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.
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.
Evaluating the maximum amount of work extractable from a nanoscale quantum system is one of the central problems in quantum thermodynamics. Previous works identified the free energy of the input state as the optimal rate of extractable work under the crucial assumption: experimenters know the description of the given quantum state, which restricts the applicability to significantly limited settings. Here, we show that this optimal extractable work can be achieved without knowing the input states at all, removing the aforementioned fundamental operational restrictions. We achieve this by presenting the construction of a quantum channel whose description does not depend on input states but nevertheless extracts work quantified by the free energy of the unknown input state. Remarkably, our result partially encompasses the case of infinite-dimensional systems, for which optimal extractable work has not been known even for the standard state-aware setting. Our results clarify that, even though whether the description of the given state is provided at the beginning of the protocol generally makes the operational setting fundamentally different in accomplishing information-theoretic tasks, not knowing the input state does not influence the optimal performance of the asymptotic work extraction. The maximum work extracted from independent and identically distributed quantum states is characterised only in the state-aware scenario, and it remains unknown with no prior knowledge of the state. Here, the authors show that optimal work extraction can be achieved by a single operation, referred as universal work extraction.
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 n 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 n-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 n 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.
Abstract We consider a theory of quantum thermodynamics with multiple conserved quantities (or charges). To this end, we generalize the seminal results of Sparaciari et al. (Phys. Rev. A 96:052112, 2017) to the case of multiple, in general non-commuting charges, for which we formulate a resource theory of thermodynamics of asymptotically many non-interacting systems. To every state we associate the vector of its expected charge values and its entropy, forming the phase diagram of the system. Our fundamental result is the Asymptotic Equivalence Theorem, which allows us to identify the equivalence classes of states under asymptotic approximately charge-conserving unitaries with the points of the phase diagram. Using the phase diagram of a system and its bath, we analyze the first and the second laws of thermodynamics. In particular, we show that to attain the second law, an asymptotically large bath is necessary. In the case that the bath is composed of several identical copies of the same elementary bath, we quantify exactly how large the bath has to be to permit a specified work transformation of a given system, in terms of the number of copies of the “elementary bath” systems per work system (bath rate). If the bath is relatively small, we show that the analysis requires an extended phase diagram exhibiting negative entropies. This corresponds to the purely quantum effect that at the end of the process, system and bath are entangled, thus permitting classically impossible transformations (unless the bath is enlarged). For a large bath, or many copies of the same elementary bath, system and bath may be left uncorrelated and we show that the optimal bath rate, as a function of how tightly the second law is attained, can be expressed in terms of the heat capacity of the bath. Our approach solves a problem from earlier investigations about how to store the different charges under optimal work extraction protocols in physically separate batteries.
Information can be converted into work, but in quantum mechanics information about a state is not freely available: it must be inferred statistically from measurements on a finite number of copies. We study work extraction in this finite-resource setting by introducing a partial-information and finite-resources (PIFR) quantum Maxwell's demon. Given N identical copies of a state with known Hamiltonian, the demon measures M copies to estimate the state and the corresponding ergotropic unitary, which is then applied to the remaining N−M copies. This protocol induces a trade-off between information acquisition, reconstruction accuracy, and thermodynamic yield, making the total extracted work normalized to the ideal ergotropic benchmark the relevant figure of merit. As our central result, we derive a universal closed-form trade-off bound that places this ergotropic efficiency between a Carnot-type ceiling 1−M/N and a floor controlled by a reconstruction precision rooted in finite-sample quantum estimation theory; optimizing the copy allocation yields M∗∝N2/3 and an N−1/3 approach to the ideal limit, set by a conservative, worst-case reconstruction precision. By considering standard quantum state tomography, we numerically verify the presence of an optimal resource distribution, which also depends on the purity of the state under consideration. Our results identify finite-copy work extraction as a genuinely task-dependent inference problem, in which estimation strategies should be judged by thermodynamic performance rather than reconstruction fidelity alone.
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.
Free energy fixes the maximum work of a thermodynamic process once the state and Hamiltonian are specified. A work-extraction task asks a different question: how much average work can a single device realize across several preparations and Hamiltonian settings? A classical work device is one whose Hamiltonian settings are mutually commuting. We place every branch at its best free-energy-limited work envelope and derive the corresponding classical limit on the task average. For pure preparations, the source is specified only by pairwise maximal-energy constraints: for each pair, the intrinsic maximal average energy under one common normalized Hamiltonian is bounded as part of the task data, while the work device is otherwise microscopically unrestricted. The benchmark is optimized over arbitrary-dimensional classical implementations. Incompatible Hamiltonian settings exceed this limit, even though every branch remains bounded by its own free-energy maximum. The advantage therefore does not arise in any single process, but in the average work of the task: incompatible Hamiltonians realize a value that no classical work device can attain. Hamiltonian incompatibility is thus a thermodynamic resource for work extraction.