发表机构
International Centre for Theory of Quantum Technologies, University of Gdańsk（格但斯克大学量子理论国际中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究证明量子热力学中多个单独优化的相干性转移无法通过同一热操作同时实现，经半定规划分析验证了特定哈密顿量下的不相容性。
AI 中文摘要
不同能级间的相干性受到热力学的严格约束。在此，我们提出一个相关问题：若多个相干性转移可单独优化，它们是否也能通过同一热力学过程同时优化？我们证明这本质上是一个兼容性问题。利用热操作的能量分辨Stinespring表示，我们将基本相干性转移振幅表示为与总能量壳相关的浴加权向量的内积。相应柯西-施瓦茨界的饱和要求这些向量共线。由于所有转移必须源自同一能量守恒的系统-浴幺正变换，此类饱和条件通常无法独立施加。迹与吉布斯守恒会导致额外的相位闭合条件和多边形不等式，对于固定的布居转移数据，这些条件可排除同时饱和的可能性。我们通过严格的计算机辅助半定规划分析补充这些解析结果。对于混合简并哈密顿量$H=\text{diag}(0,1,1,3)$，经机器验证的原始和对偶界表明，不存在协变且吉布斯守恒的信道能同时实现三个单独最优的定向相干性转移。由于所有热操作均是协变且吉布斯守恒的，因此同一组最优值无法由热操作实现。我们进一步将这种不相容性与混合简并能级的Choi sector格拉姆矩阵中的范围包含约束关联起来。我们的结果表明，单独考虑时最优的相干性转移未必与单一物理热力学过程兼容。直接在热操作中对这种不相容性进行完整表征仍有待解决。
英文摘要
Coherences between different energy levels are strongly constrained by thermodynamics. Here we ask a related question: if several coherence transfers can be optimized separately, can they also be optimized simultaneously by the same thermodynamic process? We show that this is in general a compatibility problem. Using an energy-resolved Stinespring representation of thermal operations, we express elementary coherence-transfer amplitudes as inner products of bath-weighted vectors associated with total-energy shells. Saturation of the corresponding Cauchy--Schwarz bounds requires these vectors to be collinear. Since all transfers have to arise from the same energy-preserving system--bath unitary, such saturation conditions cannot in general be imposed independently. Trace and Gibbs preservation lead to additional phase-closure conditions and to polygon inequalities that can rule out simultaneous saturation for fixed population-transfer data. We complement these analytic results with a rigorous computer-assisted semidefinite-program analysis. For the mixed-degenerate Hamiltonian \(H=\operatorname{diag}(0,1,1,3)\), machine-certified primal and dual bounds show that no covariant Gibbs-preserving channel can simultaneously attain three individually optimal directional coherence transfers. Since every thermal operation is covariant and Gibbs preserving, the same triple of \(\CGP\)-optimal values cannot be attained by a thermal operation. We also analyze auxiliary Choi-sector Gram matrices for mixed-degenerate ladders. Under specified directional rank assumptions, positivity imposes range-inclusion conditions, from which we obtain conditional non-genericity statements for physical joint saturation.
Comments27 pages, v2: some clarifications about reasons and sources of joint obstruction in coherences transfer made
