Classification of Multipartite Entanglement via Negativity Fonts

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.

5 pages, No figures, Corrected typos

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• Polynomial invariants of degree 4 for even-$n$ qubits and their applications in entanglement classification
• Unitary Invariants and Classification of Four-Qubit States via Negativity Fonts
• Sequential generation of Polynomial Invariants and N-body non-local correlations
• More Communication with Less Entanglement
• Special core tensors of multi-qubit states and the concurrency of three lines
• Entanglement classification via integer partitions