Preprint Article Version 1 This version is not peer-reviewed

Quantum Correlations and Permutation Symmetries

Version 1 : Received: 24 July 2018 / Approved: 25 July 2018 / Online: 25 July 2018 (12:20:21 CEST)

How to cite: Majumdar, M.G. Quantum Correlations and Permutation Symmetries. Preprints 2018, 2018070482 (doi: 10.20944/preprints201807.0482.v1). Majumdar, M.G. Quantum Correlations and Permutation Symmetries. Preprints 2018, 2018070482 (doi: 10.20944/preprints201807.0482.v1).

Abstract

In this paper, the connections between quantum non-locality and permutation symmetries are explored. This includes two types of symmetries: permutation across a superposition and permutation of qubits in a quantum system. An algorithm is proposed for nding the separability class of a quantum state using a method based on factorizing an arbitrary multipartite state into possible partitions, cyclically permuting qubits of the vectors in a superposition to check which separability class it falls into and thereafter using a reduced density-matrix analysis of the system is proposed. For the case of mixed quantum states, conditions for separability are found in terms of the partial transposition of the density matrices of the quantum system. One of these conditions turns out to be the Partial Positive Transpose (PPT) condition. A graphical method for analyzing separability is also proposed. The concept of permutation of qubits is shown to be useful in de ning a new entanglement measure in the `engle'.

Subject Areas

Quantum Entanglement, Separability, Positive Partial Transpose Criterion, Permutation, Quantum Information, Quantum Computing, Quantum Communication, Quantum Non-locality, Quantum Correlations, SWAP Operator

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