The Gambler's Ruin Problem and Quantum Measurement

• URL: http://arxiv.org/abs/2004.01335v1
• Date: Fri, 3 Apr 2020 01:52:59 GMT
• Title: The Gambler's Ruin Problem and Quantum Measurement
• Authors: Fabrice Debbasch (Sorbonne Universite)
• Abstract summary: It is shown that a general unbiased quantum measurement can be reformulated as a gambler's ruin problem where the game is a martingale. Explicit computations are worked out in detail on a specific simple example.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The dynamics of a single microscopic or mesoscopic non quantum system interacting with a macroscopic environment is generally stochastic. In the same way, the reduced density operator of a single quantum system interacting with a macroscopic environment is a priori a stochastic variable, and decoherence describes only the average dynamics of this variable, not its fluctuations. It is shown that a general unbiased quantum measurement can be reformulated as a gambler's ruin problem where the game is a martingale. Born's rule then appears as a direct consequence of the optional stopping theorem for martingales. Explicit computations are worked out in detail on a specific simple example.

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