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arXiv:2411.06709 · Physical Review X

Experimentally Probing Entropy Reduction via Iterative Quantum Information Transfer

Toshihiro Yada, Pieter-Jan Stas, Aziza Suleymanzade, Erik Knall, Nobuyuki Yoshioka, Takahiro Sagawa, Mikhail D. Lukin

Published Jul 17, 2025• 6 citations
arXivHTMLPDF

Abstract

Thermodynamic principles governing energy and information are important tools for a deeper understanding and better control of quantum systems. In this work, we experimentally investigate the interplay of the thermodynamic costs and information flow in a quantum system undergoing iterative quantum measurement and feedback. Our study employs a state stabilization protocol involving repeated measurement and feedback on an electronic spin qubit associated with a silicon-vacancy center in diamond, which is strongly coupled to a diamond nanocavity. This setup allows us to verify the fundamental laws of nonequilibrium quantum thermodynamics, including the second law and the fluctuation theorem, both of which incorporate measures of quantum information flow induced by iterative measurement and feedback. We further assess the reducible entropy based on the feedback’s causal structure and quantitatively demonstrate the thermodynamic advantages of non-Markovian feedback over Markovian feedback. For that purpose, we extend the theoretical framework of quantum thermodynamics to include the causal structure of the applied feedback protocol. Our work lays the foundation for investigating the entropic and energetic costs of real-time quantum control in various quantum systems.

DOI
10.1103/5lp2-9sps

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Thermodynamic principles governing energy and information are important tools for a deeper understanding and better control of quantum systems. In this work, we experimentally investigate the interplay of the thermodynamic costs and information flow in a quantum system undergoing iterative quantum measurement and feedback. Our study employs a state stabilization protocol involving repeated measurement and feedback on an electronic spin qubit associated with a silicon-vacancy center in diamond, which is strongly coupled to a diamond nanocavity. This setup allows us to verify the fundamental laws of nonequilibrium quantum thermodynamics, including the second law and the fluctuation theorem, both of which incorporate measures of quantum information flow induced by iterative measurement and feedback. We further assess the reducible entropy based on the feedback’s causal structure and quantitatively demonstrate the thermodynamic advantages of non-Markovian feedback over Markovian feedback. For that purpose, we extend the theoretical framework of quantum thermodynamics to include the causal structure of the applied feedback protocol. Our work lays the foundation for investigating the entropic and energetic costs of real-time quantum control in various quantum systems.
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.
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.
Fluctuations are intrinsic to microscopic systems and impose fundamental limits on nonequilibrium precision, as captured by the thermodynamic uncertainty relation (TUR), which links current fluctuations to entropy production. While feedback control is expected to further suppress fluctuations, its role within the TUR framework has remained unclear, particularly in quantum systems where control is inherently information-driven. In this Letter, we consider open quantum systems weakly coupled to a thermal environment, in which quantum jumps are continuously monitored, and Markovian feedback is applied. Using quantum mutual information to quantify the information contribution induced by feedback, we derive a finite-time TUR for arbitrary time-integrated currents in terms of entropy production and mutual information. Our results uncover how feedback control suppresses fluctuations together with thermodynamic cost and establish a fundamental precision bound imposed by information-based control. As an application, we analyze a quantum clock model and demonstrate that the clock precision can be enhanced by feedback control in the presence of a single thermal reservoir.
Maxwell's demon explores the role of information in physical processes.Employing information about microscopic degrees of freedom, this "intelligent observer" is capable of compensating entropy production (or extracting work), apparently challenging the second law of thermodynamics.In a modern standpoint, it is regarded as a feedback control mechanism and the limits of thermodynamics are recast incorporating information-to-energy conversion.We derive a trade-off relation between information-theoretic quantities empowering the design of an efficient Maxwell's demon in a quantum system.The demon is experimentally implemented as a spin-1=2 quantum memory that acquires information, and employs it to control the dynamics of another spin-1=2 system, through a natural interaction.Noise and imperfections in this protocol are investigated by the assessment of its effectiveness.This realization provides experimental evidence that the irreversibility in a nonequilibrium dynamics can be mitigated by assessing microscopic information and applying a feed-forward strategy at the quantum scale.
The laws of thermodynamics are a cornerstone for describing nanoscale and open quantum systems. However, formulating these laws for systems under continuous feedback control and under experimentally relevant conditions is challenging. In this work, we lay out a formalism for the laws of thermodynamics in an open quantum system under continuous measurement and feedback described by a Quantum Fokker Planck Master Equation. We derive expressions for work, heat, and measurement-induced energy changes, and we investigate entropy production and fluctuation theorems. We illustrate our results with a continuous version of a measurement-driven Szilard engine, as well as a work extraction scheme in a two-level system under bang-bang control. Our results provide insights into the energetics as well as the irreversibility of classical and quantum systems under continuous feedback control.
Maxwell's demon explores the role of information in physical processes. Employing information about microscopic degrees of freedom, this "intelligent observer" is capable of compensating entropy production (or extracting work), apparently challenging the second law of thermodynamics. In a modern standpoint, it is regarded as a feedback control mechanism and the limits of thermodynamics are recast incorporating information-to-energy conversion. We derive a trade-off relation between information-theoretic quantities empowering the design of an efficient Maxwell's demon in a quantum system. The demon is experimentally implemented as a spin-1/2 quantum memory that acquires information, and employs it to control the dynamics of another spin-1/2 system, through a natural interaction. Noise and imperfections in this protocol are investigated by the assessment of its effectiveness. This realization provides experimental evidence that the irreversibility in a nonequilibrium dynamics can be mitigated by assessing microscopic information and applying a feed-forward strategy at the quantum scale.