scholarly journals ENTANGLEMENT MONOTONES AND MAXIMALLY ENTANGLED STATES IN MULTIPARTITE QUBIT SYSTEMS

2006 ◽  
Vol 04 (03) ◽  
pp. 531-540 ◽  
Author(s):  
ANDREAS OSTERLOH ◽  
JENS SIEWERT
Keyword(s):  
Entangled States ◽  
Expectation Values ◽  
Entanglement Measures ◽  
Pure States ◽  
Maximally Entangled States ◽  
Antilinear Operator

We present a method to construct entanglement measures for pure states of multipartite qubit systems. The key element of our approach is an antilinear operator that we call comb in reference to the hairy-ball theorem. For qubits (i.e. spin 1/2) the combs are automatically invariant under SL (2, ℂ). This implies that the filters obtained from the combs are entanglement monotones by construction. We give alternative formulae for the concurrence and the 3-tangle as expectation values of certain antilinear operators. As an application we discuss inequivalent types of genuine four-, five- and six-qubit entanglement.

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.

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.

Mixed maximally entangled states

2012 ◽  
Vol 12 (1&2) ◽  
pp. 63-73
Author(s):  
Z. G. Li ◽  
M. G. Zhao ◽  
S. M. Fei ◽  
H. Fan ◽  
W. M. Liu
Keyword(s):  
Entangled States ◽  
Classical Communication ◽  
Entanglement Of Formation ◽  
Entanglement Measures ◽  
Maximally Entangled States

We find that the mixed maximally entangled states exist and prove that the form of the mixed maximally entangled states is unique in terms of the entanglement of formation. Moreover, even if the entanglement is quantified by other entanglement measures, this conclusion is still proven right. This result is a supplementary to the generally accepted fact that all maximally entangled states are pure. These states possess important properties of the pure maximally entangled states, for example, these states can be used as a resource for faithful teleportation and they can be distinguished perfectly by local operations and classical communication.

scholarly journals ALTERNATIVE DECOMPOSITION OF TWO-QUTRIT PURE STATES AND ITS RELATION WITH ENTANGLEMENT INVARIANTS

2011 ◽  
Vol 09 (06) ◽  
pp. 1499-1509
Author(s):  
RUI-JUAN GU ◽  
FU-LIN ZHANG ◽  
SHAO-MING FEI ◽  
JING-LING CHEN
Keyword(s):  
Entangled States ◽  
Schmidt Decomposition ◽  
Unitary Transformations ◽  
Pure States ◽  
Maximally Entangled States

Based on maximally entangled states in the full- and sub-spaces of two-qutrits, we present an alternative decomposition of two-qutrit pure states in a form [Formula: see text]. Similar to the Schmidt decomposition, all two-qutrit pure states can be transformed into the alternative decomposition under local unitary transformations, and the parameter p1 is shown to be an entanglement invariant.

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

scholarly journals Construction of genuinely entangled subspacesand the associated bounds on entanglement measures for mixed states

2021 ◽  
Author(s):  
Konstantin Antipin
Keyword(s):  
Information Processing ◽  
Quantum Information ◽  
Lower Bounds ◽  
Quantum Information Processing ◽  
Multipartite Entanglement ◽  
Quantum Channels ◽  
Valuable Resource ◽  
Mixed States ◽  
Entanglement Measures ◽  
Pure States

Abstract Genuine entanglement is the strongest form of multipartite entanglement. Genuinely entangled pure states contain entanglement in every bipartition and as such can be regarded as a valuable resource in the protocols of quantum information processing. A recent direction of research is the construction of genuinely entangled subspaces — the class of subspaces consisting entirely of genuinely entangled pure states. In this paper we present methods of construction of such subspaces including those of maximal possible dimension. The approach is based on the composition of bipartite entangled subspaces and quantum channels of certain types. The examples include maximal subspaces for systems of three qubits, four qubits, three qutrits. We also provide lower bounds on two entanglement measures for mixed states, the concurrence and the convex-roof extended negativity, which are directly connected with the projection on genuinely entangled subspaces.

scholarly journals On-demand maximally entangled states with a parity meter and continuous feedback

2014 ◽  
Vol 90 (15) ◽  
Author(s):  
Clemens Meyer zu Rheda ◽  
Géraldine Haack ◽  
Alessandro Romito
Keyword(s):  
Entangled States ◽  
On Demand ◽  
Continuous Feedback ◽  
Maximally Entangled States

Most robust and fragile two-qubit entangled states under deploarizing channels

2013 ◽  
Vol 13 (7&8) ◽  
pp. 645-660
Author(s):  
Chao-Qian Pang ◽  
Fu-Lin Zhang ◽  
Yue Jiang ◽  
Mai-Lin Liang ◽  
Jing-Ling Chen
Keyword(s):  
Evolution Equation ◽  
Numerical Calculations ◽  
Entangled States ◽  
Fragile States ◽  
Qubit System ◽  
Uniform Channel ◽  
Pure States ◽  
The One ◽  
Major Factors ◽  
The Impact

For a two-qubit system under local depolarizing channels, the most robust and most fragile states are derived for a given concurrence or negativity. For the one-sided channel, the pure states are proved to be the most robust ones, with the aid of the evolution equation for entanglement given by Konrad \emph{et al.} [Nat. Phys. 4, 99 (2008)]. Based on a generalization of the evolution equation for entanglement, we classify the ansatz states in our investigation by the amount of robustness, and consequently derive the most fragile states. For the two-sided channel, the pure states are the most robust for a fixed concurrence. Under the uniform channel, the most fragile states have the minimal negativity when the concurrence is given in the region $[1/2,1]$. For a given negativity, the most robust states are the ones with the maximal concurrence, and the most fragile ones are the pure states with minimum of concurrence. When the entanglement approaches zero, the most fragile states under general nonuniform channels tend to the ones in the uniform channel. Influences on robustness by entanglement, degree of mixture, and asymmetry between the two qubits are discussed through numerical calculations. It turns out that the concurrence and negativity are major factors for the robustness. When they are fixed, the impact of the mixedness becomes obvious. In the nonuniform channels, the most fragile states are closely correlated with the asymmetry, while the most robust ones with the degree of mixture.

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