从受限投影数据识别无记忆顺序量子过程的因果顺序
Causal-Order Identification of Memoryless Sequential Quantum Processes from Restricted Projective Data
AI总结：
本文研究了从受限投影数据中识别无记忆顺序量子过程因果顺序的充要条件，通过引入代数一致性要求完善了基于伪密度矩阵的判据。
摘要：
从受限投影数据中识别因果顺序通常是非平凡的。当两个量子玩家仅通过未观测环境相互作用时，可用的局部测量统计通常不是层析完备的，因此无法从观测分布精确重建底层过程。因此，因果方向在某些情况下是统计可识别的，而在其他情况下则根本不可区分。在这项工作中，我们确定了判断观测分布是否与固定方向的无记忆顺序量子过程兼容的充要条件。我们证明了基于伪密度矩阵的方向条件独立结构和正性判据（如Liu、Qiu、Dahlsten和Vedral最近的工作所发展的）本身并不充分。缺失的成分是一个额外的代数一致性要求，这些条件共同给出了无记忆顺序类成员关系的完整判据。然后我们专门研究两量子比特泡利设置，其中问题仍然是非层析的，但变得明确可处理。在此情形下，我们刻画了两个顺序方向统计不可区分的条件，并通过例子表明仅正性不能排除更一般的记忆策略，而额外的代数一致性要求可以。
英文摘要：
Identifying causal order from restricted projective data is generally nontrivial. When two quantum players interact only through an unobserved environment, the available local measurement statistics are typically not tomographically complete, so the underlying process cannot in general be reconstructed exactly from the observed distribution. As a result, causal direction can be statistically identifiable in some cases but fundamentally indistinguishable in others. In this work, we determine necessary and sufficient conditions for deciding when an observed distribution is compatible with a memoryless sequential quantum process in a fixed direction. We show that directional conditional-independence structure and the positivity criterion based on the pseudo-density matrix, as developed in recent work by We show that directional conditional-independence structure and PDM-based positivity criteria are not sufficient by themselves. We then specialize to the two-qubit Pauli setting, where the problem remains non-tomographic but becomes explicitly tractable. In this regime, we characterize when the two sequential directions are statistically indistinguishable, and we show by example that positivity alone does not exclude more general memoryful strategies, whereas the additional algebraic consistency requirement does.
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