Relative quantum phase, $m$-tangle, and multi-local Lorentz-group invariant

TL;DR

This paper introduces a new quantity linking quantum relative phase, $m$-tangle, and multi-local Lorentz-group invariants, providing a unified perspective on multi-qubit entanglement measures.

Contribution

It establishes a novel relation between quantum phase, $m$-tangle, and Lorentz-group invariants using a construction based on quantum phase orthogonal complement.

Findings

The proposed quantity coincides with $m$-tangle.

It also matches the multi-local Lorentz-group invariant.

Provides a new framework for understanding multi-qubit entanglement.

Abstract

In this paper we establish a relation between quantum relative phase, $m$-tangle, and multi-local Lorentz-group invariant or $SL(2,\mathbb{C})^{\times m}$-invariant $S^{2}_{(m)}$. Our construction is based on the orthogonal complement of a positive operator valued measure on quantum phase. In particular, we propose a quantity based on the quantum relative phase of a multi-qubit operator that coincides with $m$-tangle, and multi-local Lorentz-group invariant.