Uranga Anton, Akhmatskaya Elena, Sokolovski Dmitri
Basque Center for Applied Mathematics (BCAM), Alameda de Mazarredo 14, 48009 Bilbao, Spain.
Departmento de Química-Física, Universidad del País Vasco, UPV/EHU, 48940 Leioa, Spain.
Entropy (Basel). 2025 Mar 1;27(3):259. doi: 10.3390/e27030259.
The Uncertainty Principle forbids one to determine which of the two paths a quantum system has travelled, unless interference between the alternatives had been destroyed by a measuring device, e.g., by a pointer. One can try to weaken the coupling between the device and the system in order to avoid the veto. We demonstrate, however, that a weak pointer is at the same time an inaccurate one, and the information about the path taken by the system in each individual trial is inevitably lost. We show also that a similar problem occurs if a classical system is monitored by an inaccurate quantum meter. In both cases, one can still determine some characteristic of the corresponding statistical ensemble, a relation between path probabilities in the classical case, and a relation between the probability amplitudes if a quantum system is involved.
不确定性原理禁止人们确定量子系统所走的两条路径中的哪一条，除非替代路径之间的干涉已被测量装置（例如指针）破坏。人们可以尝试减弱装置与系统之间的耦合以避免这种否决。然而，我们证明，一个弱指针同时也是一个不准确的指针，并且在每个单独试验中关于系统所走路径的信息不可避免地会丢失。我们还表明，如果一个经典系统由一个不准确的量子测量仪监测，也会出现类似的问题。在这两种情况下，人们仍然可以确定相应统计系综的某些特征，经典情况下路径概率之间的关系，以及如果涉及量子系统时概率幅之间的关系。
