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arXiv:2110.05211 · Journal of Physics A Mathematical and Theoretical

Detecting genuine multipartite entanglement in three-qubit systems with eternal non-Markovianity

Ankit Vaishy, Subhadip Mitra, Samyadeb Bhattacharya

Published Apr 14, 2022• 9 citations
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Abstract

Abstract We devise a novel protocol to detect genuinely multipartite entangled states by harnessing quantum non-Markovian operations. We utilize a particular type of non-Markovianity known as the eternal non-Markovianity to construct a non-complete positive map to filter out the bi-separable states and detect genuine multipartite entanglement. We further propose a witness operator to detect genuinely multipartite entangled states experimentally based on this theory. Our study sheds light on a hitherto unexplored connection between entanglement theory and quantum non-Markovianity.

DOI
10.1088/1751-8121/ac677e

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Abstract We devise a novel protocol to detect genuinely multipartite entangled states by harnessing quantum non-Markovian operations. We utilize a particular type of non-Markovianity known as the eternal non-Markovianity to construct a non-complete positive map to filter out the bi-separable states and detect genuine multipartite entanglement. We further propose a witness operator to detect genuinely multipartite entangled states experimentally based on this theory. Our study sheds light on a hitherto unexplored connection between entanglement theory and quantum non-Markovianity.
We devise a novel protocol to detect genuinely multipartite entangled states by harnessing quantum non-Markovian operations. We utilize a particular type of non-Markovianity known as the eternal non-Markovianity to construct a non-complete positive map to filter out the bi-separable states and detect genuine multipartite entanglement. We further propose a dynamical procedure to detect genuinely multipartite entangled states in real-time based on this theory. Our study sheds light on a hitherto unexplored connection between entanglement theory and quantum non-Markovianity.
Abstract We present a formalism to detect genuine multipartite entanglement by considering projection map which is a positive but not completely positive map. Projection map has been motivated by the no-pancake theorem which repudiates the existence of a quantum operation that maps the Bloch sphere onto a disk along its equator. The not-complete positivity feature of projection map is explored to investigate genuine multipartite entanglement in arbitrary N-qubit quantum systems. Our proposed framework can detect some important classes of genuinely entangled states in tripartite and quadripartite scenarios. We provide illustrative example to show the efficacy of our formalism to detect a class of tripartite PPT bound entangled states. Finally, we construct a suitable witness operator based on projection map to certify genuine tripartite entanglement, which is likely to be feasible experimentally.
We derive a general framework that lifts any set of bipartite to multipartite entanglement witnesses and we show how positive maps can naturally be incorporated into this framework. We show that some previous approaches for multipartite entanglement detection are intimately connected to the witnesses derived from partial transposition and that such criteria can easily be outperformed in higher dimensions by nondecomposable maps. As an exemplary case we present a witness that is capable of detecting genuine multipartite entanglement in bound entangled states.
Positive maps applied to a subsystem of a bipartite quantum state constitute a central tool in characterising entanglement. In the multipartite case, however, the direct application of a positive but not completely positive map cannot distinguish if a state is genuinely multipartite entangled or just entangled across some bipartition. We thus generalise this bipartite concept to the multipartite setting by introducing non-positive maps that are positive on the subset of biseparable states but can map to a non-positive element if applied to a genuine multipartite entangled state. We explicitly construct examples of multipartite non-positive maps, obtained from positive maps via a lifting procedure, that in this fashion can reveal genuine multipartite entanglement in a robust way.
We study the genuine multipartite entanglement of arbitrary n-partite quantum states by representing the density matrices in terms of the generalized Pauli operators. We introduce a general framework for detecting genuine multipartite entanglement and non full-separability of multipartite quantum states with arbitrary dimensions based on correlation tensors. Effective criterion is derived to verify the genuine multipartite entanglement. Detailed examples are given to show that the criterion detects more genuine multipartite entanglement than the existing criteria.