The Born rule describes the probability of obtaining an outcome when measuring an observable of a quantum system. As it can only be tested by measuring many copies of the system under consideration, it does not hold for non-replicable systems. For these systems, we give a procedure to predict the future statistics of measurement outcomes through Repeated Measurements (RM). This is done by extending the validity of quantum mechanics to those systems admitting no replicas; we prove that if the statistics of the results acquired by performing RM on such systems is sufficiently similar to that obtained by the Born rule, the latter can be used effectively. We apply our framework to a repeatedly measured Unruh-DeWitt detector interacting with a massless scalar quantum field, which is an example of a system (detector) interacting with an uncontrollable environment (field) for which using RM is necessary. Analysing what an observer learns from the RM outcomes, we find a regime where history-dependent RM probabilities are close to the Born ones. Consequently, the latter can be used for all practical purposes. Finally, we numerically study inertial and accelerated detectors, showing that an observer can see the Unruh effect via RM.

中文翻译：

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不可复制系统上的重复测量及其对 Unruh-DeWitt 探测器的影响


Born 规则描述了在测量量子系统的可观察对象时获得结果的概率。由于它只能通过测量所考虑的系统的许多副本来进行测试，因此它不适用于不可复制的系统。对于这些系统，我们提供了一个程序，通过重复测量 （RM） 预测测量结果的未来统计数据。这是通过将量子力学的有效性扩展到那些不接受复制的系统来实现的;我们证明，如果通过在此类系统上执行 RM 获得的结果的统计数据与 Born 规则获得的结果统计数据足够相似，则可以有效地使用后者。我们将框架应用于重复测量的 Unruh-DeWitt 探测器与无质量标量量子场交互，这是系统（探测器）与需要使用 RM 的不可控环境（场）交互的一个例子。分析观察者从 RM 结果中学到的东西，我们发现一个机制，其中历史依赖的 RM 概率接近 Born 概率。因此，后者可用于所有实际目的。最后，我们对惯性和加速探测器进行了数值研究，表明观察者可以通过 RM 看到 Unruh 效应。