Extracting work from quantum states is a fundamental task in quantum thermodynamics. Previous studies have primarily focused on determining the best achievable rate of work extraction, and remarkably, this characterization appeared to remain unchanged regardless of the choice of allowed processes: whether one considers the operationally motivated class of energy-conserving thermal operations, or the axiomatic class of Gibbs-preserving operations, the optimal extractable work is given by the Helmholtz free energy. Here, we challenge this perspective, showing that a more refined analysis of the asymptotic performance of work extraction reveals significant differences in the performance for the two different classes of free operations. Precisely, we focus on the trade-off between the extraction rate and its reliability, characterized by the optimal asymptotic speed at which the extraction error can be suppressed. We establish that the reliability of Gibbs-preserving operations and of thermal operations are respectively characterized by the Petz and the sandwiched Rényi relative entropies, demonstrating that the former in general strictly outperforms the latter, and providing new interpretations of several information-theoretic divergences. Our analysis reveals that operational constraints such as energy conservation impose stronger limitations on the achievable precision of quantum tasks than can be inferred from their asymptotic rates, thereby questioning the use of Gibbs-preserving operations as a mathematically convenient substitute for the physically realizable thermal processes.
Extracting work from quantum states is a fundamental task in quantum thermodynamics. Previous studies have primarily focused on determining the best achievable rate of work extraction, and remarkably, this characterization appeared to remain unchanged regardless of the choice of allowed processes: whether one considers the operationally motivated class of energy-conserving thermal operations, or the axiomatic class of Gibbs-preserving operations, the optimal extractable work is given by the Helmholtz free energy. Here, we challenge this perspective, showing that a more refined analysis of the asymptotic performance of work extraction reveals significant differences in the performance for the two different classes of free operations. Precisely, we focus on the trade-off between the extraction rate and its reliability, characterized by the optimal asymptotic speed at which the extraction error can be suppressed. We establish that the reliability of Gibbs-preserving operations and of thermal operations are respectively characterized by the Petz and the sandwiched Rényi relative entropies, demonstrating that the former in general strictly outperforms the latter, and providing new interpretations of several information-theoretic divergences. Our analysis reveals that operational constraints such as energy conservation impose stronger limitations on the achievable precision of quantum tasks than can be inferred from their asymptotic rates, thereby questioning the use of Gibbs-preserving operations as a mathematically convenient substitute for the physically realizable thermal processes.
A recurring structural pattern appears across three apparently distinct areas of quantum information theory: the asymptotic rates at which quantum resources can be converted, concentrated, or distilled depend sensitively on the *operational class* of allowed processes — and this sensitivity is not captured by the leading-order rate alone. This paper synthesizes findings from quant-ph and cond-mat.stat-mech preprints to argue, as a heuristic reading rather than a derivation, that a shared geometry underlies asymptotic resource conversion: the relevant figure of merit is not the optimal rate but the *reliability* or *precision* of that rate, and different operational classes produce characteristically different reliability profiles even when their leading rates coincide. Specifically, we draw on five corpus findings: (1) the demonstration that Gibbs-preserving and thermal operations achieve identical leading-order work-extraction rates but are distinguished by Petz versus sandwiched Rényi divergences at the level of error-suppression speed [corpus:arxiv:2606.06318]; (2) the proof that almost-i.i.d. entanglement manipulation is robust at the rate level but may require source-dependent protocols at the distillation level [corpus:arxiv:2606.06392]; (3) the discovery that magic state distillation protocols can achieve near-linear asymptotic rates while carrying overhead exponents larger than one, decoupling rate from overhead in a previously unappreciated way [corpus:arxiv:2605.30108]; (4) the universal thermokinetic decomposition showing that energy dissipation suppresses *fluctuations* in information predictability rather than raising its mean [corpus:arxiv:2605.29957]; and (5) the finding that excessive entanglement can *reduce* channel discriminability, establishing that resource abundance does not monotonically improve task performance [corpus:arxiv:2605.31519]. The falsification path is concrete: if the heuristic is correct, then for any resource theory admitting two operational classes with equal leading-order rates, the error-exponent functions must be distinguishable by a divergence-class argument analogous to Petz vs. sandwiched. A computation showing that two such classes share both their leading rate *and* their full error-exponent function would falsify the central claim. --- Authorship: Saluca Agentic AI Research Team (Saluca LLC). AI-drafted from arXiv preprint corpus on the date in the filename. Cited arXiv preprints: 2605.29957, 2605.30108, 2605.30199, 2605.30558, 2605.30806, 2605.31379, 2605.31519, 2606.06107, 2606.06318, 2606.06392, 2606.06455, 2606.06456
Universal work extraction shows that input-state knowledge is unnecessary to attain the asymptotic free-energy rate. We ask whether this first-order universality extends to reliability, the exponential decay rate of extraction failure. In the work-battery fidelity formulation, we prove that no phase-independent Gibbs-preserving protocol can retain the state-aware Gibbs-preserving exponent throughout a coherent qubit time-translation orbit: at every positive target rate, its worst pointwise exponent is bounded by the corresponding state-aware thermal-operation value. The proof first establishes an exact finite-blocklength identity between phase-robust Gibbs-preserving extraction and state-aware thermal extraction. A trigonometric Remez inequality then upgrades this minimax identity to a pointwise theorem by ruling out exponential localization of the worst phase. For an explicit coherent-qubit family, known-phase Gibbs-preserving extraction is error free, whereas every phase-independent protocol has a finite worst-pointwise exponent. Thus input-state knowledge can be irrelevant to the first-order work rate yet indispensable for optimal exponential reliability.
We introduce the resource-theoretic free energy of a quantum channel as the maximal work extractable from the channel as its output equilibrates to a thermal state and its reference system remains locally intact. It is proportional to the relative entropy between the given channel and the absolutely thermal channel. It attains a clear operational meaning as twice the asymptotic rates of athermality distillation and formation under Gibbs-preserving superchannels, which map one absolutely thermal channel to another for a given bath, thereby revealing the asymptotic reversibility of the resource theory of athermality for quantum channels. Consequently, we establish that the optimal extractable work in converting one channel to another through the asymptotic athermality distillation and formation tasks equals the difference in their free energies. We call this optimal work the thermodynamic work capacity of channel conversion. Quantum information processing and computing fundamentally concern the manipulation and transformation of quantum channels, which encompass quantum states, their transformations, and measurements. A quantitative characterization of the optimal thermodynamic work gain or expenditure in quantum information processing constitutes a key step toward formulating thermodynamics of quantum processes.
Maximal Rényi Relative Entropy for α>2
Quantum relative entropies play a fundamental role in quantum information theory. In the classical setting, Rényi relative entropies constitute, up to linear combinations, the most general class of relative entropies, naturally motivating the search for their minimal and maximal quantum extensions. The minimal extension is known to be the reverse sandwiched Rényi relative entropy for α∈[0,1/2) and the sandwiched Rényi relative entropy for α≥1/2. In contrast, the maximal extension had previously been identified only for α∈[0,2], where it is given by the geometric Rényi relative entropy. In this work, we complete this characterization by proving that for α>2, the maximal extension is given by the α-z Rényi relative entropy with z=α−1. As an application, we determine when an energy-incoherent state can be transformed into an energy-coherent state by a Gibbs-preserving operation assisted by an uncorrelated catalyst, thereby fully characterizing the coherence-generating power of this class of operations in the catalytic 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.
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.