2005/08/29 by Filippo Neri · 1 citation
Computer Science · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Quantum Information and Cryptography #Quantum Mechanics and Applications #quant-ph
paper · pdf · doi:10.1103/physreva.72.062306
published as Phys.Rev.A 72, 062306 (2005) · Expanded and corrected version. 13 pages, 1 figure
arxiv created 2005/08/29 · openalex publication_date 2005/12/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
The use of Bayes theorem in quantum mechanics is discussed. It is shown that the quantum Bayes theorem follows from the ordinary quantum measurement theory, when applied to density operators that represent our knowledge of a system. The examples studied involve measurements on multiple copies of the same (unknown) state. The theorem is used to determine the unknown state by successive measurements on several of the copies of the state. An idealized information-theoretic description of propagating CW laser beams is treated in detail. It is shown how photon detections on part of the beams can be used to determine the phase of the rest of the beams. Also discussed, are the limitations on the accuracy of the phase determination that follow from the fact that it is accomplished by the detection of a finite number of photons. Explicit expressions are derived for the conditional probabilities of detecting photons at different locations, given the numbers of photons detected in the past. The quantitative predictions could be used, in principle, to test proposed quantum states of propagating laser beams.