Fluctuation theorems in feedback-controlled open quantum systems: Quantum coherence and absolute irreversibility

Abstract

Thermodynamics of quantum coherence has attracted growing attention recently, where the thermodynamic advantage of quantum superposition is characterized in terms of quantum thermodynamics. We investigate thermodynamic effects of quantum coherent driving in the context of the fluctuation theorem. We adopt a quantum-trajectory approach to investigate open quantum systems under feedback control. In these systems, the measurement backaction in the forward process plays a key role, and therefore the corresponding time-reversed quantum measurement and post-selection must be considered in the backward process in sharp contrast to the classical case. The state reduction associated with quantum measurement, in general, creates a zero-probability region in the space of quantum trajectories of the forward process, which causes singularly strong irreversibility with divergent entropy production (i.e., absolute irreversibility) and hence makes the ordinary fluctuation theorem break down. In the classical case, the error-free measurement ordinarily leads to absolute irreversibility because the measurement restricts classical paths to the region compatible with the measurement outcome. In contrast, in open quantum systems, absolute irreversibility is suppressed even in the presence of the projective measurement due to those quantum rare events that go through the classically forbidden region with the aid of quantum coherent driving. This suppression of absolute irreversibility exemplifies the thermodynamic advantage of quantum coherent driving. Absolute irreversibility is shown to emerge in the absence of coherent driving after the measurement, especially in systems under time-delayed feedback control. We show that absolute irreversibility is mitigated by increasing the duration of quantum coherent driving or decreasing the delay time of feedback control. arXiv:1705.06513v3 [cond-mat.stat-mech]

An autonomous quantum machine to measure the thermodynamic arrow of time

“…We show that the evolution of the complete machine is characterized by a generalized IFT, that quantitatively involves the amount of extracted information. This situation gives rise to so-called absolute irreversibility, in agreement with recent theoretical predictions and experimental results [30][31][32][33] . Our proposal is robust against finite measurement precision 34,35 and can be probed with state-of-the-art arXiv:1804.02296v2 [quant-ph] 17 Sep 2018 experimental devices.…”

Quantum thermodynamics under continuous monitoring: a general framework

“…168 . Some extra insight can be obtained by explicitly calculating the average non-equilibrium potential changes rate: (75) where we used the commutation relation in Eq. (69).…”

“…[55][56][57][58] . Contributions from several groups within the community working in quantum thermodynamics [59][60][61][62][63][64][65][66][67][68][69][70][71][72] generalized and tested the framework in the last 8 years, including extensions to scenarios with feedback control [73][74][75][76][77] , diffusive noise 66,[78][79][80][81] and arbitrary environments 68 . Applications to quantum heat engines [82][83][84] , probing correlations 85,86 and the erasure of information 87,88 have been proposed, as well as the development of experimental proposals for measuring heat and work along individual trajectories [89][90][91][92][93] .…”

Quantum Fluctuation Theorem under Continuous Measurement and Feedback

“…We here make several remarks related to the results in this Letter, whose detailed explanations are given in Supplemental Material [61]. First, when absolute irreversibility [62,63] is caused by continuous measurement, the correction term λ irr > 0 must be incorporated to the generalized FT as e −σ−iQC = 1 − λ irr . We can derive a simple sufficient condition for λ irr = 0 in our setup.…”

“…This gap is nonzero when the measurement {M yn } works as the projection onto the Hilbert subspace. Such absolute irreversibility term is also present in single quantum measurement case [62,63]. We derive a sufficient condition for λ irr = 0 in Section S3 C. The inverse process introduced here cannot be interpreted as the ordinary time-reversal of the forward process as in the conventional detailed FT [4].…”