Spin flip of multiqubit states in discrete phase space

TL;DR

This paper explores how multiqubit states' discrete Wigner functions relate to their spin-flipped versions, revealing a Hadamard matrix connection that aids in quantum state analysis and entanglement characterization.

Contribution

It establishes a universal Hadamard matrix relationship between a multiqubit state's DWF and its spin-flipped state, independent of the quantum net choice.

Findings

The DWF of a multiqubit state and its spin-flipped counterpart are related via a Hadamard matrix.

The Hadamard matrix relation is independent of the quantum net used for tomography.

Results facilitate direct tomographic reconstruction and entanglement analysis using DWFs.

Abstract

Time reversal and spin flip are discrete symmetry operations of substantial import to quantum information and quantum computation. Spin flip arises in the context of separability, quantification of entanglement and the construction of Universal NOT gates. The present work investigates the relationship between the quantum state of a multiqubit system represented by the Discrete Wigner Function (DWFs) and its spin-flipped counterpart. The two are shown to be related through a Hadamard matrix that is independent of the choice of the quantum net used for the tomographic reconstruction of the DWF. These results would be of interest to cases involving the direct tomographic reconstruction of the DWF from experimental data and in the analysis of entanglement related properties purely in terms of the Discrete Wigner function.