Quantum Harmonic Analysis of the Density Matrix

Abstract

We will study rigorously the notion of mixed states and their density operators (or matrices.) We will also discuss the quantum-mechanical consequences of possible variations of Planck's constant h. This Review has been written having in mind two readerships: mathematical physicists and quantum physicists. The mathematical rigor is maximal, but the language and notation we use throughout should be familiar to physicists.

Revised version, published in "Quanta"

References in corpus (8)

• Experimental Quantum State Tomography of Optical Fields and Ultrafast Statistical Sampling
• Stronger uncertainty relations for the sum of variances
• Algebras of distributions suitable for phase-space quantum mechanics. I
• How fundamental are fundamental constants?
• Quantum States and Hardy's Formulation of the Uncertainty Principle : a Symplectic Approach
• GPS test of the local position invariance of Planck's constant
• Unified framework to determine Gaussian states in continuous variable systems
• Relative Phase Shifts for Metaplectic Isotopies Acting on Mixed Gaussian States

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• Symplectic Coarse-Grained Classical and Semi-Classical Evolution of Subsystems: New Theoretical Aspects
• Uncertainty Relations for MIMO Ambiguity Functions
• Symplectic Transformations on Wigner Distributions and Time Frequency Signal Design
• Quantum Polar Duality and the Symplectic Camel: a Geometric Approach to Quantization
• Probability representation of photon states and tomography
• Probability representation of quantum mechanics and star product quantization