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This is a theoretical quantum thermodynamics paper on which quasiclassical state transformations are achievable under thermal operations, using "population capacities" as accessibility constraints. It is primarily foundational work with no direct hardware or computing results, so its relevance to quantum computing is indirect, through resource-theoretic limits on energy-based state preparation and control. Readers tracking quantum technology should treat it as a mathematical framework rather than an applied advance.
Population Capacity and the Geometry of Thermomajorization
arXiv:2610.35433v1 Announce Type: new Abstract: We characterize quasiclassical state conversion under thermal operations through population capacities: the maximum population that thermal operations can concentrate on each set of energy levels. These capacities form a normalized, nondecreasing submodular rank function whose base polytope is exactly the thermally reachable population region. Their bounds therefore provide a complete system of accessibility constraints. Every nested chain of capacities can be simultaneously saturated by a reachable state, yielding the maximum expectation value of any prescribed observable, including the system Hamiltonian. For a prescribed target, its thermomajorization prefixes suffice to certify exact conversion through at most $n-1$ binary work-extraction probes. For approximate conversion, we construct a distinguished reachable state from active capacity constraints using a weighted principal sequence in $O(n^2 \log n)$ operations. At fixed comparison weights, this state minimizes every weighted convex separable residual cost and realizes a common first contact with the corresponding target-centered smoothing regions. Finally, the optimal trace-distance error equals the largest capacity advantage of the target over the initial state. This gap is attained at a target prefix and equals the largest positive optimized energy-storage deficit among the same binary probes, divided by their energy gap. Thus a common population capacity geometry determines accessibility, observable optimization, conversion certificates, and universal approximation.
Abstract:We characterize quasiclassical state conversion under thermal operations through population capacities: the maximum population that thermal operations can concentrate on each set of energy levels. These capacities form a normalized, nondecreasing submodular rank function whose base polytope is exactly the thermally reachable population region. Their bounds therefore provide a complete system of accessibility constraints. Every nested chain of capacities can be simultaneously saturated by a reachable state, yielding the maximum expectation value of any prescribed observable, including the system Hamiltonian. For a prescribed target, its thermomajorization prefixes suffice to certify exact conversion through at most $n-1$ binary work-extraction probes. For approximate conversion, we construct a distinguished reachable state from active capacity constraints using a weighted principal sequence in $O(n^2 \log n)$ operations. At fixed comparison weights, this state minimizes every weighted convex separable residual cost and realizes a common first contact with the corresponding target-centered smoothing regions. Finally, the optimal trace-distance error equals the largest capacity advantage of the target over the initial state. This gap is attained at a target prefix and equals the largest positive optimized energy-storage deficit among the same binary probes, divided by their energy gap. Thus a common population capacity geometry determines accessibility, observable optimization, conversion certificates, and universal approximation.
arXiv:2610.35433 [quant-ph]
(or arXiv:2610.35433v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2610.35433 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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