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arXiv:2404.07786 · New Journal of Physics

Impossibility of universal work extraction from coherence: reconciling axiomatic and resource-theory approaches

Samuel Plesnik, Maria Violaris

Published Sep 25, 2024• 2 citations
arXivHTMLPDF

Abstract

Abstract We compare how the impossibility of a universal work extractor from coherence arises from different approaches to quantum thermodynamics: an explicit protocol accounting for all relevant quantum resources, and axiomatic, information-theoretic constraints imposed by constructor theory. We first explain how the impossibility of a universal work extractor from coherence is directly implied by a recently proposed constructor-theoretic theorem based on distinguishability, which is scale- and dynamics- independent. Then we give an explicit demonstration of this result within quantum theory, by proving the impossibility of generalising a proposed quantum protocol for deterministically extracting work from coherence. We demonstrate a new connection between the impossibility of universal work extractors and constructor-based irreversibility, which was recently shown using the quantum homogenizer. Finally we discuss additional avenues for applying the constructor-theoretic formulation of work extraction to quantum thermodynamics, including the irreversibility of quantum computation and thermodynamics of multiple conserved quantities.

DOI
10.1088/1367-2630/ad7f7c

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Abstract We compare how the impossibility of a universal work extractor from coherence arises from different approaches to quantum thermodynamics: an explicit protocol accounting for all relevant quantum resources, and axiomatic, information-theoretic constraints imposed by constructor theory. We first explain how the impossibility of a universal work extractor from coherence is directly implied by a recently proposed constructor-theoretic theorem based on distinguishability, which is scale- and dynamics- independent. Then we give an explicit demonstration of this result within quantum theory, by proving the impossibility of generalising a proposed quantum protocol for deterministically extracting work from coherence. We demonstrate a new connection between the impossibility of universal work extractors and constructor-based irreversibility, which was recently shown using the quantum homogenizer. Finally we discuss additional avenues for applying the constructor-theoretic formulation of work extraction to quantum thermodynamics, including the irreversibility of quantum computation and thermodynamics of multiple conserved quantities.
How irreversibility arises in a universe with time-reversal symmetric laws is a central problem in physics. In this Letter, we discuss a radically different take on the emergence of irreversibility, adopting the recently proposed constructor theory framework. Irreversibility is expressed as the requirement that a task is possible, while its inverse is not. We prove the compatibility of such irreversibility with quantum theory's time-reversal symmetric laws, using a dynamical model based on the universal quantum homogenizer. We also test the physical realizability of this model by means of an experimental demonstration with high-quality single-photon qubits.
We study thermodynamic state transformations in the resource theory of work and heat when the initial quantum state is unknown. Moving beyond state-dependent protocols, we develop a universal framework in which a single transformation applies to all admissible input states. For mutually commuting conserved charges, we construct charge-conserving protocols whose transformation error, quantified by trace distance, decays super-polynomially with the number of system copies. As an application, we demonstrate universal work extraction: asymptotically optimal work can be extracted without microscopic knowledge of the initial state, with a super-polynomially small error. Our results show that thermodynamic state transformations remain achievable under limited prior information and establish a universal framework for resource-theoretic thermodynamics beyond the state-aware setting.
I give a self-contained introduction to the resource theory approach to quantum thermodynamics. I will introduce in an elementary manner the technical machinery necessary to unpack and prove the core statements of the theory. The topics covered include the so-called 'many second laws of thermodynamics', thermo-majorisation and symmetry constraints on the evolution of quantum coherence. Among the elementary applications, I explicitly work out the bounds on deterministic work extraction and formation, discuss the complete solution of the theory for a single qubit and present the irreversibility of coherence transfers. The aim is to facilitate the task of those researchers interested in engaging and contributing to this topic, presenting scope and motivation of its core assumptions and discussing the relation between the resource theory and complementary approaches.
A key concept in quantum thermodynamics is extractable work, which specifies the maximum amount of work that can be extracted from a quantum system. Different quantities are used to measure extractable work, the most prevalent of which are ergotropy and the difference between the non-equilibrium and equilibrium quantum free energies. Using the latter, we investigate the evolution of extractable work when an open quantum system undergoes a general quantum process described by a completely-positive and trace-preserving dynamical map. We derive a fundamental equation of thermodynamics for such processes as a relation between the distinct sorts of energy change in such a way that the first and the second law of thermodynamics are combined. We then identify the contributions from the reversible and irreversible processes in this equation and demonstrate that they are respectively responsible for the evolution of heat and extractable work of the open quantum system. Furthermore, we show how this correspondence between irreversibility and extractable work has the potential to provide a clear explanation of how the quantum properties of a system affect its extractable work evolution. Specifically, we establish this by directly connecting the change in extractable work with the change in standard quantifiers of quantum non-Markovianity and quantum coherence during a general quantum process. We illustrate these results with two examples.
The minimum amount of thermodynamic work required in order to implement a quantum computation or a quantum state transformation can be quantified using frameworks based on the resource theory of thermodynamics, deeply rooted in the works of Landauer and Bennett. For instance, the work we need to invest in order to implement nnn independent and identically distributed (i.i.d.) copies of a quantum channel is quantified by the thermodynamic capacity of the channel when we require the implementation's accuracy to be guaranteed in diamond norm over the nnn-system input. Recent work showed that work extraction can be implemented universally, meaning the same implementation works for a large class of input states, while achieving a variable work cost that is optimal for each individual i.i.d. input state. Here, we revisit some techniques leading to derivation of the thermodynamic capacity, and leverage them to construct a thermodynamic implementation of nnn i.i.d. copies of any time-covariant quantum channel, up to some process decoherence that is necessary because the implementation reveals the amount of consumed work. The protocol uses so-called thermal operations and achieves the optimal per-input work cost for any i.i.d. input state; it relies on the conditional erasure protocol in our earlier work, adjusted to yield variable work. We discuss the effect of the work-cost decoherence. While it can significantly corrupt the correlations between the output state and any reference system, we show that for any time-covariant i.i.d. input state, the state on the output system faithfully reproduces that of the desired process to be implemented. As an immediate consequence of our results, we recover recent results for optimal work extraction from i.i.d. states up to the error scaling and implementation specifics, and propose an optimal preparation protocol for time-covariant i.i.d. states.
The resource-theoretic approach to quantum thermodynamics typically assumes perfect knowledge of the thermal equilibrium state, an idealization incompatible with finite experimental precision. We develop a framework for equilibrium uncertainty by representing the equilibrium reference as a set of candidate states. Under a generic geometric condition, we prove a no-go theorem that sharply limits athermality ``purification'': converting an uncertain athermal state into a definite target is either trivial or impossible. We then derive exact one-shot entropic characterizations of work extraction and formation for two work-storage models, a clean battery with known equilibrium and a dirty battery with uncertain equilibrium. Both models exhibit strong asymptotic irreversibility even under arbitrarily small uncertainty. An explicit example reveals two distinct extremes: clean batteries display a bound-entanglement-like phenomenon, with positive formation cost but zero extractable work, whereas dirty batteries allow positive work extraction but require infinite formation cost. These phenomena show that equilibrium uncertainty is not a minor perturbation of the standard theory, but a structural ingredient that fundamentally reshapes the limits of quantum thermodynamics.