Fully quantum second-law--like statements from the theory of statistical comparisons

Abstract

In generalized resource theories, one aims to reformulate the problem of deciding whether a suitable transition (typically a transition that preserves the Gibbs state of the theory) between two given states $\rho$ and $\sigma$ exists or not, into the problem of checking whether a set of second-law--like inequalities hold or not. The aim of these preliminary notes is to show how the theory of statistical comparisons (in the sense of Blackwell, LeCam, and Torgersen) can be useful in such scenarios. In particular, we propose one construction, in which the second laws are formulated in terms of a suitable conditional min-entropy. Though a general, fully quantum result is also presented, stronger results are obtained for the case of qubits, and the case of $\sigma$ commuting with the Gibbs state.

11 pages of preliminary notes to be presented at QIT32, 25/26 May 2015, Osaka University

References in corpus (10)

• Description of quantum coherence in thermodynamic processes requires constraints beyond free energy
• Quantum coherence, time-translation symmetry and thermodynamics
• Clean Positive Operator Valued Measures
• Reexamination of Pure Qubit Work Extraction
• An example of a quantum statistical model which cannot be mapped to a less informative one by any trace preserving positive map
• Randomization theorems for quantum channels
• On the condition of conversion of classical probability distribution families into quantum families
• When is an input state always better than the others ?: universally optimal input states for statistical inference of quantum channels
• Loss of Memory and Convergence of Quantum Markov Processes
• Convertibility of Observables

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