The relationship between quantum statistics and classical probability theory is discussed. Meeting Bell’s inequalities is treated as reducing quantum measurements to classical probability distributions. The question of whether or not this is possible is given a mathematical formulation involving singular-value decomposition and the concept of quasi-probabilities. All the possible quasi-probability distributions are presented in compact form, and are shown not to be positive definite. The concept of a regularized solution that minimizes variance is introduced. An invariant is defined and discussed that provides an intuitive representation of Bell’s inequality and its violation. The method of quasi-probabilities and the density-matrix formalism are compared in the context of the tomographic description of quantum states. A statistical interpretation is given to Greenberger-Horne-Zeilinger states.
Russian Microelectronics – Springer Journals
Published: Sep 21, 2008
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