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.
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.
We present a unified operational framework for the arrow of time grounded in irreversible information loss. While microscopic physical laws are time-reversal invariant, macroscopic irreversibility arises when systems overwrite metastable records. We show that recent reversible quantum-control experiments do not reverse time, but instead operate in regimes where no logically irreversible record is created. To formalize this, we introduce the **forgetting rate** (Ξcr), a coarse-grained rate defined on physically selected metastable record states (e.g., pointer states, memory registers, or macroscopic configurations). Unlike standard entropy production, which is expressed in terms of microscopic transition asymmetry, (Ξcr) captures the **rate of irreversible record overwriting**. In this formulation, entropy production obeys the lower boundS˙irr≥kBΞcr,consistent with Landauer's principle but expressed at the level of record dynamics. Within this framework, thermodynamic, quantum-measurement, psychological, and cosmological arrows emerge as substrate-dependent manifestations of Ξcr>0. Temporal asymmetry is therefore not a single global property, but a distributed feature of physical information-processing systems. The approach naturally explains the decoupling of arrows in composite systems and identifies experimentally accessible regimes where irreversibility can be locally suppressed. This work does not introduce a new microscopic law but provides a unifying, operational reformulation that connects information thermodynamics, decoherence theory, and memory dynamics through a single coarse-grained rate.
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 proposes a novel continual learning model leveraging the unique properties of quantum entanglement to mitigate the catastrophic forgetting problem prevalent in classical machine learning. The core idea involves constructing a "quantum memory" based on entangled states, enabling the encoding, updating, and retrieval of knowledge through controlled manipulation of these states and subsequent quantum measurements. We present a theoretical framework outlining this approach, focusing on the mathematical representation of the entanglement-based learning process. Specifically, we define the state vectors (s1, s2, ..., sK) representing the entangled quantum memory, where K denotes the number of learned concepts. The learning algorithm utilizes unitary transformations (Ui) applied to the state vectors, updating the representation of each concept. Quantum measurement (Mi) is employed to extract information and assess the accuracy of the learned concepts. The central challenge lies in designing the appropriate unitary transformations and measurement operators to effectively capture new information while preserving previously learned knowledge. We explore the mathematical relationships between the state vectors, unitary transformations, and measurement operators, demonstrating how these elements contribute to the continual learning process. This research contributes to the emerging field of quantum machine learning, offering a potential pathway to overcoming the limitations of traditional models in scenarios requiring long-term memory and adaptive learning. The proposed model's ability to maintain and update knowledge without forgetting represents a significant advancement in the field.
Abstract The transition from microscopic reversible dynamics to macroscopic irreversible thermodynamics in statistical mechanics, the transformation from pure states to mixed states during quantum decoherence, and the transition from quantum superposition states to classical definite states in quantum measurement have long been regarded as three independent fundamental physical puzzles. This paper demonstrates that the three processes share a unified mathematical root: the filtering, truncation or projection of system degrees of freedom renders the information carried by partial degrees of freedom unreconstructable within the reduced description framework, and irreversibility spontaneously emerges in the remaining description space. Based on the rigorous derivation of Hilbert’s sixth problem proposed by Deng et al., Zurek’s environment-induced decoherence theory, and the three-stage model of temporal relativity proposed by the author, this paper extracts the mathematical structure of the three types of physical processes and constructs an axiomatic unified framework. This paper further clarifies that various filtering operations are essentially equivalent to the selection of reference frames by the observation system; any descriptive subject with finite information bandwidth must select a reference benchmark, and the arrow of time is an emergent characteristic of this selection behavior under reduced description. This paper distinguishes between global information conservation and local unreconstructable information, emphasizing that the theoretical framework does not violate unitary quantum evolution, and proposes quantitative predictions verifiable by attosecond physics and superconducting quantum experiments.
Erasing memory is a fundamental operational task in quantum information processing, governed by Landauer's principle, which links information loss to thermodynamic work. We introduce and analyze assisted quantum erasure, where correlations with a remote system reduce the energetic cost of resetting a memory. We identify exclusive control of erasure as the central operational requirement: only a designated party should be able to achieve the minimal cost, whereas any adversary must fail. In the device-dependent regime, we show that entanglement of formation exactly characterizes exclusivity, establishing entanglement as the decisive thermodynamic resource. Moving to a one-sided device-independent scenario, in which only the memory holder's device is trusted, we develop an operational erasure protocol based on random dephasing and conditional operations. Finally, in a fully device-independent setting, we show how Bell nonlocality and self-testing translate observed violations into lower bounds on any adversary's erasure capability, yielding a device-independent notion of exclusive thermodynamic control. Taken together, these results elevate quantum erasure from a thermodynamic constraint to an operational primitive: the erasure work cost quantifies secure, exclusive control over quantum memory, ensuring that an unauthorized agent cannot fully erase information under a bounded work budget.
The emergence of irreversibility in physical processes, despite the fundamentally reversible nature of quantum mechanics, remains an open question in physics. This thesis explores the intricate relationship between quantum mechanics and thermodynamics, with a particular focus on minimizing entropy production in finite-time processes. By employing tools from quantum information theory and geometric thermodynamics, we tackle the challenge of deriving irreversible thermodynamic behavior from the reversible microscopic framework of quantum mechanics. We begin with a comprehensive review of the laws of thermodynamics, setting the stage for the subsequent analyses. We introduce novel developments in quantum thermodynamics through a generalized framework for geometric thermodynamics, which enables the derivation of finite-time corrections beyond the Markovian regime. Building on this foundation, we extend Landauer's principle by incorporating a finite-time correction that highlights the necessity of strong coupling for optimal information erasure processes. This result underscores the emergence of Planckian time as a fundamental speed limit to thermalization. Additionally, we explore how collective effects can be harnessed to reduce energy dissipation in thermodynamic operations, revealing that classical correlations between systems can significantly mitigate dissipation, though this may pose new questions regarding the third law of thermodynamics. Finally, we optimize thermodynamic processes in mesoscopic systems, including quantum dot engines and information engines. These findings not only enhance our understanding of the fundamental limits of irreversibility but also open new avenues for research. Future works will focus on fully exploiting collective effects, aligning these with the third law of thermodynamics, and understanding the thermodynamic consistency of master equations.