Analytic expressions for geometric measure of three-qubit states

Tamaryan, Levon; Park, DaeKil; Tamaryan, Sayatnova

doi:10.1103/physreva.77.022325

Cited by 37 publications

(60 citation statements)

References 36 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(95) can be performed in many cases, e.g. for W-type states [263,291] or certain graph states [292,293]. Also the convex roof can be computed in important cases [214,263].…”

Section: Distance Measuresmentioning

confidence: 99%

Entanglement detection

Gühne¹,

Tóth²

2009

Physics Reports

2,170

2,499

View full text Add to dashboard Cite

How can one prove that a given state is entangled? In this paper we review different methods that have been proposed for entanglement detection. We first explain the basic elements of entanglement theory for two or more particles and then entanglement verification procedures such as Bell inequalities, entanglement witnesses, the determination of nonlinear properties of a quantum state via measurements on several copies, and spin squeezing inequalities. An emphasis is given to the theory and application of entanglement witnesses. We also discuss several experiments, where some of the presented methods have been implemented.

show abstract

“…(95) can be performed in many cases, e.g. for W-type states [263,291] or certain graph states [292,293]. Also the convex roof can be computed in important cases [214,263].…”

Section: Distance Measuresmentioning

confidence: 99%

Entanglement detection

Gühne¹,

Tóth²

2009

Physics Reports

2,170

2,499

View full text Add to dashboard Cite

show abstract

“…Tamaryan et al [149,150] noticed that some highly entangled n qubit W-type states have a continuous one-parametric range of closest separable states, and for the W-states themselves this continuous range was already given in Equation (2.9). For three qubits |W 3 〉 is known to be the maximally entangled state [151], and with the parameterisation |Λ(ϕ)〉 = 2 3…”

Section: Results For General Statesmentioning

confidence: 99%

Classification of Entanglement in Symmetric States

Aulbach

2012

Int. J. Quantum Inform.

View full text Add to dashboard Cite

Quantum states that are symmetric with respect to permutations of their subsystems appear in a wide range of physical settings, and they have a variety of promising applications in quantum information science. In this thesis, the entanglement of symmetric multipartite states is categorized, with a particular focus on the pure multi-qubit case and the geometric measure of entanglement. An essential tool for this analysis is the Majorana representation, a generalization of the single-qubit Bloch sphere representation, which allows for a unique representation of symmetric n-qubit states by n points on the surface of a sphere. Here this representation is employed to search for the maximally entangled symmetric states of up to 12 qubits in terms of the geometric measure, and an intuitive visual understanding of the upper bound on the maximal symmetric entanglement is given. Furthermore, it will be seen that the Majorana representation facilitates the characterization of entanglement equivalence classes such as stochastic local operations and classical communication (SLOCC) and the degeneracy configuration (DC). It is found that SLOCC operations between symmetric states can be described by the Möbius transformations of complex analysis, which allows for a clear visualization of the SLOCC freedoms and facilitates the understanding of SLOCC invariants and equivalence classes. In particular, explicit forms of representative states for all symmetric SLOCC classes of up to five qubits are derived. Well-known entanglement classification schemes such as the four qubit entanglement families or polynomial invariants are reviewed in the light of the results gathered here, which leads to sometimes surprising connections. Some interesting links and applications of the Majorana representation to related fields of mathematics and physics are also discussed.

show abstract

“…The calculation method is elaborated in Ref. [26] and here we present only final results. In three different ranges of definition the maximal success probability is differently expressed.…”

Section: Analytic Expressions For Maximum Probability Of Successmentioning

confidence: 99%

Reduced state uniquely defines the Groverian measure of the original pure state

et al. 2008

Self Cite

View full text Add to dashboard Cite

Groverian and Geometric entanglement measures of the n-party pure state are expressed by the (n − 1)-party reduced state density operator directly. This main theorem derives several important consequences. First, if two pure n-qudit states have reduced states of (n-1)-qudits, which are equivalent under local unitary(LU) transformations, then they have equal Groverian and Geometric entanglement measures. Second, both measures have an upper bound for pure states. However, this upper bound is reached only for two qubit systems. Third, it converts effectively the nonlinear eigenvalue problem for three qubit Groverian measure into linear eigenvalue equations. Some typical solutions of these linear equations are written explicitly and the features of the general solution are discussed in detail.

show abstract

Analytic expressions for geometric measure of three-qubit states

Cited by 37 publications

References 36 publications

Entanglement detection

Entanglement detection

Classification of Entanglement in Symmetric States

Reduced state uniquely defines the Groverian measure of the original pure state

Contact Info

Product

Resources

About