scholarly journals MIXING AND DECOHERENCE TO NEAREST SEPARABLE STATES

2009 ◽  
Vol 07 (04) ◽  
pp. 829-846
Author(s):  
AVIJIT LAHIRI ◽  
GAUTAM GHOSH ◽  
SANKHASUBHRA NAG
Keyword(s):  
Quantum Correlation ◽  
Entangled States ◽  
Entanglement Measure ◽  
Measuring Apparatus ◽  
Separable State ◽  
Mixed States ◽  
Classical Correlation ◽  
Separable States ◽  
System A ◽  
Pure States

We consider a class of entangled states of a quantum system (S) and a second system (A) where pure states of the former are correlated with mixed states of the latter, and work out the entanglement measure with reference to the nearest separable state. Such "pure-mixed" entanglement is expected when the system S interacts with a macroscopic measuring apparatus in a quantum measurement, where the quantum correlation is destroyed in the process of environment-induced decoherence whereafter only the classical correlation between S and A remains, the latter being large compared to the former. We present numerical evidence that the entangled S–A state drifts towards the nearest separable state through decoherence, with an additional tendency of equimixing among relevant groups of apparatus states.

Multipartite entanglement and hyperdeterminants

2002 ◽  
Vol 2 (Special) ◽  
pp. 540-555
Author(s):  
A. Miyake ◽  
M. Wadati
Keyword(s):  
Entangled States ◽  
Multipartite Entanglement ◽  
Maximal Dimension ◽  
Ordered Structure ◽  
Mixed States ◽  
Separable States ◽  
Entanglement Measures ◽  
Pure States ◽  
Maximally Entangled States ◽  
Bipartite Case

We classify multipartite entanglement in a unified manner, focusing on a duality between the set of separable states and that of entangled states. Hyperdeterminants, derived from the duality, are natural generalizations of entanglement measures, the concurrence, 3-tangle for 2, 3 qubits respectively. Our approach reveals how inequivalent multipartite entangled classes of pure states constitute a partially ordered structure under local actions, significantly different from a totally ordered one in the bipartite case. Moreover, the generic entangled class of the maximal dimension, given by the nonzero hyperdeterminant, does not include the maximally entangled states in Bell's inequalities in general (e.g., in the \(n \!\geq\! 4\) qubits), contrary to the widely known bipartite or 3-qubit cases. It suggests that not only are they never locally interconvertible with the majority of multipartite entangled states, but they would have no grounds for the canonical \(n\)-partite entangled states. Our classification is also useful for that of mixed states.

scholarly journals MEASUREMENT-INDUCED NONLOCALITY OVER TWO-SIDED PROJECTIVE MEASUREMENTS

2013 ◽  
Vol 27 (16) ◽  
pp. 1350067 ◽  
Author(s):  
YU GUO
Keyword(s):  
Lower Bound ◽  
Quantum Correlation ◽  
Quantum Discord ◽  
Mixed States ◽  
Infinite Dimensional ◽  
Pure States ◽  
Projective Measurements

Measurement-induced nonlocality (MIN), introduced by Luo and Fu [Phys. Rev. Lett.106, 120401 (2011)], is a kind of quantum correlation which is different from entanglement and quantum discord (QD). MIN is defined over one-sided projective measurements. In this paper, we introduce a MIN over two-sided projective measurements. The nullity of this two-sided MIN is characterized, a formula for calculating two-sided MIN for pure states is proposed, and a lower bound of (two-sided) MIN for maximally entangled mixed states is given. In addition, we find that (two-sided) MIN is not continuous. Both finite- and infinite-dimensional cases are considered.

scholarly journals Unified Monogamy Relations of Multipartite Entanglement

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Awais Khan ◽  
Junaid ur Rehman ◽  
Kehao Wang ◽  
Hyundong Shin
Keyword(s):  
Analytic Formula ◽  
Entangled States ◽  
Multipartite Entanglement ◽  
Entanglement Measure ◽  
Mixed States ◽  
Bipartite Entanglement ◽  
Entanglement Of Formation ◽  
Special Cases ◽  
Qubit States ◽  
Monogamy Relations

Abstract Unified-(q, s) entanglement $$({{\mathscr{U}}}_{q,s})$$ ( U q , s ) is a generalized bipartite entanglement measure, which encompasses Tsallis-q entanglement, Rényi-q entanglement, and entanglement of formation as its special cases. We first provide the extended (q; s) region of the generalized analytic formula of  $${{\mathscr{U}}}_{q,s}$$ U q , s . Then, the monogamy relation based on the squared  $${{\mathscr{U}}}_{q,s}$$ U q , s for arbitrary multiqubit mixed states is proved. The monogamy relation proved in this paper enables us to construct an entanglement indicator that can be utilized to identify all genuine multiqubit entangled states even the cases where three tangle of concurrence loses its efficiency. It is shown that this monogamy relation also holds true for the generalized W-class state. The αth power $${{\mathscr{U}}}_{q,s}$$ U q , s based general monogamy and polygamy inequalities are established for tripartite qubit states.

scholarly journals Distance between Bound Entangled States from Unextendible Product Bases and Separable States

2020 ◽  
Vol 2 (1) ◽  
pp. 49-56 ◽  
Author(s):  
Marcin Wieśniak ◽  
Palash Pandya ◽  
Omer Sakarya ◽  
Bianka Woloncewicz
Keyword(s):  
The State ◽  
Reference State ◽  
Entangled States ◽  
Separable State ◽  
Entanglement Witness ◽  
Separable States ◽  
Entanglement Witnesses

We discuss the use of the Gilbert algorithm to tailor entanglement witnesses for unextendible product basis bound entangled states (UPB BE states). The method relies on the fact that an optimal entanglement witness is given by a plane perpendicular to a line between the reference state, entanglement of which is to be witnessed, and its closest separable state (CSS). The Gilbert algorithm finds an approximation of CSS. In this article, we investigate if this approximation can be good enough to yield a valid entanglement witness. We compare witnesses found with Gilbert algorithm and those given by Bandyopadhyay–Ghosh–Roychowdhury (BGR) construction. This comparison allows us to learn about the amount of entanglement and we find a relationship between it and a feature of the construction of UPBBE states, namely the size of their central tile. We show that in most studied cases, witnesses found with the Gilbert algorithm in this work are more optimal than ones obtained by Bandyopadhyay, Ghosh, and Roychowdhury. This result implies the increased tolerance to experimental imperfections in a realization of the state.

scholarly journals LOCAL UNITARY EQUIVALENT CLASSES OF SYMMETRIC N-QUBIT MIXED STATES

2013 ◽  
Vol 11 (08) ◽  
pp. 1350072 ◽  
Author(s):  
SAKINEH ASHOURISHEIKHI ◽  
SWARNAMALA SIRSI
Keyword(s):  
Mixed State ◽  
Classification Scheme ◽  
Ghz State ◽  
Mixed States ◽  
Separable States ◽  
State Classification ◽  
Pure States ◽  
Two Parameters ◽  
Special Case

Majorana representation (MR) of symmetric N-qubit pure states has been used successfully in entanglement classification. Generalization of this has been a long standing open problem due to the difficulties faced in the construction of a Majorana like geometric representation for symmetric mixed state. We have overcome this problem by developing a method of classifying local unitary (LU) equivalent classes of symmetric N-qubit mixed states based on the geometrical multiaxial representation (MAR) of the density matrix. In addition to the two parameters defined for the entanglement classification of the symmetric pure states based on MR, namely, diversity degree and degeneracy configuration, we show that another parameter called rank needs to be introduced for symmetric mixed state classification. Our scheme of classification is more general as it can be applied to both pure and mixed states. To bring out the similarities/differences between the MR and MAR, N-qubit GHZ state is taken up for a detailed study. We conclude that pure state classification based on MR is not a special case of our classification scheme based on MAR. We also give a recipe to identify the most general symmetric N-qubit pure separable states. The power of our method is demonstrated using several well-known examples of symmetric two-qubit pure and mixed states as well as three-qubit pure states. Classification of uniaxial, biaxial and triaxial symmetric two-qubit mixed states which can be produced in the laboratory is studied in detail.

ENTANGLEMENT MEASURE OF BIPARTITE SYSTEM STATES

2010 ◽  
Vol 07 (06) ◽  
pp. 1051-1064 ◽  
Author(s):  
K. BERRADA ◽  
Y. HASSOUNI
Keyword(s):  
Coherent States ◽  
Linear Entropy ◽  
Entanglement Measure ◽  
Mixed States ◽  
Maximal Entanglement ◽  
Bipartite System ◽  
Pure States ◽  
System States ◽  
Entangled Coherent States

Linear entropy as a measure of entanglement is applied to explain conditions for minimal and maximal entanglement of bipartite nonorthogonal pure states. We formulate this measure in terms of the amplitudes of coherent states in the case of entangled coherent states and calculate the conditions. We generalize this formalism to the case of bipartite mixed states and show that the entanglement measure is also a function of the probabilities.

scholarly journals Some Remarks on the Entanglement Number

Quanta ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 22-36
Author(s):  
George Androulakis ◽  
Ryan McGaha
Keyword(s):  
Point Of View ◽  
Entanglement Measure ◽  
Mixed States ◽  
Interesting Point ◽  
Finite Dimensional ◽  
Entanglement Measures ◽  
Pure States ◽  
Tree Representations ◽  
Natural Way ◽  
Finite Dimensional Hilbert Space

Gudder, in a recent paper, defined a candidate entanglement measure which is called the entanglement number. The entanglement number is first defined on pure states and then it extends to mixed states by the convex roof construction. In Gudder's article it was left as an open problem to show that Optimal Pure State Ensembles (OPSE) exist for the convex roof extension of the entanglement number from pure to mixed states. We answer Gudder's question in the affirmative, and therefore we obtain that the entanglement number vanishes only on the separable states. More generally we show that OPSE exist for the convex roof extension of any function that is norm continuous on the pure states of a finite dimensional Hilbert space. Further we prove that the entanglement number is an LOCC monotone, (and thus an entanglement measure), by using a criterion that was developed by Vidal in 2000. We present a simplified proof of Vidal's result where moreover we use an interesting point of view of tree representations for LOCC communications. Lastly, we generalize Gudder's entanglement number by producing a monotonic family of entanglement measures which converge in a natural way to the entropy of entanglement.Quanta 2020; 9: 22–36.

Genuine tripartite entanglement semi-monotone for 2x2xn-dimensional systems

2007 ◽  
Vol 7 (7) ◽  
pp. 584-593
Author(s):  
C.-S. Yu ◽  
H.-S. Song ◽  
Y.-H. Wang
Keyword(s):  
Kronecker Product ◽  
Approximation Technique ◽  
Analytic Approximation ◽  
Mixed States ◽  
Tripartite Entanglement ◽  
New Approach ◽  
Separable States ◽  
Good Criterion ◽  
W States ◽  
Pure States

In this paper, we present a new approach to study genuine tripartite entanglement existing in $(2\times 2\times n)-$dimensional quantum pure states. By utilizing the approach, we introduce a particular quantity to measure genuine tripartite entanglement. The quantity is shown to be an entanglement monotone in 2-dimensional subsystems (semi-monotone) and reaches zero for separable states and $(2\times 2\times 2)-$dimensional $W$ states, hence is a good criterion to characterize genuine tripartite entanglement. Furthermore, the formulation for pure states can be conveniently extended to the case of mixed states by utilizing the kronecker product approximation technique. As applications, we give the analytic approximation for weakly mixed states, and study the genuine tripartite entanglement of two given weakly mixed states.

scholarly journals Ent: A Multipartite entanglement measure, and parameterization of entangled states

2018 ◽  
Vol 18 (5&6) ◽  
pp. 389-442
Author(s):  
Samuel R. Hedemann
Keyword(s):  
Sufficient Conditions ◽  
Special Property ◽  
Entangled States ◽  
Multipartite Entanglement ◽  
Entanglement Measure ◽  
Mixed States ◽  
Schmidt Decomposition ◽  
Multipartite System ◽  
Necessary And Sufficient ◽  
Maximally Entangled Basis

A multipartite entanglement measure called the ent is presented and shown to be an entanglement monotone, with the special property of automatic normalization. Necessary and sufficient conditions are developed for constructing maximally entangled states in every multipartite system such that they are true-generalized X states (TGX) states, a generalization of the Bell states, and are extended to general nonTGX states as well. These results are then used to prove the existence of maximally entangled basis (MEB) sets in all systems. A parameterization of general pure states of all ent values is given, and proposed as a multipartite Schmidt decomposition. Finally, we develop an ent vector and ent array to handle more general definitions of multipartite entanglement, and the ent is extended to general mixed states, providing a general multipartite entanglement measure.

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