Extrema of discrete Wigner functions and applications
Andrea Casaccino, Ernesto F. Galvao, Simone Severini
TL;DR
This paper investigates the extrema of discrete Wigner functions in finite-dimensional quantum systems and applies these findings to construct quantum random access codes, demonstrating their effectiveness in small Hilbert spaces.
Contribution
It characterizes the extrema of discrete Wigner functions and introduces a novel application in quantum information through the construction of quantum random access codes.
Findings
Extrema of discrete Wigner functions identified for small dimensions.
Constructed quantum random access codes with high success rates.
Demonstrated applicability in dimensions 2,3,4,5,7,8.
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.
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