Simulation

Quantifying the Sensitivity to Errors in Analog Quantum Simulation

Quantum Martingale Theory and Entropy Production

Taking snapshots of a quantum thermalization process: Emergent classicality in quantum jump trajectories

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