Minimal sets of dequantizers and quantizers for finite-dimensional quantum systems

TL;DR

This paper investigates minimal sets of dequantizers and quantizers for finite-dimensional quantum systems, providing explicit descriptions for qubits and linking to known sets, advancing the understanding of operator-function mappings.

Contribution

It offers a comprehensive characterization of minimal dequantizer and quantizer sets, including explicit formulas for qubits, and connects these to existing known sets.

Findings

Explicit description of all minimal self-dual sets for qubits

Connection established between known sets and derived formulas

General properties of minimal dequantizer and quantizer sets identified

Abstract

The problem of finding and characterizing minimal sets of dequantizers and quantizers applied in the mapping of operators onto functions is considered, for finite-dimensional quantum systems. The general properties of such sets are determined. An explicit description of all the minimum self-dual sets of dequantizers and quantizers for a qubit system is derived. The connection between some known sets of dequantizers and quantizers and the derived formulae is presented.