Optimum Phase Space Probabilities From Quantum Tomography

Abstract

We determine a positive normalised phase space probability distribution $P$ with minimum mean square fractional deviation from the Wigner distribution $W$ .The minimum deviation, an invariant under phase space rotations, is a quantitative measure of the quantumness of the state.The positive distribution closest to $W$ will be useful in quantum mechanics and in time frequency analysis .

6 pages, 4 figures

References in corpus (4)

• Experimental Quantum State Tomography of Optical Fields and Ultrafast Statistical Sampling
• Heisenberg's Uncertainty Principle
• The Froissart bound for inelastic cross-sections
• Exact Quantum Correlations of Conjugate Variables From Joint Quadrature Measurements

Cited by in corpus (2)

• Phase space density limitation in laser cooling without spontaneous emission
• The Phase Space Formulation of Time-Symmetric Quantum Mechanics, I: the Wigner Formalism