scholarly journals Unextendible product bases and extremal density matrices with positive partial transpose

2011 ◽  
Vol 84 (4) ◽  
Author(s):  
Per Øyvind Sollid ◽  
Jon Magne Leinaas ◽  
Jan Myrheim
Keyword(s):  
Density Matrices ◽  
Positive Partial Transpose ◽  
Partial Transpose

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

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Gleb A. Skorobagatko
Keyword(s):  
Quantum Systems ◽  
Many Body ◽  
Density Matrices ◽  
Positive Partial Transpose ◽  
Separability Criterion ◽  
Pair Density ◽  
Wide Range ◽  
The Family ◽  
Partial Transpose ◽  
General Physical

AbstractGeneral 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.

scholarly journals Geometry and Entanglement of Two-Qubit States in the Quantum Probabilistic Representation

Entropy ◽  
2018 ◽  
Vol 20 (9) ◽  
pp. 630 ◽  
Author(s):  
Julio López-Saldívar ◽  
Octavio Castaños ◽  
Eduardo Nahmad-Achar ◽  
Ramón López-Peña ◽  
Margarita Man’ko ◽  
...  
Keyword(s):  
Probability Distributions ◽  
Entangled States ◽  
Geometric Representation ◽  
Level System ◽  
Probabilistic Representation ◽  
Density Matrices ◽  
Positive Partial Transpose ◽  
Partial Transpose ◽  
Qubit States ◽  
Ppt Criterion

A new geometric representation of qubit and qutrit states based on probability simplexes is used to describe the separability and entanglement properties of density matrices of two qubits. The Peres–Horodecki positive partial transpose (ppt) -criterion and the concurrence inequalities are formulated as the conditions that the introduced probability distributions must satisfy to present entanglement. A four-level system, where one or two states are inaccessible, is considered as an example of applying the elaborated probability approach in an explicit form. The areas of three Triadas of Malevich’s squares for entangled states of two qubits are defined through the qutrit state, and the critical values of the sum of their areas are calculated. We always find an interval for the sum of the square areas, which provides the possibility for an experimental checkup of the entanglement of the system in terms of the probabilities.

scholarly journals Postponing Distillability Sudden Death in a Correlated Dephasing Channel

Entropy ◽  
2020 ◽  
Vol 22 (8) ◽  
pp. 827
Author(s):  
Guanghao Xue ◽  
Liang Qiu
Keyword(s):  
Sudden Death ◽  
Quantum Channel ◽  
Positive Partial Transpose ◽  
Partial Correlations ◽  
Partial Transpose ◽  
Correlated Channel

We investigated the dynamics of a two-qutrit system in a correlated quantum channel. The partial correlations between consecutive actions of the channel can effectively postpone the phenomenon of distillability sudden death (DSD) and broaden the range of the time cutoff that indicates entanglement of the positive partial transpose states. Particularly, the negativity of the system will revive and DSD will disappear in the fully correlated channel.

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