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Ordinarily, quantum-measurement based state discrimination methods use Bayesian inference to determine the maximally likely optical input state out of N possible inputs. Each practical single-shot measurement yields a unique vector of N likelihood values (one per each possible outcome) whose significance is not appreciated. Here we show theoretically and experimentally that measured Bayesian likelihood values are equal to observed probabilities of a successful state discrimination. Thus, the vector of Bayesian likelihoods provides significantly more information about the input state than is available in a typical state discrimination measurement.
Sergey V. Polyakov,Ivan Burenkov,M.V. Jabir,Fajar N. Annafianto, andAbdella Battou
"Shot-by-shot estimation of quantum measurement accuracy via quantum Bayesian inference", Proc. SPIE 11700, Optical and Quantum Sensing and Precision Metrology, 117003P (5 March 2021); https://doi.org/10.1117/12.2578972
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Sergey V. Polyakov, Ivan Burenkov, M.V. Jabir, Fajar N. Annafianto, Abdella Battou, "Shot-by-shot estimation of quantum measurement accuracy via quantum Bayesian inference," Proc. SPIE 11700, Optical and Quantum Sensing and Precision Metrology, 117003P (5 March 2021); https://doi.org/10.1117/12.2578972