Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1307.2362 · Physical Review E

Integral quantum fluctuation theorems under measurement and feedback control

Ken Funo, Yu Watanabe, Masahito Ueda

Published Nov 14, 2013• 73 citations
arXivHTMLPDF

Abstract

We derive integral quantum fluctuation theorems and quantum Jarzynski equalities for a feedback-controlled system and a memory which registers outcomes of the measurement. The obtained equalities involve the information content, which reflects the information exchange between the system and the memory, and take into account the back action of a general measurement contrary to the classical case. The generalized second law of thermodynamics under measurement and feedback control is reproduced from these equalities.

DOI
10.1103/physreve.88.052121

Related papers

Fluctuation theorems in the presence of information gain and feedback

Sourabh Lahiri, Shubhashis Rana, A. M. Jayannavar

In this study, we rederive the fluctuation theorems in the presence of feedback by assuming the known Jarzynski equality and detailed fluctuation theorems. We find that both the classical and quantum systems can be analyzed using a similar treatment in terms of state space trajectories. We first briefly reproduce the already known work theorems for a classical system in order to show its equivalence with the quantum treatment. We then extend the treatment to arrive at new results, namely the generalizations of Seifert's entropy production theorem and the Hatano–Sasa fluctuation theorem, in the presence of feedback. We have also derived the extended version of the Tasaki–Crooks fluctuation theorem for a quantum particle in the presence of multiple loop feedback. For deriving the extended quantum fluctuation theorems, we have considered open systems. No assumption is made on the nature of environment and the strength of system–bath coupling. However, it is assumed that the measurement process involves classical errors.

arXiv:1109.6508•Journal of Physics A Mathematical and Theoretical•Jan 20, 2012•55 citations

Quantum Fluctuation Theorem for Arbitrary Measurement and Feedback Schemes

Kacper Prech, Patrick P. Potts

Fluctuation theorems and the second law of thermodynamics are powerful relations constraining the behavior of out-of-equilibrium systems. While there exist generalizations of these relations to feedback controlled quantum systems, their applicability is limited, in particular when considering strong and continuous measurements. In this Letter, we overcome this shortcoming by deriving a novel fluctuation theorem, and the associated second law of information thermodynamics, which remain applicable in arbitrary feedback control scenarios. In our second law, the entropy production is bounded by the coarse-grained entropy production that is inferrable from the measurement outcomes, an experimentally accessible quantity that does not diverge even under strong continuous measurements. We illustrate our results by a qubit undergoing discrete and continuous measurement, where our approach provides a useful bound on the entropy production for all measurement strengths.

arXiv:2306.12281•Physical Review Letters•Oct 1, 2024•4 citations

Fluctuation Theorem with Information Exchange: Role of Correlations in Stochastic Thermodynamics

Takahiro Sagawa, Masahito Ueda

We establish the fluctuation theorem in the presence of information exchange between a nonequilibrium system and other degrees of freedom such as an observer and a feedback controller, where the amount of information exchange is added to the entropy production. The resulting generalized second law sets the fundamental limit of energy dissipation and energy cost during the information exchange. Our results apply not only to feedback-controlled processes but also to a much broader class of information exchanges, and provide a unified framework of nonequilibrium thermodynamics of measurement and feedback control.

arXiv:1206.2479•Physical Review Letters•Nov 2, 2012•256 citations

Fluctuation theorems for quantum processes

Tameem Albash, Daniel A. Lidar, Milad Marvian +1 more

We present fluctuation theorems and moment generating function equalities for generalized thermodynamic observables and quantum dynamics described by completely positive trace preserving maps, with and without feedback control. Our results include the quantum Jarzynski equality and Crooks fluctuation theorem, and clarify the special role played by the thermodynamic work and thermal equilibrium states in previous studies. We show that for a specific class of generalized measurements, which include projective measurements, unitality replaces microreversibility as the condition for the physicality of the reverse process in our fluctuation theorems. We present an experimental application of our theory to the problem of extracting the system-bath coupling magnitude, which we do for a system of pairs of coupled superconducting flux qubits undergoing quantum annealing.

arXiv:1212.6589•Physical Review E•Sep 30, 2013•114 citations

Quantum-trajectory thermodynamics with discrete feedback control

Zongping Gong, Yuto Ashida, Masahito Ueda

We employ the quantum-jump-trajectory approach to construct a systematic framework to study the thermodynamics at the trajectory level in a nonequilibrium open quantum system under discrete feedback control. Within this framework, we derive quantum versions of the generalized Jarzynski equalities, which are demonstrated in an isolated pseudospin system and a coherently driven two-level open quantum system. Due to quantum coherence and measurement backaction, a fundamental distinction from the classical generalized Jarzynski equalities emerges in the quantum versions, which is characterized by a large negative information gain reflecting genuinely quantum rare events. A possible experimental scheme to test our findings in superconducting qubits is discussed.

arXiv:1602.04616•Physical Review A•Jul 8, 2016•44 citations

Quantum Fluctuation Theorem under Quantum Jumps with Continuous Measurement and Feedback

Toshihiro Yada, Nobuyuki Yoshioka, Takahiro Sagawa

While the fluctuation theorem in classical systems has been thoroughly generalized under various feedback control setups, an intriguing situation in quantum systems, namely under continuous feedback, remains to be investigated. In this work, we derive the generalized fluctuation theorem under quantum jumps with continuous measurement and feedback. The essence for the derivation is to newly introduce the operationally meaningful information, which we call quantum-classical-transfer (QC-transfer) entropy. QC-transfer entropy can be naturally interpreted as the quantum counterpart of transfer entropy that is commonly used in classical time series analysis. We also verify our theoretical results by numerical simulation and propose an experiment-numerics hybrid verification method. Our work reveals a fundamental connection between quantum thermodynamics and quantum information, which can be experimentally tested with artificial quantum systems such as circuit quantum electrodynamics.

arXiv:2112.09351•Physical Review Letters•Apr 28, 2022•22 citations
We derive integral quantum fluctuation theorems and quantum Jarzynski equalities for a feedback-controlled system and a memory which registers outcomes of the measurement. The obtained equalities involve the information content, which reflects the information exchange between the system and the memory, and take into account the back action of a general measurement contrary to the classical case. The generalized second law of thermodynamics under measurement and feedback control is reproduced from these equalities.
In this study, we rederive the fluctuation theorems in the presence of feedback by assuming the known Jarzynski equality and detailed fluctuation theorems. We find that both the classical and quantum systems can be analyzed using a similar treatment in terms of state space trajectories. We first briefly reproduce the already known work theorems for a classical system in order to show its equivalence with the quantum treatment. We then extend the treatment to arrive at new results, namely the generalizations of Seifert's entropy production theorem and the Hatano–Sasa fluctuation theorem, in the presence of feedback. We have also derived the extended version of the Tasaki–Crooks fluctuation theorem for a quantum particle in the presence of multiple loop feedback. For deriving the extended quantum fluctuation theorems, we have considered open systems. No assumption is made on the nature of environment and the strength of system–bath coupling. However, it is assumed that the measurement process involves classical errors.
Fluctuation theorems and the second law of thermodynamics are powerful relations constraining the behavior of out-of-equilibrium systems. While there exist generalizations of these relations to feedback controlled quantum systems, their applicability is limited, in particular when considering strong and continuous measurements. In this Letter, we overcome this shortcoming by deriving a novel fluctuation theorem, and the associated second law of information thermodynamics, which remain applicable in arbitrary feedback control scenarios. In our second law, the entropy production is bounded by the coarse-grained entropy production that is inferrable from the measurement outcomes, an experimentally accessible quantity that does not diverge even under strong continuous measurements. We illustrate our results by a qubit undergoing discrete and continuous measurement, where our approach provides a useful bound on the entropy production for all measurement strengths.
We establish the fluctuation theorem in the presence of information exchange between a nonequilibrium system and other degrees of freedom such as an observer and a feedback controller, where the amount of information exchange is added to the entropy production. The resulting generalized second law sets the fundamental limit of energy dissipation and energy cost during the information exchange. Our results apply not only to feedback-controlled processes but also to a much broader class of information exchanges, and provide a unified framework of nonequilibrium thermodynamics of measurement and feedback control.
We present fluctuation theorems and moment generating function equalities for generalized thermodynamic observables and quantum dynamics described by completely positive trace preserving maps, with and without feedback control. Our results include the quantum Jarzynski equality and Crooks fluctuation theorem, and clarify the special role played by the thermodynamic work and thermal equilibrium states in previous studies. We show that for a specific class of generalized measurements, which include projective measurements, unitality replaces microreversibility as the condition for the physicality of the reverse process in our fluctuation theorems. We present an experimental application of our theory to the problem of extracting the system-bath coupling magnitude, which we do for a system of pairs of coupled superconducting flux qubits undergoing quantum annealing.
We employ the quantum-jump-trajectory approach to construct a systematic framework to study the thermodynamics at the trajectory level in a nonequilibrium open quantum system under discrete feedback control. Within this framework, we derive quantum versions of the generalized Jarzynski equalities, which are demonstrated in an isolated pseudospin system and a coherently driven two-level open quantum system. Due to quantum coherence and measurement backaction, a fundamental distinction from the classical generalized Jarzynski equalities emerges in the quantum versions, which is characterized by a large negative information gain reflecting genuinely quantum rare events. A possible experimental scheme to test our findings in superconducting qubits is discussed.
While the fluctuation theorem in classical systems has been thoroughly generalized under various feedback control setups, an intriguing situation in quantum systems, namely under continuous feedback, remains to be investigated. In this work, we derive the generalized fluctuation theorem under quantum jumps with continuous measurement and feedback. The essence for the derivation is to newly introduce the operationally meaningful information, which we call quantum-classical-transfer (QC-transfer) entropy. QC-transfer entropy can be naturally interpreted as the quantum counterpart of transfer entropy that is commonly used in classical time series analysis. We also verify our theoretical results by numerical simulation and propose an experiment-numerics hybrid verification method. Our work reveals a fundamental connection between quantum thermodynamics and quantum information, which can be experimentally tested with artificial quantum systems such as circuit quantum electrodynamics.