Finite-resource coherent thermal conversion
Characterize coherent state conversion under thermal operations without catalysts or with bounded catalyst dimension and energy; determine the cost of target error , exact catalyst restoration and permitted system–catalyst correlations.
Problem statement
Characterize coherent state conversion under thermal operations without catalysts or with bounded catalyst dimension and energy; determine the cost of target error , exact catalyst restoration and permitted system–catalyst correlations.
Lean 4
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Background
The resource theory of thermodynamics studies which state transformations are possible using 'thermal operations' (energy-conserving unitaries with a thermal bath) for free. For states diagonal in the energy basis, the theory is complete; coherence between energy eigenspaces is a second, independent resource that the diagonal theory does not capture.
What is known: Thermomajorization characterizes energy-diagonal conversion in the usual thermal-operation setting, while catalytic and many-copy settings have their own second laws. Time-translation asymmetry imposes additional restrictions on coherence. Operation class, catalyst return convention and exact versus approximate output must be distinguished.
Preprint theorem (October 2025): Shiraishi–Takagi characterize approximate correlated-catalytic conversion under thermal operations. If the target's resonant coherent modes are contained in the input's, conversion with an exactly restored catalyst and arbitrarily accurate target is possible iff free energy does not increase; the final correlation can be arbitrarily small. This does not bound catalyst dimension or energy. Shiraishi's separate published 2025 result concerns the larger class of covariant Gibbs-preserving operations, not thermal operations themselves.
Remaining targets are catalyst-free or exact-output conversion and quantitative resource bounds for a fixed input/target pair: minimum catalyst dimension, energy spread and generated correlation at error . Determine the boundary when the resonant-mode condition fails rather than assuming the theorem covers it. These are more precise questions than declaring all coherent conversion open. Related: E11, O8.
Progress & source assessment
Source catalogue review: 4 September 2026. Improved indicates partial progress, including qualified preprint claims.
preprint: Approximate correlated-catalytic thermal conversion is characterized by free energy when target resonant coherent modes are contained in input modes; bounded catalyst resources and exact target output are not covered. Evidence
published: A related conversion theorem uses covariant Gibbs-preserving operations, a different operation class from thermal operations. Evidence
- [1]Lostaglio, Jennings, Rudolph, 'Description of quantum coherence in thermodynamic processes requires constraints beyond free energy', Nat. Commun. 6, 6383 (2015) link
- [2]Brandão, Horodecki, Ng, Oppenheim, Wehner, 'The second laws of quantum thermodynamics', PNAS 112, 3275 (2015) link
- [3]Shiraishi & Takagi, 'Recovery of the second law in fully quantum thermodynamics' (2025), preprint link
- [4]Shiraishi, PRL 134, 160402 (2025), covariant Gibbs-preserving conversion link
Recorded progress
Add yours →Nothing recorded yet. A pointer to a paper the entry is missing counts.
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