scholarly journals Generalized Weyl-Heisenberg Algebra, Qudit Systems and Entanglement Measure of Symmetric States via Spin Coherent States. Part II: The Perma-Concurrence Parameter

Symmetry ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 875
Author(s):  
Mohammed Daoud ◽  
Maurice R. Kibler
Keyword(s):  
Heisenberg Algebra ◽  
Entangled States ◽  
Entanglement Measure ◽  
Bloch Sphere ◽  
Maximally Entangled States ◽  
Qubit States ◽  
Range Of Variation ◽  
Symmetric States ◽  
Unit Vectors ◽  
Spin Coherent States

This paper deals with separable and entangled qudits | ψ d ⟩ (quantum states in dimension d) constructed from Dicke states made of N = d - 1 qubits. Such qudits present the property to be totally symmetric under the interchange of the N qubits. We discuss the notion of perma-concurrence P d for the qudit | ψ d ⟩ , introduced by the authors (Entropy 2018, 20, 292), as a parameter for characterizing the entanglement degree of | ψ d ⟩ . For d = 3 , the perma-concurrence P 3 constitutes an alternative to the concurrence C for symmetric two-qubit states. We give several expressions of P d (in terms of matrix permanent and in terms of unit vectors of R 3 pointing on the Bloch sphere) and precise the range of variation of P d (going from separable to maximally entangled states). Numerous examples are presented for P d . Special attention is devoted to states of W type and to maximally entangled states of Bell and Greenberger–Horne–Zeilinger type.

ENTANGLEMENT DISTRIBUTION AND STATE DISCRIMINATION IN TRIPARTITE QUBIT SYSTEMS

2008 ◽  
Vol 06 (02) ◽  
pp. 237-253 ◽  
Author(s):  
J. BATLE ◽  
M. CASAS
Keyword(s):  
Monte Carlo ◽  
Entangled States ◽  
Perfect State ◽  
Mixed States ◽  
W States ◽  
State Discrimination ◽  
Entanglement Measures ◽  
Entanglement Distribution ◽  
Maximally Entangled States ◽  
Qubit States

This work reviews and extends recent results concerning the distribution of entanglement, as well as nonlocality (in terms of inequality violations) in tripartite qubit systems. With recourse to a Monte Carlo generation of pure and mixed states of three-qubits, we explore several features related to the distribution of entanglement (expressed in the form of different measures of multiqubit entanglement based upon bipartitions). Also, special interest is paid to maximally entangled states (such as the GHZ for three-qubits) and W states. This study also sheds some light on the interesting relation existing between some entanglement measures and perfect state discrimination in LOCC measurements relevant to cryptographic protocols. We round off the results by studying the distribution of entanglement between Alice and Bob in a modified teleportation protocol toy model over three-qubit states.

Geometrical analysis and entanglement measure of symmetric multiqubit states

2020 ◽  
Vol 17 (08) ◽  
pp. 2050119
Author(s):  
Bilal Benzimoun ◽  
Mohammed Daoud
Keyword(s):  
Coherent States ◽  
Entanglement Measure ◽  
Bloch Sphere ◽  
Geometrical Analysis ◽  
Majorana Representation ◽  
Multipartite States ◽  
Symmetric Multiqubit States ◽  
Spin Coherent States

We geometrically examine the entanglement in symmetric multiquibt states using the spin coherent states properties. We employ the Majorana representation to examine how coherent (polarized) and unpolarized states can be represented in the Bloch sphere and subsequently to quantify entanglement in multipartite systems. Entanglement can be viewed as a distance separate two points in Bloch sphere and how this notion can be extended for multipartite states in W class. This provides us with an entanglement measure for [Formula: see text]-states analogue to the notion of Concurrence.

Remote preparation of four-qubit states via two-qubit maximally entangled states

2019 ◽  
Vol 18 (4) ◽  
Author(s):  
Yang Xue ◽  
Lei Shi ◽  
Xinyu Da ◽  
Kaihang Zhou ◽  
Lihua Ma ◽  
...  
Keyword(s):  
Entangled States ◽  
Remote Preparation ◽  
Maximally Entangled States ◽  
Qubit States

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 Generation of Maximally Entangled States by a Kerr-like Nonlinear Coupler Interactive with External Fields

2019 ◽  
Vol 29 (3) ◽  
Author(s):  
Doan Quoc Khoa ◽  
Luong Thi Tu Oanh ◽  
Chu Van Lanh ◽  
Do Hong Son
Keyword(s):  
Initial Conditions ◽  
Simulation Method ◽  
Entangled States ◽  
Quantum State Engineering ◽  
Nonlinear Properties ◽  
Nonlinear Quantum ◽  
Maximally Entangled States ◽  
Photon States ◽  
Nonlinear Coupler ◽  
Qubit States

We study a model with two nonlinear oscillators (Kerr-like nonlinear coupler) pumped by two external coherent fields as a nonlinear quantum scissor (NQS). Using the numerical simulation method introduced before for quantum state engineering in NQS of such type, we obtain the wave function describing the evolution of the system as a combination of n-photon states. Considered NQS generates a truncation of optical states that leads to achieve two-qubit states due to the nonlinear properties of oscillators and their interaction. In particular, evolution of the system generates maximally entangled states as so-called Bell-like states. We will show that a proper choice of initial conditions for such evolution implies the increase of efficiency of entanglement creation process. We consider our model for both damping and without damping cases.

Entanglement concentration for non-maximally entangled states of qudits

2009 ◽  
Vol 282 (7) ◽  
pp. 1482-1487 ◽  
Author(s):  
M. Yang ◽  
A. Delgado ◽  
L. Roa ◽  
C. Saavedra
Keyword(s):  
Entanglement Concentration ◽  
Entangled States ◽  
Maximally Entangled States

Entanglement criteria for the three-qubit states

2017 ◽  
Vol 15 (07) ◽  
pp. 1750049 ◽  
Author(s):  
Y. Akbari-Kourbolagh
Keyword(s):  
White Noise ◽  
Tensor Products ◽  
W State ◽  
Entangled States ◽  
Mean Values ◽  
W States ◽  
Pauli Matrices ◽  
The Mean ◽  
Simple Sets ◽  
Qubit States

We present sufficient criteria for the entanglement of three-qubit states. For some special families of states, the criteria are also necessary for the entanglement. They are formulated as simple sets of inequalities for the mean values of certain observables defined as tensor products of Pauli matrices. The criteria are good indicators of the entanglement in the vicinity of three-qubit GHZ and W states and enjoy the capability of detecting the entangled states with positive partial transpositions. Furthermore, they improve the best known result for the case of W state mixed with the white noise. The efficiency of the criteria is illustrated through several examples.

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