Extrema of discrete Wigner functions and applications

Abstract

We study the class of discrete Wigner functions proposed by Gibbons et al. [Phys. Rev. A 70, 062101 (2004)] to describe quantum states using a discrete phase-space based on finite fields. We find the extrema of such functions for small Hilbert space dimensions, and present a quantum information application: a construction of quantum random access codes. These are constructed using the complete set of phase-space point operators to find encoding states and to obtain the codes' average success rates for Hilbert space dimensions 2,3,4,5,7 and 8.

7 pages, 1 figure. v2: minor changes, published version

References in corpus (7)

• Quantum Cryptography using larger alphabets
• Discrete phase space based on finite fields
• Mutually unbiased binary observable sets on N qubits
• Quantum computers in phase space
• Classicality in discrete Wigner functions
• Qubits in phase space: Wigner function approach to quantum error correction and the mean king problem
• Discrete Wigner functions and the phase space representation of quantum computers

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