Universal separability criterion for arbitrary density matrices from causal properties of separable and entangled quantum states

Abstract General physical background of famous Peres–Horodecki positive partial transpose (PH- or PPT-) separability criterion is revealed. Especially, the physical sense of partial transpose operation is shown to be equivalent to what one could call as the “local causality reversal” (LCR-) procedur...

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Autor principal:	Gleb A. Skorobagatko
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/61be3e7ffd0d4755ba7dcfd19624240b
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spelling	oai:doaj.org-article:61be3e7ffd0d4755ba7dcfd19624240b2021-12-02T16:35:19ZUniversal separability criterion for arbitrary density matrices from causal properties of separable and entangled quantum states10.1038/s41598-021-94804-22045-2322https://doaj.org/article/61be3e7ffd0d4755ba7dcfd19624240b2021-08-01T00:00:00Zhttps://doi.org/10.1038/s41598-021-94804-2https://doaj.org/toc/2045-2322Abstract General physical background of famous Peres–Horodecki positive partial transpose (PH- or PPT-) separability criterion is revealed. Especially, the physical sense of partial transpose operation is shown to be equivalent to what one could call as the “local causality reversal” (LCR-) procedure for all separable quantum systems or to the uncertainty in a global time arrow direction in all entangled cases. Using these universal causal considerations brand new general relations for the heuristic causal separability criterion have been proposed for arbitrary $$ D^{N} \times D^{N}$$ D N × D N density matrices acting in $$ {\mathcal {H}}_{D}^{\otimes N} $$ H D ⊗ N Hilbert spaces which describe the ensembles of N quantum systems of D eigenstates each. Resulting general formulas have been then analyzed for the widest special type of one-parametric density matrices of arbitrary dimensionality, which model a number of equivalent quantum subsystems being equally connected (EC-) with each other to arbitrary degree by means of a single entanglement parameter p. In particular, for the family of such EC-density matrices it has been found that there exists a number of N- and D-dependent separability (or entanglement) thresholds $$ p_{th}(N,D) $$ p th ( N , D ) for the values of the corresponded entanglement parameter p, which in the simplest case of a qubit-pair density matrix in $$ {\mathcal {H}}_{2} \otimes {\mathcal {H}}_{2} $$ H 2 ⊗ H 2 Hilbert space are shown to reduce to well-known results obtained earlier independently by Peres (Phys Rev Lett 77:1413–1415, 1996) and Horodecki (Phys Lett A 223(1–2):1–8, 1996). As the result, a number of remarkable features of the entanglement thresholds for EC-density matrices has been described for the first time. All novel results being obtained for the family of arbitrary EC-density matrices are shown to be applicable to a wide range of both interacting and non-interacting (at the moment of measurement) multi-partite quantum systems, such as arrays of qubits, spin chains, ensembles of quantum oscillators, strongly correlated quantum many-body systems with the possibility of many-body localization, etc.Gleb A. SkorobagatkoNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 11, Iss 1, Pp 1-32 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Gleb A. Skorobagatko Universal separability criterion for arbitrary density matrices from causal properties of separable and entangled quantum states
description	Abstract General physical background of famous Peres–Horodecki positive partial transpose (PH- or PPT-) separability criterion is revealed. Especially, the physical sense of partial transpose operation is shown to be equivalent to what one could call as the “local causality reversal” (LCR-) procedure for all separable quantum systems or to the uncertainty in a global time arrow direction in all entangled cases. Using these universal causal considerations brand new general relations for the heuristic causal separability criterion have been proposed for arbitrary $$ D^{N} \times D^{N}$$ D N × D N density matrices acting in $$ {\mathcal {H}}_{D}^{\otimes N} $$ H D ⊗ N Hilbert spaces which describe the ensembles of N quantum systems of D eigenstates each. Resulting general formulas have been then analyzed for the widest special type of one-parametric density matrices of arbitrary dimensionality, which model a number of equivalent quantum subsystems being equally connected (EC-) with each other to arbitrary degree by means of a single entanglement parameter p. In particular, for the family of such EC-density matrices it has been found that there exists a number of N- and D-dependent separability (or entanglement) thresholds $$ p_{th}(N,D) $$ p th ( N , D ) for the values of the corresponded entanglement parameter p, which in the simplest case of a qubit-pair density matrix in $$ {\mathcal {H}}_{2} \otimes {\mathcal {H}}_{2} $$ H 2 ⊗ H 2 Hilbert space are shown to reduce to well-known results obtained earlier independently by Peres (Phys Rev Lett 77:1413–1415, 1996) and Horodecki (Phys Lett A 223(1–2):1–8, 1996). As the result, a number of remarkable features of the entanglement thresholds for EC-density matrices has been described for the first time. All novel results being obtained for the family of arbitrary EC-density matrices are shown to be applicable to a wide range of both interacting and non-interacting (at the moment of measurement) multi-partite quantum systems, such as arrays of qubits, spin chains, ensembles of quantum oscillators, strongly correlated quantum many-body systems with the possibility of many-body localization, etc.
format	article
author	Gleb A. Skorobagatko
author_facet	Gleb A. Skorobagatko
author_sort	Gleb A. Skorobagatko
title	Universal separability criterion for arbitrary density matrices from causal properties of separable and entangled quantum states
title_short	Universal separability criterion for arbitrary density matrices from causal properties of separable and entangled quantum states
title_full	Universal separability criterion for arbitrary density matrices from causal properties of separable and entangled quantum states
title_fullStr	Universal separability criterion for arbitrary density matrices from causal properties of separable and entangled quantum states
title_full_unstemmed	Universal separability criterion for arbitrary density matrices from causal properties of separable and entangled quantum states
title_sort	universal separability criterion for arbitrary density matrices from causal properties of separable and entangled quantum states
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/61be3e7ffd0d4755ba7dcfd19624240b
work_keys_str_mv	AT glebaskorobagatko universalseparabilitycriterionforarbitrarydensitymatricesfromcausalpropertiesofseparableandentangledquantumstates
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Universal separability criterion for arbitrary density matrices from causal properties of separable and entangled quantum states

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