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.
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.
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.
Historically, entanglement and coherence distillation focused on the distillable rate under full knowledge of the initial state. In this paper, we develop a unified finite-blocklength and asymptotic theory for universal distillation from convex compact sequences of possible states stable under tensor products. We first resolve an open question by showing that two regularized variants of the generalized quantum Hoeffding divergence need not coincide, and establish fundamental properties of the Hoeffding divergence and anti-divergence. For universal entanglement distillation, we connect finite-blocklength performance under non-entangling, PPT-preserving, and dually free operations to composite correlated hypothesis testing, yielding reliability functions for non-entangling and PPT-preserving operations characterized by regularized quantum Hoeffding divergences and strong converse bounds via the anti-divergence. We recover the entanglement concentration error exponent, zero-rate exponents under a continuity condition, and distillable entanglements, and characterize the dually free cases by regularized relative entropies under restricted measurements. Additionally, five concrete noise models justify the black-box assumptions for both resources. For coherence distillation under maximally incoherent and dephasing-covariant incoherent operations, we extend the one-shot semidefinite program characterization to universal inputs; relating a relaxed optimization to hypothesis testing yields the high-rate reliability function. A coherent-seed approach extends the single-state formula to the entire direct regime when the zero-error rate is positive. Finally, we completely characterize the states with positive zero-error coherence distillation rate, show that the rate equals the order-zero Petz Rényi relative entropy of coherence, and derive dimension-independent one-shot bounds ......
Universal channel coding enables communication without a complete description of the channel. For classical channels, universal codes can attain both capacity and the optimal high-rate reliability. We show that this compatibility fails for classical-quantum channels in general; that is, the optimal reliability in the channel-aware scenario is not always achievable with universal coding due to the ignorance of the unitary rotation of the output system. We exhibit a family of classical-quantum channels for which one cannot achieve the channel-aware optimal reliability by a fixed coding scheme. We further derive a converse bound on the reliability for unitary-invariant decoders, a natural assumption for the universal coding scheme, that can be strictly smaller than the optimal channel-aware error exponent. Conversely, we construct a channel-independent encoder-decoder pair and establish a universally achievable bound on the reliability that matches this converse bound in the high-rate regime, thereby characterizing the optimal universal reliability. Specifically, the channel-aware and universal exponents are governed by the Petz and sandwiched Rényi divergences, respectively. These divergences coincide for commuting outputs but differ for noncommuting ones, explaining why universality preserves optimal reliability classically but can reduce it quantumly. Our results showcase the fundamental reliability cost of performing the classical-quantum channel coding task universally.
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 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.
The Quantum Reverse Shannon Theorem has been a milestone in quantum information theory. It states that asymptotically reliable simulation of a quantum channel, assisted by unlimited shared entanglement, requires a rate of classical communication equal to the channel’s entanglement-assisted classical capacity. In this paper, we study the error exponent of quantum channel simulation, which characterizes the optimal speed of exponential convergence of the performance towards the perfect, as the blocklength increases. Based on channel purified distance, we derive lower and upper bounds for the error exponent. Then we show that the two bounds coincide when the classical communication rate is below a critical value, and hence, we have determined the exact formula of the error exponent in the low-rate case. This enables us to obtain an operational interpretation to the channel’s sandwiched Rényi information of order from 1 to 2, since our formula is expressed as a transform of this quantity. In the derivation, we have also obtained an achievability bound for quantum channel simulation in the finite-blocklength setting, which is of realistic significance.