Towards a geometrical interpretation of quantum information compression

Abstract

Let S be the von Neumann entropy of a finite ensemble E of pure quantum states. We show that S may be naturally viewed as a function of a set of geometrical volumes in Hilbert space defined by the states and that S is monotonically increasing in each of these variables. Since S is the Schumacher compression limit of E, this monotonicity property suggests a geometrical interpretation of the quantum redundancy involved in the compression process. It provides clarification of previous work in which it was shown that S may be increased while increasing the overlap of each pair of states in the ensemble. As a byproduct, our mathematical techniques also provide a new interpretation of the subentropy of E.

arXiv comment11 pages, latex2e

References in corpus (5)

• Distinguishability of States and von Neumann Entropy
• Coding Theorems of Quantum Information Theory
• A General Fidelity Limit for Quantum Channels
• Limits for compression of quantum information carried by ensembles of mixed states
• Entropy as a function of Geometric Phase

Cited by in corpus (11)

• Roofs and Convexity
• Bloch sphere representation of three-vertex geometric phases
• Properties of subentropy
• A quantum channel with additive minimum output entropy
• Multiplicativity of Maximal p-Norms in Werner-Holevo channels for $1\le p\le 2$
• Matrices of fidelities for ensembles of quantum states and the Holevo quantity
• A three state invariant
• Monotonicity of the von Neumann entropy expressed as a function of Rényi entropies
• Entropy, subentropy and the elementary symmetric functions
• Entropy of quantum channel in the theory of quantum information
• A classical interpretation of the Scrooge distribution