On the Stratifications of 2-Qubits X-State Space

EPJ Web of Conferences ◽

10.1051/epjconf/201817302011 ◽

2018 ◽

Vol 173 ◽

pp. 02011

Author(s):

Arsen Khvedelidze ◽

Astghik Torosyan

Keyword(s):

State Space ◽

Unitary Group ◽

X State ◽

Orbit Types

The 7-dimensional family ℬX of the so-called mixed X-states of 2-qubits is considered. Two versions of stratifications of ℬX , i.e., its decomposition into strata according to orbit types of the adjoint actions of two groups, are described. The first stratification is due to the action of global unitary group GX ⊂ S U(4), while the second one corresponds to the action of the local unitary group LGX ⊂ GX . The equations and in-equalities in the invariants of the corresponding groups, determining each stratification component, are given.

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UNITARIES IN A SIMPLE C*-ALGEBRA OF TRACIAL RANK ONE

International Journal of Mathematics ◽

10.1142/s0129167x10006446 ◽

2010 ◽

Vol 21 (10) ◽

pp. 1267-1281 ◽

Cited By ~ 3

Author(s):

HUAXIN LIN

Keyword(s):

State Space ◽

Unitary Group ◽

Affine Function ◽

Connected Component ◽

Finite Spectrum ◽

C Algebra ◽

Infinite Dimensional ◽

Tracial State ◽

Rank One ◽

Tracial Rank

Let A be a unital separable simple infinite dimensional C*-algebra with tracial rank not more than one and with the tracial state space T(A) and let U(A) be the unitary group of A. Suppose that u ∈ U0(A), the connected component of U(A) containing the identity. We show that, for any ϵ > 0, there exists a self-adjoint element h ∈ As.a such that [Formula: see text] We also study the problem when u can be approximated by unitaries in A with finite spectrum. Denote by CU(A) the closure of the subgroup of unitary group of U(A) generated by its commutators. It is known that CU(A) ⊂ U0(A). Denote by [Formula: see text] the affine function on T(A) defined by [Formula: see text]. We show that u can be approximated by unitaries in A with finite spectrum if and only if u ∈ CU(A) and [Formula: see text] for all n ≥ 1. Examples are given for which there are unitaries in CU(A) which cannot be approximated by unitaries with finite spectrum. Significantly these results are obtained in the absence of amenability.

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MAXIMIZING GENUINE MULTIPARTITE ENTANGLEMENT OF N MIXED QUBITS

International Journal of Quantum Information ◽

10.1142/s0219749913500433 ◽

2013 ◽

Vol 11 (04) ◽

pp. 1350043 ◽

Cited By ~ 6

Author(s):

SHANTANU AGARWAL ◽

SEYED MOHAMMAD HASHEMI RAFSANJANI

Keyword(s):

Hilbert Space ◽

Density Matrix ◽

State Space ◽

Maximum Amount ◽

Multipartite Entanglement ◽

Qubit System ◽

Analytic Expressions ◽

X State ◽

Two Parameters ◽

Genuine Multipartite Entanglement

Beyond the simplest case of bipartite qubits, the composite Hilbert space of multipartite systems is largely unexplored. In order to explore such systems, it is important to derive analytic expressions for parameters which characterize the system's state space. Two such parameters are the degree of genuine multipartite entanglement and the degree of mixedness of the system's state. We explore these two parameters for an N-qubit system whose density matrix has an X form. We derive the class of states that has the maximum amount of genuine multipartite entanglement for a given amount of mixedness. We compare our results with the existing results for the N = 2 case. The critical amount of mixedness above which no N-qubit X-state possesses genuine multipartite entanglement is derived. It is found that as N increases, states with higher mixedness can still be entangled.

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