Quantum measurement has traditionally been conceptualized as a fundamentally dissipative, irreversible process that inevitably incurs an energy cost and destroys quantum coherence through backaction. In this work, we challenge this paradigm by introducing the theoretical framework of Quantum Measurement Energy Recovery (QMER). We demonstrate that the state updates and information acquisition generated during specific classes of quantum measurements are not purely parasitic; rather, under appropriate conditions, the backaction-induced energy variation can be harnessed, managed, and partially recovered as usable work. By establishing a rigorous thermodynamic formulation that links continuous quantum measurement, real-time feedback control, and quantum batteries, we define the core metrics of recovery work, measurement efficiency, and energy variation. We show that when the measurement efficiency satisfies the bound zero less than eta_M less than one, the extracted work satisfies W_rec greater than zero. This framework bridges information thermodynamics, quantum control theory, and open quantum systems, providing a foundation for a new class of energy-efficient quantum technologies and redefining the fundamental interplay between information, measurement, and energy.
Quantum measurement has traditionally been conceptualized as a fundamentally dissipative, irreversible process that inevitably incurs an energy cost and destroys quantum coherence through backaction. In this work, we challenge this paradigm by introducing the theoretical framework of Quantum Measurement Energy Recovery (QMER). We demonstrate that the state updates and information acquisition generated during specific classes of quantum measurements are not purely parasitic; rather, under appropriate conditions, the backaction-induced energy variation can be harnessed, managed, and partially recovered as usable work. By establishing a rigorous thermodynamic formulation that links continuous quantum measurement, real-time feedback control, and quantum batteries, we define the core metrics of recovery work, measurement efficiency, and energy variation. We show that when the measurement efficiency satisfies the bound zero less than eta_M less than one, the extracted work satisfies W_rec greater than zero. This framework bridges information thermodynamics, quantum control theory, and open quantum systems, providing a foundation for a new class of energy-efficient quantum technologies and redefining the fundamental interplay between information, measurement, and energy.
This paper presents a comprehensive exposition of quantum thermodynamics, aiming to bridge the foundational concepts of classical thermodynamics and quantum mechanics.Beginning with a rigorous overview of classical thermodynamic laws and statistical ensembles, the work transitions into the quantum domain by introducing quantum states, density operators, and von Neumann entropy.Core thermodynamic quantities such as work, heat, energy, and entropy are redefined in the quantum regime, with emphasis on operational frameworks like the twopoint measurement scheme.The study explores the role of quantum resource theories in formulating generalizations of the second law and delves into the intricacies of nonequilibrium thermodynamics through fluctuation theorems, such as the Jarzynski equality and Crooks theorem.Special attention is given to the influence of coherence, entanglement, and measurement backaction, which contribute uniquely to quantum thermodynamic behavior.The treatise concludes with a discussion on quantum heat engines, thermodynamic consistency of quantum master equations, and information-theoretic approaches, establishing quantum thermodynamics as a vital framework for understanding energy and information flow 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.
Quantum fluctuations are fundamental to quantum technologies, affecting quantum computing, sensing, cryptography, and thermodynamics. A paradigmatic example is quantum work, which, for a thermally isolated driven system, is identified with the variation of its energy. Although quantum mechanics provides precise rules for measuring energy and other observables at individual instants of time, it does not provide a standard framework for characterizing the statistics of their variations between two times. This ambiguity has led to competing protocols that can assign different work distributions--and, more generally, different fluctuation statistics--to the same physical process, with consequences for both foundational physics and quantum technologies. In this work, we propose four fundamental criteria that any consistent protocol for measuring energy variations must satisfy, grounded in conservation laws, state independence of the measurement apparatus, the no-signaling principle, and constraints on physical reality. We prove that these criteria uniquely select the two-time quantum observable protocol. We then show that this conclusion extends beyond work and energy to the variation of arbitrary physical observables, including charge, particle number, and momentum. This result has the potential to establish the foundations for measurements of quantum processes, possibly resolving ambiguities in quantum fluctuation measurements. Moreover, it enables the extension of quantum information concepts, such as entanglement and Bell's inequalities, to processes rather than instantaneous observables.
Quantum information processing is fundamentally governed by the principles of unitarity and reversibility at the microscopic level, yet macroscopic reality and specific quantum measurement processes often introduce apparent irreversibility and information loss. This paper introduces the theoretical framework of Reversible Quantum Forgetting (RQF), a novel paradigm proposing that a quantum system can undergo highly controlled operations to selectively eliminate historical observable traces without degrading or losing the integrity of its current state information. We formally define the transformation from a historical state |psi_history> to a present state |psi_present> via targeted unitary and non-unitary operations. We introduce the quantitative efficiency metric of forgetting, denoted as eta_F = 1 - (I_past / I_initial), while rigorously maintaining a present state fidelity of F_present approximately equal to 1. By decoupling historical correlations from current system observables without incurring thermodynamic penalties associated with destructive classical erasure, RQF offers profound implications for rethinking quantum memory management, the arrow of time in quantum mechanics, and the fundamental thermodynamics of information erasure.
The unification of information theory and thermodynamics represents one of the most profound intellectual achievements in modern physics, historically bridged by principles such as Landauer's erasure bound and Szilard's engine. Concurrently, the exploration of structured light has revealed that photons can carry well-defined orbital angular momentum (OAM), opening vast multidimensional state spaces for optical communication, quantum information processing, and optical manipulation. In this paper, we propose the Photon Angular-Momentum-Entropy Conversion (PASEC) framework, establishing a rigorous theoretical foundation that demonstrates a direct, reversible, and quantitative conversion between the mechanical orbital angular momentum of light and information entropy. By conceptualizing programmable optical phase transformations as thermodynamic state functions, we derive the fundamental governing equations for PASEC, showing that changes in the OAM spectrum map directly onto Shannon and von Neumann entropy variations under constraint conditions. This formulation bypasses the traditional necessity of thermal dissipation for entropy changes, offering an alternative purely mechanical-informational pathway. We explore the thermodynamic consistency of the framework, formulating a generalized optical Landauer principle where spatial mode compression and expansion act as thermodynamic compression and expansion cycles. Finally, we discuss the profound implications of establishing photon angular-momentum thermodynamics, outlining pathways toward macroscopic quantum entropy control using modern programmable spatial light modulators and metasurfaces.
Considering a general microscopic model for a quantum measuring apparatus comprising a quantum probe coupled to a thermal bath, we analyze the energetic resources necessary for the realization of a quantum measurement, which includes the creation of system-apparatus correlations, the irreversible transition to a statistical mixture of definite outcomes, and the apparatus resetting. Crucially, we do not resort to another quantum measurement to capture the emergence of objective measurement results, but rather exploit the properties of the thermal bath which redundantly records the measurement result in its degrees of freedom, naturally implementing the paradigm of quantum Darwinism. In practice, this model allows us to perform a quantitative thermodynamic analysis of the measurement process. From the expression of the second law, we show how the minimal required work depends on the energy variation of the system being measured plus information-theoretic quantities characterizing the performance of the measurement – efficiency and completeness. Additionally, we show that it is possible to perform a thermodynamically reversible measurement, thus reaching the minimal work expenditure, and provide the corresponding protocol. Finally, for finite-time measurement protocols, we illustrate the increasing work cost induced by rising entropy production inherent in finite-time thermodynamic processes. This highlights an emerging trade-off between velocity of the measurement and work cost, on top of a trade-off between efficiency of the measurement and work cost. We apply those findings to bring new insights in the thermodynamic balance of the measurement-powered quantum engines.