By extending the usual Wigner operator to the -parameterized one, we find that in the process of the generalized Weyl quantization the parameter plays the role of correlation between two quadratures and . This can be exposed by comparing the normally ordered form of Ω with the standard form of the Gaussian bivariate normal distribution of random variables in statistics. Three different expressions of Ω and the quantization scheme with use of it are presented.
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