Whilst the complexity of acquiring knowledge of a quantum state has been extensively studied in the fields of quantum tomography and quantum learning, a physical understanding of its operational role and cost in quantum thermodynamics is lacking. Knowledge is central to thermodynamics, as exemplified by Maxwell's demon thought experiment, where a demonic agent is able to extract paradoxical amounts of work -- reconciled by the thermodynamic costs of acquiring this knowledge. In this work, we address this gap by extending unitary models of measurement to incorporate the resources available to an agent. We view an agent's knowledge of a quantum state as their ability to reconstruct it unitarily given access to states with partial knowledge of the true state. In our model, an agent correlates an unknown $d$-dimensional system, with copies of a $k$-dimensional probe ($k\leq d$), which are then used to unitarily reconstruct an estimate state in $d$-dimensional memories. We find that this framework is a unitary representation of coarse-grained POVMs. As an application, we investigate the role of knowledge in an extended Szilard Engine scenario.
Whilst the complexity of acquiring knowledge of a quantum state has been extensively studied in the fields of quantum tomography and quantum learning, a physical understanding of its operational role and cost in quantum thermodynamics is lacking. Knowledge is central to thermodynamics, as exemplified by Maxwell's demon thought experiment, where a demonic agent is able to extract paradoxical amounts of work -- reconciled by the thermodynamic costs of acquiring this knowledge. In this work, we address this gap by extending unitary models of measurement to incorporate the resources available to an agent. We view an agent's knowledge of a quantum state as their ability to reconstruct it unitarily given access to states with partial knowledge of the true state. In our model, an agent correlates an unknown d-dimensional system, with copies of a k-dimensional probe (k≤d), which are then used to unitarily reconstruct an estimate state in d-dimensional memories. We find that this framework is a unitary representation of coarse-grained POVMs. As an application, we investigate the role of knowledge in an extended Szilard Engine scenario.
The emerging field of quantum thermodynamics is beginning to reveal the intriguing role that information can play in quantum thermal engines. Information enters as a resource when considering feedback-controlled thermal machines. While both a general theory of quantum feedback control as well as specific examples of quantum feedback-controlled engines have been presented, still lacking is a general framework for such machines. Here, we present a framework for a generic, two-stroke quantum heat engine interacting with N thermal baths and Maxwell's demon. The demon performs projective measurements on the engine working substance, the outcome of which is recorded in a classical memory, embedded in its own thermal bath. To perform feedback control, the demon enacts unitary operations on the working substance, conditioned on the recorded outcome. By considering the compound machine-memory as a hybrid (classical-quantum) standard thermal machine interacting with N+1 thermal baths, our framework puts the working substance and memory on equal footing, thereby enabling a comprehensible resolution to Maxwell's paradox and elucidating the intricate manner in which information impacts the performance of quantum engines. We illustrate the application of our framework with a two-qubit engine. A remarkable observation is that more information does not necessarily result in better thermodynamic performance: sometimes knowing less is better.
Information is usually treated as something we use to describe the physical world. In modern physics, however, there is growing evidence that information itself behaves like a physical resource, subject to the same laws that govern energy, heat, and matter. This paper develops that perspective through a concrete experimental proposal we call Quantum Maxwell Demon Arrays (QMDA)—systems that use measurement and feedback at the quantum scale to convert information about a system into controlled physical work. Building on established results such as the Landauer bound and the Szilard engine, we show that information acquired through measurement can be converted into usable free energy, provided that its physical costs and constraints are properly accounted for. In QMDA, measurements are not passive observations but active physical interactions whose outcomes can be stored, processed, and exploited thermodynamically. Organized into arrays, these measurement–feedback units act collectively, allowing information flow itself to shape energy extraction, entropy production, and system control. We demonstrate how QMDA can serve as experimental probes of information thermodynamics, enabling direct tests of how information constrains and enables physical processes in quantum regimes. This framework clarifies the status of measurement as a physical operation rather than a subjective act of interpretation, and it suggests new pathways toward ultra-efficient computation, precision sensing, and energy management within known thermodynamic limits. More broadly, this work supports the view that information is not merely a bookkeeping device for observers, but a fundamental ingredient of physical dynamics—one that can be quantified, manipulated, and transformed into free energy under well-defined physical rules.
Quantum thermodynamics is a blossoming research program that uses tools and ideas from quantum information theory to extend the laws of thermodynamics to the domain of systems to which the laws of quantum mechanics apply and the thermodynamic limit does not necessarily apply. The contributions of this program are both foundational, in providing an approach to constructively derive the laws of phenomenological thermodynamics from the postulates of unitary quantum mechanics in a rigorous and bottom-up fashion, but also prac- tical, in providing the theory for an increasing number of experiments that attempt to build thermodynamic machines at scales that were previously inaccessible. One key mathematical tool used in quantum thermodynamics is the framework of resource theories, specifically the resource theory of thermal operations, in which the thermodynamic interaction of a system with a heat bath and various additional components such as work batteries, clocks or catalysts are modeled. In this cumulative thesis, various extensions and modifications of this framework are studied in order to derive novel results and insights about the possible thermodynamic evolution of quantum systems. In particular, following a system- atic exposition of the resource theory of thermal operations from first principles, I develop answers to the following questions: i) What is the smallest heat bath required to provide the necessary randomness for a system to undergo a given stochastic or thermodynamical evolution? ii) Does this size differ depending on whether the interaction between bath and system is quantum or classical? iii) How can quantum systems thermodynamically evolve in the presence of catalytic bystander systems and how can this be put to use? iv) What are the thermodynamic state transitions that an agent can operationally affect when she only has access to partial information about the underlying states of system and bath? v) How can we understand the emergence of the canonical ensemble in statistical thermodynamics from quantum mechanics? These questions cover a wide ground, but it will become clear that they can in fact all be discussed using the same formal tools. As such, the answers to the above questions provided in this thesis are both interesting in their own right — showing for example that there exists a gap in how efficiently randomness can be exploited quantumly as compared to classically or that catalytic bystander systems can be used to extract finite amounts of work per particle from macroscopic systems with non-vanishing probability — as well as illustrate the power of quantum thermodynamics as a set of tools to connect quantum mechanics and the theory of thermodynamics more generally.
Adiabatic measurements, followed by feedback and erasure protocols, have often been considered as a model to embody Maxwell’s Demon paradox and to study the interplay between thermodynamics and information processing. Such studies have led to the conclusion, now widely accepted in the community, that Maxwell’s Demon and the second law of thermodynamics can peacefully coexist because any gain provided by the demon must be offset by the cost of performing the measurement and resetting the demon’s memory to its initial state. Statements of this kind are collectively referred to as second laws of information thermodynamics and have recently been extended to include quantum theoretical scenarios. However, previous studies in this direction have made several assumptions, particularly about the feedback process and the demon’s memory readout, and thus arrived at statements that are not universally applicable and whose range of validity is not clear. In this work, we fill this gap by precisely characterizing the full range of quantum feedback control and erasure protocols that are overall consistent with the second law of thermodynamics. This leads us to conclude that the second law of information thermodynamics is indeed universal : it must hold for any quantum feedback control and erasure protocol, regardless of the measurement process involved, as long as the protocol is overall compatible with thermodynamics. Our comprehensive analysis not only encompasses new scenarios but also retrieves previous ones, doing so with fewer assumptions. This simplification contributes to a clearer understanding of the theory.
We analyze an engine whose working fluid consists of a single quantum particle, paralleling Szilard's construction of a classical single-particle engine. Following his resolution of Maxwell's Second Law paradox using the latter, which turned on physically instantiating the demon (control subsystem), the quantum engine's design mirrors the classically-chaotic Szilard Map that operates a thermodynamic cycle of measurement, thermal-energy extraction, and memory reset. Focusing on the thermodynamic costs to observe and control the particle and comparing these in the quantum and classical limits, we detail the thermodynamic tradeoffs behind Landauer's Principle for information-processing-induced thermodynamic dissipation in the quantum and classical regimes. In particular, and as found with the classical engine, we show that the sum of the thermodynamic costs over a cycle obeys a generalized Landauer Principle, exactly balancing energy extraction from the heat bath. Thus, the quantum engine obeys the Second Law. However, the quantum engine does so via substantially different mechanisms: classically measurement and erasure determine the thermodynamics, while in the quantum implementation the cost of partition insertion is key.
Abstract Quantum direct coding or Schumacher compression generalised the ideas of Shannon theory, gave an operational meaning to the von Neumann entropy and established the term qubit. But remembering that information processing is carried out by physical processes prompts one to wonder what thermodynamic resources are required to compress quantum information and how they constrain one’s ability to perform this task. That is, if Alice and Bob only have access to thermal quantum states and clocks with finite accuracy, how well can they measure, encode and decode pure quantum state messages? In this work we examine these questions by modeling Alice’s typical measurement as a unitary involving a measurement probe, investigating imperfect timekeeping on encoding and decoding and considering the role of temperature in Bob’s appended qubits. In doing so, we derive fidelity bounds for this protocol involving the correlations Alice can form with their measurement probe, the variance of the clock’s ticks and the temperature of Bob’s qubits. Finally, we give an insight into the entropy produced by these two agents throughout the compression protocol by relating the resources they use to a quantum thermodynamic cooling protocol.