A New Multipartite Entanglement Measure for Arbitrary n-qudit Pure States

2015 ◽  
Vol 55 (3) ◽  
pp. 1668-1678 ◽  
Author(s):  
Chao Zhao ◽  
Guo-wu Yang ◽  
Xiao-yu Li
Keyword(s):  
Multipartite Entanglement ◽  
Entanglement Measure ◽  
Pure States

scholarly journals BUILDING AN ENTANGLEMENT MEASURE ON PHYSICAL GROUND

2012 ◽  
Vol 09 (02) ◽  
pp. 1260023
Author(s):  
D. TERESI ◽  
A. NAPOLI ◽  
A. MESSINA
Keyword(s):  
Multipartite Entanglement ◽  
Entanglement Measure ◽  
Physical Ground ◽  
Pure States

We introduce on physical grounds a new measure of multipartite entanglement for pure states. The function we define is discriminant and monotone under LOCC; moreover, it can be expressed in terms of observables of the system.

scholarly journals Local transformations of multiple multipartite states

2021 ◽  
Vol 11 (2) ◽  
Author(s):  
Antoine Neven ◽  
David Kenworthy Gunn ◽  
Martin Hebenstreit ◽  
Barbara Kraus
Keyword(s):  
Single Copy ◽  
Partial Ordering ◽  
Multipartite Entanglement ◽  
Entanglement Measure ◽  
Classical Communication ◽  
Wide Range ◽  
Pure States ◽  
Multipartite States ◽  
The Individual ◽  
Probabilistic Protocols

Understanding multipartite entanglement is vital, as it underpins a wide range of phenomena across physics. The study of transformations of states via Local Operations assisted by Classical Communication (LOCC) allows one to quantitatively analyse entanglement, as it induces a partial order in the Hilbert space. However, it has been shown that, for systems with fixed local dimensions, this order is generically trivial, which prevents relating multipartite states to each other with respect to any entanglement measure. In order to obtain a non-trivial partial ordering, we study a physically motivated extension of LOCC: multi-state LOCC. Here, one considers simultaneous LOCC transformations acting on a finite number of entangled pure states. We study both multipartite and bipartite multi-state transformations. In the multipartite case, we demonstrate that one can change the stochastic LOCC (SLOCC) class of the individual initial states by only applying Local Unitaries (LUs). We show that, by transferring entanglement from one state to the other, one can perform state conversions not possible in the single copy case; provide examples of multipartite entanglement catalysis; and demonstrate improved probabilistic protocols. In the bipartite case, we identify numerous non-trivial LU transformations and show that the source entanglement is not additive. These results demonstrate that multi-state LOCC has a much richer landscape than single-state LOCC.

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 CHARACTERIZING AND MEASURING MULTIPARTITE ENTANGLEMENT

2007 ◽  
Vol 05 (01n02) ◽  
pp. 97-103 ◽  
Author(s):  
P. FACCHI ◽  
G. FLORIO ◽  
S. PASCAZIO
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Multipartite Entanglement ◽  
Bipartite Entanglement ◽  
Pure States

A method is proposed to characterize and quantify multipartite entanglement in terms of the probability density function of bipartite entanglement over all possible balanced bipartitions of an ensemble of qubits. The method is tested on a class of random pure states.

scholarly journals CLASSIFICATION AND QUANTIFICATION OF ENTANGLED BIPARTITE QUTRIT PURE STATES

2006 ◽  
Vol 20 (11n13) ◽  
pp. 1333-1342 ◽  
Author(s):  
FENG PAN ◽  
GUOYING LU ◽  
J. P. DRAAYER
Keyword(s):  
Pure State ◽  
Complete Analysis ◽  
Entanglement Measure ◽  
Pure States

A complete analysis of entangled bipartite qutrit pure states is carried out based on a simple entanglement measure. An analysis of all possible extremally entangled pure bipartite qutrit states is shown to reduce, with the help of SLOCC transformations, to three distinct types. The analysis and the results should be helpful for finding different entanglement types in multipartite pure state systems.

scholarly journals MIXING AND DECOHERENCE TO NEAREST SEPARABLE STATES

2009 ◽  
Vol 07 (04) ◽  
pp. 829-846
Author(s):  
AVIJIT LAHIRI ◽  
GAUTAM GHOSH ◽  
SANKHASUBHRA NAG
Keyword(s):  
Quantum Correlation ◽  
Entangled States ◽  
Entanglement Measure ◽  
Measuring Apparatus ◽  
Separable State ◽  
Mixed States ◽  
Classical Correlation ◽  
Separable States ◽  
System A ◽  
Pure States

We consider a class of entangled states of a quantum system (S) and a second system (A) where pure states of the former are correlated with mixed states of the latter, and work out the entanglement measure with reference to the nearest separable state. Such "pure-mixed" entanglement is expected when the system S interacts with a macroscopic measuring apparatus in a quantum measurement, where the quantum correlation is destroyed in the process of environment-induced decoherence whereafter only the classical correlation between S and A remains, the latter being large compared to the former. We present numerical evidence that the entangled S–A state drifts towards the nearest separable state through decoherence, with an additional tendency of equimixing among relevant groups of apparatus states.

scholarly journals Simple Entanglement Measure for Multipartite Pure States

2004 ◽  
Vol 43 (5) ◽  
pp. 1241-1247 ◽  
Author(s):  
Feng Pan ◽  
Dan Liu ◽  
Guoying Lu ◽  
J. P. Draayer
Keyword(s):  
Entanglement Measure ◽  
Pure States

scholarly journals Multipartite entanglement measure for all discrete systems

2008 ◽  
Vol 78 (1) ◽  
Author(s):  
Beatrix C. Hiesmayr ◽  
Marcus Huber
Keyword(s):  
Discrete Systems ◽  
Multipartite Entanglement ◽  
Entanglement Measure
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