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Marcus Huber - One of the best experts on this subject based on the ideXlab platform.
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Genuine-Multipartite entanglement criteria based on positive maps
Journal of Mathematical Physics, 2017Co-Authors: Fabien Clivaz, Marcus Huber, Ludovico Lami, Gláucia MurtaAbstract:Positive maps applied to a subsystem of a bipartite quantum state constitute a central tool in characterising entanglement. In the Multipartite case, however, the direct application of a positive but not completely positive map cannot distinguish if a state is genuinely Multipartite entangled or just entangled across some bipartition. We thus generalise this bipartite concept to the Multipartite setting by introducing non-positive maps that are positive on the subset of biseparable states but can map to a non-positive element if applied to a genuine Multipartite entangled state. We explicitly construct examples of Multipartite non-positive maps, obtained from positive maps via a lifting procedure, that in this fashion can reveal genuine Multipartite entanglement in a robust way.
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witnessing genuine Multipartite entanglement with positive maps
Physical Review Letters, 2014Co-Authors: Marcus Huber, Ritabrata SenguptaAbstract:We derive a general framework that lifts any set of bipartite to Multipartite entanglement witnesses and we show how positive maps can naturally be incorporated into this framework. We show that some previous approaches for Multipartite entanglement detection are intimately connected to the witnesses derived from partial transposition and that such criteria can easily be outperformed in higher dimensions by nondecomposable maps. As an exemplary case we present a witness that is capable of detecting genuine Multipartite entanglement in bound entangled states.
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Examining the dimensionality of genuine Multipartite entanglement
Quantum Information Processing, 2012Co-Authors: Christoph Spengler, Marcus Huber, Andreas Gabriel, Beatrix C. HiesmayrAbstract:Entanglement in high-dimensional many-body systems plays an increasingly vital role in the foundations and applications of quantum physics. In the present paper, we introduce a theoretical concept which allows to categorize Multipartite states by the number of degrees of freedom being entangled. In this regard, we derive computable and experimentally friendly criteria for arbitrary Multipartite qudit systems that enable to examine in how many degrees of freedom a mixed state is genuine Multipartite entangled.
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Purification of genuine Multipartite entanglement
Physical Review A, 2011Co-Authors: Marcus Huber, Martin PleschAbstract:In tasks where Multipartite entanglement plays a central role, state purification is, due to inevitable noise, a crucial part of the procedure. We consider a scenario exploiting the Multipartite entanglement in a straightforward Multipartite purification algorithm and compare it to bipartite purification procedures combined with state teleportation. While complete purification requires an infinite amount of input states in both cases, we show that for an imperfect output fidelity the Multipartite procedure exhibits a major advantage in terms of input states used.
Antonio Acín - One of the best experts on this subject based on the ideXlab platform.
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A versatile construction of Bell inequalities for the Multipartite scenario
New Journal of Physics, 2019Co-Authors: Florian J. Curchod, Mafalda L. Almeida, Antonio AcínAbstract:Local measurements acting on entangled quantum states give rise to a rich correlation structure in the Multipartite scenario. We introduce a versatile technique to build families of Bell inequalities witnessing different notions of Multipartite nonlocality for any number of parties. The idea behind our method is simple: a known Bell inequality satisfying certain constraints, for example the Clauser-Horne-Shimony-Holt inequality, serves as the $seed$ to build new families of inequalities for more parties. The constructed inequalities have a clear operational meaning, capturing an essential feature of Multipartite correlations: their violation implies that numerous subgroups of parties violate the inequality chosen as seed. The more Multipartite nonlocal the correlations, the more subgroups can violate the seed. We illustrate our construction using different seeds and designing Bell inequalities to detect $m$-way nonlocal Multipartite correlations, in particular, $genuine$ $Multipartite$ $nonlocal$ correlations -- the strongest notion of Multipartite nonlocality. For one of our inequalities we prove analytically that a large class of pure states that are genuine Multipartite entangled exhibit genuine Multipartite nonlocality for any number of parties, even for some states that are almost product. We also provide numerical evidence that this family is violated by all genuine Multipartite entangled pure states of three and four qubits. Our results make us conjecture that this family of Bell inequalities can be used to prove the equivalence between genuine Multipartite pure-state entanglement and nonlocality for any number of parties.
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Fully nonlocal, monogamous, and random genuinely Multipartite quantum correlations.
Physical review letters, 2012Co-Authors: Leandro Aolita, Rodrigo Gallego, Adán Cabello, Antonio AcínAbstract:Local measurements on bipartite maximally entangled states can yield correlations that are maximally nonlocal, monogamous, and with fully random outcomes. This makes these states ideal for bipartite cryptographic tasks. Genuine-Multipartite nonlocality constitutes a stronger notion of nonlocality in the Multipartite case. Maximal genuine-Multipartite nonlocality, monogamy, and random outcomes are thus highly desired properties for genuine-Multipartite cryptographic scenarios. We prove that local measurements on any Greenberger-Horne-Zeilinger state can produce correlations that are fully genuine-Multipartite nonlocal, monogamous, and with fully random outcomes. A key ingredient in our proof is a Multipartite chained Bell inequality detecting genuine-Multipartite nonlocality, which we introduce. Finally, we discuss applications to device-independent secret sharing.
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Multipartite fully nonlocal quantum states
Physical Review A, 2010Co-Authors: Mafalda L. Almeida, Daniel Cavalcanti, Valerio Scarani, Antonio AcínAbstract:We present a general method for characterizing the quantum correlations obtained after local measurements on Multipartite systems. Sufficient conditions for a quantum system to be fully nonlocal according to a given partition, as well as being (genuinely) Multipartite fully nonlocal, are derived. These conditions allow us to identify all completely connected graph states as Multipartite fully nonlocal quantum states. Moreover, we show that this feature can also be observed in mixed states: the tensor product of five copies of the Smolin state, a biseparable and bound entangled state, is Multipartite fully nonlocal.
Anders Yeo - One of the best experts on this subject based on the ideXlab platform.
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Classes of Directed Graphs - Semicomplete Multipartite Digraphs
Springer Monographs in Mathematics, 2018Co-Authors: Anders YeoAbstract:In this chapter we will consider the class of semicomplete Multipartite digraphs (SMD). A digraph is semicomplete Multipartite if it is obtained from a complete Multipartite graph by replacing every edge by an arc or a pair of opposite arcs. In other words, the vertex set of a semicomplete Multipartite digraph can be partitioned into sets such that vertices within the same set are nonadjacent and vertices between different sets are adjacent. This chapter gives a comprehensive survey on this class of digraphs.
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Kings in semicomplete Multipartite digraphs
Journal of Graph Theory, 2000Co-Authors: Gregory Gutin, Anders YeoAbstract:A digraph obtained by replacing each edge of a complete p-partite graph by an arc or a pair of mutually opposite arcs with the same end vertices is called a semicomplete p-partite digraph, or just a semicomplete Multipartite digraph. A semicomplete Multipartite digraph with no cycle of length two is a Multipartite tournament. In a digraph D, an r-king is a vertex q such that every vertex in D can be reached from q by a path of length at most r. Strengthening a theorem by K. M. Koh and B. P. Tan (Discr Math 147 (1995), 171–183) on the number of 4-kings in Multipartite tournaments, we characterize semicomplete Multipartite digraphs, which have exactly k 4-kings for every k = 1, 2, 3, 4, 5. © 2000 John Wiley & Sons, Inc. J Graph Theory 33: 177-183, 2000
Shao-ming Fei - One of the best experts on this subject based on the ideXlab platform.
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Detection of Genuine Multipartite Entanglement in Multipartite Systems
arXiv: Quantum Physics, 2019Co-Authors: Jing Yun Zhao, Hui Zhao, Naihuan Jing, Shao-ming FeiAbstract:We investigate genuine Multipartite entanglement in general Multipartite systems. Based on the norms of the correlation tensors of a Multipartite state under various partitions, we present an analytical sufficient criterion for detecting the genuine four-partite entanglement. The results are generalized to arbitrary Multipartite systems.
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Bounds on Multipartite concurrence and tangle
Quantum Information Processing, 2016Co-Authors: Jing Wang, Shao-ming Fei, Hongfang Li, Ming Li, Xianqing Li-jostAbstract:We present an analytical lower bound of Multipartite concurrence based on the generalized Bloch representations of density matrices. It is shown that the lower bound can be used as an effective entanglement witness of genuine Multipartite entanglement. Tight lower and upper bounds for Multipartite tangles are also derived. Since the lower bounds depend on just part of the correlation tensors, the result is experimentally feasible.
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Genuine Multipartite entanglement detection and lower bound of Multipartite concurrence
Physical Review A, 2015Co-Authors: Shao-ming Fei, Xianqing Li-jost, Heng FanAbstract:The problems of genuine Multipartite entanglement detection and classification are challenging. We show that a Multipartite quantum state is genuine Multipartite entangled if the Multipartite concurrence is larger than certain quantities given by the number and the dimension of the subsystems. This result also provides a classification of various genuine Multipartite entanglements. We present a lower bound of the Multipartite concurrence in terms of bipartite concurrences. While various operational approaches are available for providing lower bounds of bipartite concurrences, our results give an effective operational way to detect and classify genuine Multipartite entanglement. As applications, genuine Multipartite entanglement of tripartite systems is analyzed in detail.
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Genuine Multipartite entanglement of superpositions
Physical Review A, 2014Co-Authors: Zhi-hua Chen, Shao-ming FeiAbstract:We investigate how the genuine Multipartite entanglement is distributed among the components of superposed states. Analytical lower and upper bounds for the usual Multipartite negativity and the genuine Multipartite entanglement negativity are derived. These bounds are shown to be tight by detailed examples.
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Local Unitary Invariants for Multipartite States
International Journal of Theoretical Physics, 2013Co-Authors: Ting-gui Zhang, Xianqing Li-jost, Ming-jing Zhao, Shao-ming FeiAbstract:We study the invariants of arbitrary dimensional Multipartite quantum states under local unitary transformations. For Multipartite pure states, we give a set of invariants in terms of singular values of coefficient matrices. For Multipartite mixed states, we propose a set of invariants in terms of the trace of coefficient matrices. For full rank mixed states with non-degenerate eigenvalues, this set of invariants is also the set of the necessary and sufficient conditions for the local unitary equivalence of such two states.
Chiara Macchiavello - One of the best experts on this subject based on the ideXlab platform.
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Multipartite entanglement detection for hypergraph states
Journal of Physics A: Mathematical and Theoretical, 2017Co-Authors: Maddalena Ghio, Dagmar Bruß, Daniele Malpetti, Matteo A. C. Rossi, Chiara MacchiavelloAbstract:We study the entanglement properties of quantum hypergraph states of n qubits, focusing on Multipartite entanglement. We compute Multipartite entanglement for hypergraph states with a single hyperedge of maximum cardinality, for hypergraph states endowed with all possible hyperedges of cardinality equal to and for those hypergraph states with all possible hyperedges of cardinality greater than or equal to . We then find a lower bound to the Multipartite entanglement of a generic quantum hypergraph state. We finally apply the Multipartite entanglement results to the construction of entanglement witness operators, able to detect genuine Multipartite entanglement in the neighbourhood of a given hypergraph state. We first build entanglement witnesses of the projective type, then propose a class of witnesses based on the stabilizer formalism, hence called stabilizer witnesses, able to reduce the experimental effort from an exponential to a linear growth in the number of local measurement settings with the number of qubits.
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Multipartite entanglement in quantum algorithms
Physical Review A, 2011Co-Authors: Dagmar Bruß, Chiara MacchiavelloAbstract:We investigate the entanglement features of the quantum states employed in quantum algorithms. In particular, we analyze the Multipartite entanglement properties in the Deutsch-Jozsa, Grover, and Simon algorithms. Our results show that for these algorithms most instances involve Multipartite entanglement.
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Multipartite entanglement in quantum spin chains
Physical Review A, 2005Co-Authors: Dagmar Bruß, Nilanjana Datta, Artur Ekert, Leong Chuan Kwek, Chiara MacchiavelloAbstract:We study the occurrence of Multipartite entanglement in spin chains. We show that certain genuine Multipartite entangled states, namely W states, can be obtained as ground states of simple XX type ferromagnetic spin chains in a transverse magnetic field, for any number of sites. Moreover, Multipartite entanglement is proven to exist even at finite temperatures. A transition from a product state to a Multipartite entangled state occurs when decreasing the magnetic field to a critical value. Adiabatic passage through this point can thus lead to the generation of Multipartite entanglement.
