scholarly journals Facial structures of separable and PPT states

2011 ◽  
Vol 96 ◽  
pp. 257-269
Author(s):  
Seung-Hyeok Kye
Keyword(s):  
Ppt States

Indecomposable Positive Maps and a New Family of Inseparable PPT States

2006 ◽  
Author(s):  
Sudhavathani Simon ◽  
S. P. Rajagopalan ◽  
R. Simon
Keyword(s):  
New Family ◽  
Positive Maps ◽  
Ppt States

CANONICAL FORM AND SEPARABILITY OF PPT STATES IN ${\mathcal C}^2\otimes {\mathcal C}^M\otimes {\mathcal C}^N$ COMPOSITE QUANTUM SYSTEMS

2003 ◽  
Vol 01 (03) ◽  
pp. 337-347
Author(s):  
XIAO-HONG WANG ◽  
SHAO-MING FEI ◽  
ZHI-XI WANG ◽  
KE WU
Keyword(s):  
Canonical Form ◽  
General Expression ◽  
Quantum Systems ◽  
Canonical Forms ◽  
Density Matrices ◽  
Partial Transposition ◽  
Separability Condition ◽  
Ppt States

We investigate the canonical forms of positive partial transposition (PPT) density matrices in [Formula: see text] composite quantum systems with rank N. A general expression for these PPT states are explicitly obtained. From this canonical form a sufficient separability condition is presented.

scholarly journals Entangling capacities and the geometry of quantum operations

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Jhih-Yuan Kao ◽  
Chung-Hsien Chou
Keyword(s):  
Quantum Information ◽  
Physical Significance ◽  
Quantum States ◽  
Important Class ◽  
Quantum Operation ◽  
Positive Partial Transpose ◽  
Quantum Operations ◽  
Partial Transpose ◽  
Ppt States

Abstract Quantum operations are the fundamental transformations on quantum states. In this work, we study the relation between entangling capacities of operations, geometry of operations, and positive partial transpose (PPT) states, which are an important class of states in quantum information. We show a method to calculate bounds for entangling capacity, the amount of entanglement that can be produced by a quantum operation, in terms of negativity, a measure of entanglement. The bounds of entangling capacity are found to be associated with how non-PPT (PPT preserving) an operation is. A length that quantifies both entangling capacity/entanglement and PPT-ness of an operation or state can be defined, establishing a geometry characterized by PPT-ness. The distance derived from the length bounds the relative entangling capability, endowing the geometry with more physical significance. We also demonstrate the equivalence of PPT-ness and separability for unitary operations.

scholarly journals CANONICAL FORM AND SEPARABILITY OF PPT STATES ON MULTIPLE QUANTUM SPACES

2005 ◽  
Vol 03 (01) ◽  
pp. 147-151 ◽  
Author(s):  
XIAO-HONG WANG ◽  
SHAO-MING FEI
Keyword(s):  
Canonical Form ◽  
Quantum Systems ◽  
Multiple Quantum ◽  
Separability Condition ◽  
Ppt States

By using the "subtracting projectors" method in proving the separability of PPT states on multiple quantum spaces, we derive a canonical form of PPT states in [Formula: see text] composite quantum systems with rank N, from which a sufficient separability condition for these states is presented.

scholarly journals Entanglement Witnesses Arising from Exposed Positive Linear Maps

2011 ◽  
Vol 18 (04) ◽  
pp. 323-337 ◽  
Author(s):  
Kil-Chan Ha ◽  
Seung-Hyeok Kye
Keyword(s):  
Matrix Algebra ◽  
Three Dimensional ◽  
Entangled States ◽  
Entangled State ◽  
Minimal Set ◽  
Large Classes ◽  
Linear Maps ◽  
Entanglement Witnesses ◽  
Positive Linear Maps ◽  
Ppt States

We consider entanglement witnesses arising from positive linear maps which generate exposed extremal rays. We show that every entangled state can be detected by one of these witnesses, and this witness detects a unique set of entangled states among those. Therefore, they provide a minimal set of witnesses to detect any kind of entanglement in a sense. Furthermore, if those maps are indecomposable then they detect large classes of entangled states with positive partial transposes which have nonempty relative interiors in the cone generated by all PPT states. We also provide a one-parameter family of indecomposable positive linear maps which generate exposed extremal rays. This gives the first examples of such maps in three-dimensional matrix algebra.

scholarly journals On PPT States in C K ⊗ C M ⊗ C N Composite Quantum Systems

2004 ◽  
Vol 42 (2) ◽  
pp. 215-222 ◽  
Author(s):  
Wang Xiao-Hong ◽  
Fei Shao-Ming ◽  
Wang Zhi-Xi ◽  
Wu Ke
Keyword(s):  
Quantum Systems ◽  
Ppt States

scholarly journals Canonical Form and Separability of PPT States in C 2 ⊗ C 2 ⊗ C 2 ⊗ C N Composite Quantum Systems

2003 ◽  
Vol 40 (5) ◽  
pp. 515-518
Author(s):  
Fei Shao-Ming ◽  
Gao Xiu-Hong ◽  
Wang Xiao-Hong ◽  
Wang Zhi-Xi ◽  
Wu Ke
Keyword(s):  
Canonical Form ◽  
Quantum Systems ◽  
Ppt States

CIRCULANT DECOMPOSITIONS FOR BIPARTITE QUANTUM SYSTEMS

2008 ◽  
Vol 06 (supp01) ◽  
pp. 627-632
Author(s):  
DARIUSZ CHRUŚCIŃSKI ◽  
ANDRZEJ KOSSAKOWSKI
Keyword(s):  
Hilbert Space ◽  
Density Matrix ◽  
Quantum Systems ◽  
Direct Sum ◽  
Circular Structure ◽  
Partial Transposition ◽  
Direct Sum Decomposition ◽  
Bipartite Quantum Systems ◽  
New States ◽  
Ppt States

We construct a large class of quantum d ⊗ d states which are positive under partial transposition (so called PPT states). The construction is based on certain direct sum decomposition of the total Hilbert space displaying characteristic circular structure — that is way we call them circulant states. It turns out that partial transposition maps any such decomposition into another one and hence both original density matrix and its partially transposed partner share similar cyclic properties. This class contains many well known examples of PPT states from the literature and gives rise to a huge family of completely new states.

scholarly journals Separability criterion for multipartite quantum states based on the Bloch representation of density matrices

2008 ◽  
Vol 8 (8&9) ◽  
pp. 773-790
Author(s):  
A.S.M. Hassan ◽  
P.S. Joag
Keyword(s):  
Quantum States ◽  
Necessary Condition ◽  
Multilinear Algebra ◽  
Necessary And Sufficient Condition ◽  
Separability Criterion ◽  
Sufficiency Condition ◽  
Ppt States ◽  
Necessary And Sufficient ◽  
Qubit States ◽  
Bloch Representation

We give a new separability criterion, a necessary condition for separability of N-partite quantum states. The criterion is based on the Bloch representation of a N-partite quantum state and makes use of multilinear algebra, in particular, the matrization of tensors. Our criterion applies to arbitrary N-partite quantum states in $\mathcal{H}=\mathcal{H}^{d_1}\otimes \mathcal{H}^{d_2} \otimes \cdots \otimes \mathcal{H}^{d_N}.$ The criterion can test whether a N-partite state is entangled and can be applied to different partitions of the $N$-partite system. We provide examples that show the ability of this criterion to detect entanglement. We show that this criterion can detect bound entangled states. We prove a sufficiency condition for separability of a 3-partite state, straightforwardly generalizable to the case N > 3, under certain condition. We also give a necessary and sufficient condition for separability of a class of N-qubit states which includes N-qubit PPT states.

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