Wigner distribution on a double cylinder phase space for studying quantum error correction protocol

TL;DR

This paper introduces a new phase space distribution tailored for quantum systems with discrete symmetry, demonstrating its application in quantum error correction and proposing an experimental measurement scheme.

Contribution

It presents a novel Wigner distribution on a double cylinder phase space and applies it to quantum error correction protocols with a proposed measurement method.

Findings

Effective description of quantum states with discrete symmetry

Application to continuous variable quantum error correction

Feasible experimental measurement scheme

Abstract

We introduce a quasi-probability phase space distribution with two pairs of azimuthal-angular coordinates. This representation is well adapted to describe quantum systems with discrete symmetry. Quantum error correction of states encoded in continuous variables using translationally invariant states is studied as an example of application. We also propose an experimental scheme for measuring such new distribution.