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.

Generalized three-party sharing of operations on remote single qutrit

2014 ◽  
Vol 12 (03) ◽  
pp. 1450011 ◽  
Author(s):  
Pengfei Xing ◽  
Yimin Liu ◽  
Chuanmei Xie ◽  
Xiansong Liu ◽  
Zhanjun Zhang
Keyword(s):  
Success Probability ◽  
Entangled States ◽  
Entangled State ◽  
Quantum Channels ◽  
Channel State ◽  
Classical Communication ◽  
Maximally Entangled State ◽  
Quantum Operations ◽  
Local Operation ◽  
Maximally Entangled States

Two three-party schemes are put forward for sharing quantum operations on a remote qutrit with local operation and classical communication as well as shared entanglements. The first scheme uses a two-qutrit and three-qutrit non-maximally entangled states as quantum channels, while the second replaces the three-qutrit non-maximally entangled state with a two-qutrit. Both schemes are treated and compared from the four aspects of quantum and classical resource consumption, necessary-operation complexity, success probability and efficiency. It is found that the latter is overall more optimal than the former as far as a restricted set of operations is concerned. In addition, comparisons of both schemes with other four relevant ones are also made to show their two features, including degree generalization and channel-state generalization. Furthermore, some concrete discussions on both schemes are made to expose their important features of security, symmetry and experimental feasibility. Particularly, it is revealed that the success probabilities and intrinsic efficiencies in both schemes are completely determined by the shared entanglement.

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.

scholarly journals Small sets of locally indistinguishable orthogonal maximally entangled states

2014 ◽  
Vol 14 (13&14) ◽  
pp. 1098-1106
Author(s):  
Alessandro Cosentino ◽  
Vincent Russo
Keyword(s):  
Affirmative Answer ◽  
Semidefinite Program ◽  
Entangled States ◽  
Classical Communication ◽  
Fundamental Interest ◽  
Positive Partial Transpose ◽  
Partial Transpose ◽  
Maximally Entangled States ◽  
First Time

We study the problem of distinguishing quantum states using local operations and classical communication (LOCC). A question of fundamental interest is whether there exist sets of $k \leq d$ orthogonal maximally entangled states in $\complex^{d}\otimes\complex^{d}$ that are not perfectly distinguishable by LOCC. A recent result by Yu, Duan, and Ying [Phys. Rev. Lett. 109 020506 (2012)] gives an affirmative answer for the case $k = d$. We give, for the first time, a proof that such sets of states indeed exist even in the case $k < d$. Our result is constructive and holds for an even wider class of operations known as positive-partial-transpose measurements (PPT). The proof uses the characterization of the PPT-distinguishability problem as a semidefinite program.

scholarly journals Entanglement distillation by extendible maps

2013 ◽  
Vol 13 (9&10) ◽  
pp. 751-770
Author(s):  
Lukasz Pankowski ◽  
Fernando G.S.L. Brandao ◽  
Michal Horodecki ◽  
Graeme Smith
Keyword(s):  
The State ◽  
Entangled States ◽  
Classical Communication ◽  
Positive Partial Transpose ◽  
Epr Pairs ◽  
Numerical Studies ◽  
Partial Transpose ◽  
Maximally Entangled States ◽  
Werner States ◽  
Open Question

It is known that from entangled states that have positive partial transpose it is not possible to distill maximally entangled states by local operations and classical communication (LOCC). A long-standing open question is whether maximally entangled states can be distilled from every state with a non-positive partial transpose. In this paper we study a possible approach to the question consisting of enlarging the class of operations allowed. Namely, instead of LOCC operations we consider $k$-extendible operations, defined as maps whose Choi-Jamio\l{}kowski state is $k$-extendible. We find that this class is unexpectedly powerful - e.g. it is capable of distilling EPR pairs even from completely product states. We also perform numerical studies of distillation of Werner states by those maps, which show that if we raise the extension index $k$ simultaneously with the number of copies of the state, then the class of $k$-extendible operations are not that powerful anymore and provide a better approximation to the set of LOCC operations.

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.

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