4 research outputs found
Classification of Multipartite Entanglement via Negativity Fonts
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.Comment: 5 pages, No figures, Corrected typo
Minimal Renyi-Ingarden-Urbanik entropy of multipartite quantum states
We study the entanglement of a pure state of a composite quantum system
consisting of several subsystems with levels each. It can be described by
the R\'enyi-Ingarden-Urbanik entropy of a decomposition of the state in a
product basis, minimized over all local unitary transformations. In the case
this quantity becomes a function of the rank of the tensor representing
the state, while in the limit the entropy becomes related to the
overlap with the closest separable state and the geometric measure of
entanglement. For any bipartite system the entropy coincides with the
standard entanglement entropy. We analyze the distribution of the minimal
entropy for random states of three and four-qubit systems. In the former case
the distributions of -tangle is studied and some of its moments are
evaluated, while in the latter case we analyze the distribution of the
hyperdeterminant. The behavior of the maximum overlap of a three-qudit system
with the closest separable state is also investigated in the asymptotic limit.Comment: 19 page