Limitations on Joint Coherence Transfer in Quantum Thermodynamics
Abstract
Coherences between different energy levels are strongly constrained by thermodynamics. Here we ask whether several coherence transfers that can be optimized separately can also be optimized simultaneously by the same thermodynamic process. Using an energy-resolved Stinespring representation of thermal operations, we express elementary transfer amplitudes as inner products of bath-weighted vectors. Joint saturation imposes collinearity and phase-closure conditions on these vectors, which must all arise from one energy-preserving system--bath unitary. This gives necessary compatibility conditions for arbitrary finite-dimensional Hamiltonians. We show that joint incompatibility persists in a system with both degenerate and nondegenerate energy levels: rigorous computer-assisted semidefinite-program bounds, combined with explicit thermal constructions, prove that three individual thermal optima cannot be approached simultaneously. We then determine how well different coherences can be protected when their optima are incompatible. For a four-level family at infinite temperature, we obtain the complete closed retention region and the cost of balancing the coherences relative to their individual optima. At positive temperature, covariance and Gibbs preservation permit joint retention that no thermal operation can approach. Finite-bath constructions and certified semidefinite relaxations bound the balanced thermal performance. When two coherences carry independent phases, these bounds describe simultaneous preservation of interference visibility and phase Fisher information.
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BibTeX
@misc{cwiklinski2026limitations,
title = {{Limitations on Joint Coherence Transfer in Quantum Thermodynamics}},
author = {Piotr Ćwikliński and Michał Studziński},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.11872},
eprint = {2608.11872},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.11872},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Limitations on Joint Coherence Transfer in Quantum Thermodynamics
AU - Piotr Ćwikliński
AU - Michał Studziński
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2608.11872
UR - https://arxiv.org/abs/2608.11872
AB - Coherences between different energy levels are strongly constrained by thermodynamics. Here we ask whether several coherence transfers that can be optimized separately can also be optimized simultaneously by the same thermodynamic process. Using an energy-resolved Stinespring representation of thermal operations, we express elementary transfer amplitudes as inner products of bath-weighted vectors. Joint saturation imposes collinearity and phase-closure conditions on these vectors, which must all arise from one energy-preserving system--bath unitary. This gives necessary compatibility conditions for arbitrary finite-dimensional Hamiltonians. We show that joint incompatibility persists in a system with both degenerate and nondegenerate energy levels: rigorous computer-assisted semidefinite-program bounds, combined with explicit thermal constructions, prove that three individual thermal optima cannot be approached simultaneously. We then determine how well different coherences can be protected when their optima are incompatible. For a four-level family at infinite temperature, we obtain the complete closed retention region and the cost of balancing the coherences relative to their individual optima. At positive temperature, covariance and Gibbs preservation permit joint retention that no thermal operation can approach. Finite-bath constructions and certified semidefinite relaxations bound the balanced thermal performance. When two coherences carry independent phases, these bounds describe simultaneous preservation of interference visibility and phase Fisher information.
ER -