Consecutive measurements performed on the same quantum system can reveal fundamental insights into quantum theory’s causal structure, and probe different aspects of the quantum measurement problem. According to the Copenhagen interpretation, measurements affect the quantum system in such a way that the quantum superposition collapses after each measurement, erasing any memory of the prior state. We show here that counter to this view, un-amplified measurements (measurements where all variables comprising a pointer are in principle controllable) have coherent ancilla density matrices that encode the memory of the entire set of (un-amplified) quantum measurements that came before, and that the chain of this entire set is therefore non-Markovian. In contrast, sequences of amplified measurements (measurements where at least one pointer variable has been lost) are equivalent to a quantum Markov chain. We argue that the non-Markovian nature of quantum measurement has empirical consequences that are incompatible with the assumption of wave function collapse, thus elevating the collapse assumption into a testable hypothesis. Finally, we find that all of the information necessary to reconstruct an arbitrary non-Markovian quantum chain of measurements is encoded on the boundary of that chain (the first and the final measurement), reminiscent of the holographic principle.

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马尔可夫和非马尔可夫量子测量

在同一量子系统上进行连续测量可以揭示对量子理论因果结构的基本见解，并探讨量子测量问题的不同方面。根据哥本哈根的解释，测量以这样一种方式影响量子系统，即每次测量后量子叠加都会崩溃，擦除对先前状态的任何记忆。我们在这里展示了与这种观点相反，未放大的测量（包括指针的所有变量原则上可控的测量）具有相干的辅助密度矩阵，这些矩阵对之前出现的整个（未放大）量子测量集的记忆进行编码，因此整个集合的链是非马尔可夫的。相比之下，一系列放大的测量（至少丢失一个指针变量的测量）相当于一个量子马尔可夫链。我们认为量子测量的非马尔可夫性质具有与波函数坍缩假设不相容的经验后果，从而将坍缩假设提升为可检验的假设。最后，我们发现重建任意非马尔可夫量子测量链所需的所有信息都编码在该链的边界上（第一次和最后一次测量），这让人想起全息原理。从而将崩溃假设提升为可检验的假设。最后，我们发现重建任意非马尔可夫量子测量链所需的所有信息都编码在该链的边界上（第一次和最后一次测量），这让人想起全息原理。从而将崩溃假设提升为可检验的假设。最后，我们发现重建任意非马尔可夫量子测量链所需的所有信息都编码在该链的边界上（第一次和最后一次测量），这让人想起全息原理。