Entropy as a function of Geometric Phase

Abstract

We give a closed-form solution of von Neumann entropy as a function of geometric phase modulated by visibility and average distinguishability in Hilbert spaces of two and three dimensions. We show that the same type of dependence also exists in higher dimensions. We also outline a method for measuring both the entropy and the phase experimentally using a simple Mach-Zehnder type interferometer which explains physically why the two concepts are related.

19 pages, 7 figures

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• Distinguishability and many-particle interference
• Towards a geometrical interpretation of quantum information compression
• Distinguishability and mixedness in quantum interference
• Parametric representation of open quantum systems and crossover from quantum to classical environment
• Pancharatnam phase deficit can detect macroscopic entanglement