Bayesian inference for complex and quaternionic two-level quantum systems

Paul B. Slater

Physica A: Statistical Mechanics and its Applications, 1996, vol. 223, issue 1, 167-174

Abstract: Jeffreys' approach for generating reparameterization-invariant prior distributions is applied to the three-dimensional convex set of complex two-level quantum systems. For this purpose, such systems are identified with bivariate complex normal distributions over the vectors of two-dimensional complex Hilbert space. The trivariate prior obtained is improper or non-normalizable over the convex set. However, its three bivariate marginals are — through a limiting procedure — normalizable to probability distributions and are, consequently, suitable for the Bayesian inference of two-level systems. Analogous results hold for the five-dimensional convex set of quaternionic two-level systems. The complex univariate and quaternionic trivariate marginals of the improper priors are uniform distributions. The bivariate marginals in the two cases are opposite in character.

Date: 1996
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:223:y:1996:i:1:p:167-174

DOI: 10.1016/0378-4371(95)00205-7

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