Classification of Multipartite Entanglement via Negativity Fonts

TL;DR

This paper introduces a method to classify multipartite entanglement in quantum states by analyzing the structure of the global partial transpose and negativity fonts, revealing intrinsic correlations and entanglement types.

Contribution

It proposes a new classification scheme for multipartite entangled states based on the structure of the global partial transpose and negativity fonts, extending understanding of quantum correlations.

Findings

Number of N-partite entanglement types is 2^{N-1}-N+2.

Number of major entanglement classes is 2^{N-1}-1.

Classifications for three and four qubit states are provided.

Abstract

Partial transposition of state operator is a well known tool to detect quantum correlations between two parts of a composite system. In this letter, the global partial transpose (GPT) is linked to conceptually multipartite underlying structures in a state - the negativity fonts. If K-way negativity fonts with non zero determinants exist, then selective partial transposition of a pure state, involving K of the N qubits (K leq N) yields an operator with negative eigevalues, identifying K-body correlations in the state. Expansion of GPT interms of K-way partially transposed (KPT) operators reveals the nature of intricate intrinsic correlations in the state. Classification criteria for multipartite entangled states, based on underlying structure of global partial transpose of canonical state, are proposed. Number of N-partite entanglement types for an N qubit system is found to be 2^{N-1}-N+2, while the number of major entanglement classes is 2^{N-1}-1. Major classes for three and four qubit states are listed. Subclasses are determined by the number and type of negativity fonts in canonical state.