scholarly journals MULTIPARTITE ENTANGLEMENT UNDER STOCHASTIC LOCAL OPERATIONS AND CLASSICAL COMMUNICATION

2004 ◽  
Vol 02 (01) ◽  
pp. 65-77 ◽  
Author(s):  
AKIMASA MIYAKE
Keyword(s):  
Quantum System ◽  
Multipartite Entanglement ◽  
Mixed States ◽  
Classical Communication ◽  
Quantum Operations ◽  
Essential Properties ◽  
Pure States ◽  
Local Filtering

Stochastic local operations and classical communication (SLOCC), also called local filtering operations, are a convenient, useful set of quantum operations in grasping essential properties of entanglement. We give a quick overview of the characteristics of multipartite entanglement in terms of SLOCC, illustrating the 2-qubit and the rest (2×2×n) quantum system. This not only includes celebrated results of 3-qubit pure states, but also has implications to 2-qubit mixed 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 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 Relations between bipartite entanglement measures

2018 ◽  
Vol 18 (1&2) ◽  
pp. 85-113 ◽  
Author(s):  
Katharina Schwaiger ◽  
Barbara Kraus
Keyword(s):  
Pure State ◽  
Single Copy ◽  
Point Of View ◽  
Multipartite Entanglement ◽  
Bipartite Entanglement ◽  
Classical Communication ◽  
Main Emphasis ◽  
Entanglement Measures ◽  
Pure States

We investigate the entanglement of bipartite systems from an operational point of view. Main emphasis is put on bipartite pure states in the single copy regime. First, we present an operational characterization of bipartite pure state entanglement, viewing the state as a multipartite state. Then, we investigate the properties and relations of two classes of operational bipartite and multipartite entanglement measures, the so-called source and the accessible entanglement. The former measures how easy it is to generate a given state via local operations and classical communication (LOCC) from some other state, whereas the latter measures the potentiality of a state to be convertible to other states via LOCC. We investigate which parameter regime is physically available, i.e. for which values of these measures does there exist a bipartite pure state. Moreover, we determine, given some state, which parameter regime can be accessed by it and from which parameter regime it can be accessed. We show that this regime can be determined analytically using the Positivstellensatz. We compute the boundaries of these sets and the boundaries of the corresponding source and accessible sets. Furthermore, we relate these results to other entanglement measures and compare their behaviors.

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.

A numerically efficient approach to the modelling of double-Qdot channels

2013 ◽  
Vol 2 (1) ◽  
Author(s):  
A. Shamloo ◽  
A.P. Sowa
Keyword(s):  
Quantum Dots ◽  
Quantum Computing ◽  
Ab Initio ◽  
Quantum System ◽  
Electronic Properties ◽  
Density Of States ◽  
Potential Application ◽  
Ab Initio Simulation ◽  
Efficient Approach ◽  
Essential Properties

AbstractWe consider the electronic properties of a system consisting of two quantum dots in physical proximity, which we will refer to as the double-Qdot. Double-Qdots are attractive in light of their potential application to spin-based quantum computing and other electronic applications, e.g. as specialized sensors. Our main goal is to derive the essential properties of the double-Qdot from a model that is rigorous yet numerically tractable, and largely circumvents the complexities of an ab initio simulation. To this end we propose a novel Hamiltonian that captures the dynamics of a bi-partite quantum system, wherein the interaction is described via a Wiener-Hopf type operator. We subsequently describe the density of states function and derive the electronic properties of the underlying system. The analysis seems to capture a plethora of electronic profiles, and reveals the versatility of the proposed framework for double-Qdot channel modelling.

Distillation of multipartite entanglement by local filtering operations

2014 ◽  
Vol 89 (6) ◽  
Author(s):  
Yi-Sheng Huang ◽  
Hai-Bo Xing ◽  
Ming Yang ◽  
Qing Yang ◽  
Wei Song ◽  
...  
Keyword(s):  
Multipartite Entanglement ◽  
Local Filtering

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.

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.

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