Classical Invasive Description of Informationally-Complete Quantum Processes
arXiv:2312.06545 · doi:10.1002/andp.202300304
Abstract
In classical stochastic theory, the joint probability distributions of a stochastic process obey by definition the Kolmogorov consistency conditions. Interpreting such a process as a sequence of physical measurements with probabilistic outcomes, these conditions reflect that the measurements do not alter the state of the underlying physical system. Prominently, this assumption has to be abandoned in the context of quantum mechanics, yet there are also classical processes in which measurements influence the measured system. Here, we derive conditions that characterize uniquely classical processes that are probed by a reasonable class of invasive measurements. We then analyse under what circumstances such classical processes can simulate the statistics arising from quantum processes associated with informationally-complete measurements. We expect that our investigation will help build a bridge between two fundamental traits of non-classicality, namely, coherence and contextuality.
arXiv comment9+10 pages, 3 figures. Comments are welcome!
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