# Generalized reduction formula for Discrete Wigner functions of multiqubit systems

## TL;DR

This paper derives a generalized reduction formula for discrete Wigner functions of multiqubit states, enabling subsystem analysis in discrete phase space regardless of the quantum net used, aiding quantum state analysis.

## Contribution

It introduces a universal reduction formula for discrete Wigner functions applicable to any quantum net, filling a gap in quantum state subsystem analysis.

## Key findings

- Provides a reduction formula valid for arbitrary quantum nets
- Facilitates analysis of entangled states and decoherence in discrete phase space
- Enhances tools for quantum computing applications

## Abstract

Density matrices and Discrete Wigner Functions are equally valid representations of multiqubit quantum states. For density matrices, the partial trace operation is used to obtain the quantum state of subsystems, but an analogous prescription is not available for discrete Wigner Functions. Further, the discrete Wigner function corresponding to a density matrix is not unique but depends on the choice of the quantum net used for its reconstruction. In the present work, we derive a reduction formula for discrete Wigner functions of a general multiqubit state which works for arbitrary quantum nets. These results would be useful for the analysis and classification of entangled states and the study of decoherence purely in a discrete phase space setting and also in applications to quantum computing