量子通道对测量不相容性的操作隐藏
Operational Concealment of Measurement Incompatibility by Quantum Channels: Rank Loss versus Contraction
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中文总结 AI 辅助
研究量子通道对测量不相容性的操作隐藏，通过伴随-核框架对通道分类，给出隐藏鲁棒性度量及公式，表明其对单射和非单射通道的不同情况，为操作上不可达的测量不相容性提供系统表征和定量处理。
中文摘要 AI 辅助
测量不相容性在算子层面可能保持不变，但当观测限于量子通道输出时在操作上变得不可达，此现象称为操作隐藏。我们为操作隐藏开发了一个系统的伴随-核框架，其中可观测量按伴随通道的核确定的操作等价类组织。该框架通过核等价和单调性对通道进行结构分类，给出隐藏鲁棒性度量及显式半定规划公式。还给出近似隐藏框架和对特定情况的几何特征描述。表明隐藏鲁棒性对单射通道与标准不相容性鲁棒性一致，对非单射通道可能更小。这些结果对操作上不可达的测量不相容性进行了系统表征和定量处理，对受限访问量子信息和半设备无关认证有影响。
英文摘要
Quantum measurements can remain incompatible yet become impossible to certify when all probe states first pass through a quantum channel. We formulate this loss of certifiability as operational concealment and identify its exact finite-dimensional threshold. Under tomographically complete input access, a channel conceals some incompatible binary POVM pair if and only if its Heisenberg adjoint has nontrivial kernel. Thus, in this channel restricted single-use setting, rank loss rather than contraction is the universal transition for exact concealment: injective dissipative dynamics may render the effective measurements compatible while leaving exact concealment impossible. We quantify this distinction through a minimum-gain lower bound and show that regular time-local dynamics cannot produce exact concealment at finite time. We then classify all qubit channels whose adjoint fibres admit a positive unital retraction, reducing concealment to ordinary joint measurability of canonical representatives. For orthogonal projected qubit measurements we obtain an exact robustness formula and a strict separation from ordinary incompatibility robustness. Finally, quotient-space duality expresses this robustness as an experimentally accessible additive advantage in positive-payoff channel-output games. We also prove invariance under adjoining a passive finite-dimensional reference system for lifted target measurements, even when arbitrary joint compatible simulators are allowed on the enlarged output space. These results establish rank-sensitive criteria for certifying measurement incompatibility under restricted channel access.
