Scalability of Greenberger-Horne-Zeilinger and random-state entanglement in the presence of decoherence

Aolita, Leandro; Cavalcanti, Daniel; Acín, Antonio; Salles, A.; Tiersch, Markus; Buchleitner, Andreas; Melo, Fernando de

doi:10.1103/physreva.79.032322

Cited by 38 publications

(48 citation statements)

References 48 publications

(62 reference statements)

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“…As mentioned in the main part of the paper, a previously studied set of states with an X shaped density matrix is the generalized GHZ-diagonal states [15]. In this Appendix I prove that generalized GHZ-diagonal states do not include all possible X-states by constructing an explicit state with an X-shaped density matrix that is not part of the aforementioned set.…”

Section: Discussionmentioning

confidence: 93%

“…This demonstrates that the entanglement of an X-state is either tri-partite or biseparable but not completely separable. Before calculating any specific entanglement metric and studying its decay in a given decohering environment, we note that an upper bound on the entanglement decay was derived in [15] for a number of different decohering environments. Though these bounds were calculated for the more limited generalized GHZ-diagonal states they appear to be appropriate to the states studied in this work.…”

Section: X-state Entanglementmentioning

confidence: 99%

“…In this paper, I explore the entanglement dynamics of three qubit X-states in dephasing and depolarizing environments as a function of decoherence strength. Previous studies of three qubit Xshaped states utilize more restrictive sets of states: GHZdiagonal states [14] and generalized GHZ-diagonal states [15]. Other papers have examined specific examples of three qubit X-state entanglement including the effects of dephasing on a three-qubit quantum error correction protocol [16].…”

Section: Introductionmentioning

confidence: 99%

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Entanglement dynamics in three-qubitXstates

Weinstein

2010

Phys. Rev. A

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I explore the entanglement dynamics of a three qubit system in an initial X-state undergoing decoherence including the possible exhibition of entanglement sudden death (ESD). To quantify entanglement I utilize negativity measures and make use of appropriate entanglement witnesses. The negativity results are then extended to X-states with an arbitraty number of qubits. I also demonstrate non-standard behavior of the tri-partite negativity entanglement metric, its sudden appearance after some amount of decoherence followed quickly by its disappearance. Finally, I solve for a lower bound on the three qubit X-state concurrence, demonstrate when this bound goes to zero, and outline simplifcations for the calculation of higher order X-state concurrences.

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Section: Discussionmentioning

confidence: 93%

Section: X-state Entanglementmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Entanglement dynamics in three-qubitXstates

Weinstein

2010

Phys. Rev. A

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“…It is thus important to make both classifications of entangled states: into admitting and not admitting local realistic models, and into violating and not violating a given Bell inequality. Entanglement and Bell violation of different noisy states has already been studied by several authors [20][21][22][23][24]. All this indicates that entanglement and impossibility of a local hidden variable model are not only different concepts, but also truly different resources [25].…”

Section: Introductionmentioning

confidence: 99%

Entanglement and communication-reducing properties of noisyN-qubit states

et al. 2010

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We consider properties of states of many qubits, which arise after sending certain entangled states via various noisy channels (white noise, coloured noise, local depolarization, dephasing and amplitude damping). Entanglement of these states is studied and their ability to violate certain classes of Bell inequalities. States which violate them allow for higher than classical efficiency of solving related distributed computational tasks with constrained communication. This is a direct property of such states -not requiring their further modification via stochastic local operations and classical communication such as entanglement purification or distillation procedures. We identify novel families of multi-particle states which are entangled but nevertheless allow local realistic description of specific Bell experiments. For some of them, the "gap" between the critical values for entanglement and violation of Bell inequality remains finite even in the limit of infinitely many qubits.

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“…Finite-time disentanglement, sometimes referred to as "entanglement sudden death" [116,149], has been experimentally demonstrated [158,159,161,162]. Moreover, the entanglement of important classes of multipartite states exhibit, for a fixed time, an exponential decay with the number of parties [107,143,167], which contributes to the concerns regarding the viability of large-scale quantum information processing. For the case of collective decoherence, however, it is possible to construct decoherence-free subspaces of entangled states immune to the noise [168,169].…”

mentioning

confidence: 99%

Open-system dynamics of entanglement:a key issues review

2015

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One of the greatest challenges in the fields of quantum information processing and quantum technologies is the detailed coherent control over each and every constituent of quantum systems with an ever increasing number of particles. Within this endeavor, harnessing of many-body entanglement against the detrimental effects of the environment is a major pressing issue. Besides being an important concept from a fundamental standpoint, entanglement has been recognized as a crucial resource for quantum speed-ups or performance enhancements over classical methods. Understanding and controlling many-body entanglement in open systems may have strong implications in quantum computing, quantum simulations of many-body systems, secure quantum communication or cryptography, quantum metrology, our understanding of the quantum-to-classical transition, and other important questions of quantum foundations.In this paper we present an overview of recent theoretical and experimental efforts to underpin the dynamics of entanglement under the influence of noise. Entanglement is thus taken as a dynamic quantity on its own, and we survey how it evolves due to the unavoidable interaction of the entangled system with its surroundings. We analyze several scenarios, corresponding to different families of states and environments, which render a very rich diversity of dynamical behaviors.In contrast to single-particle quantities, like populations and coherences, which typically vanish only asymptotically in time, entanglement may disappear at a finite time. In addition, important classes of entanglement display an exponential decay with the number of particles when subject to local noise, which poses yet another threat to the already-challenging scaling of quantum technologies. Other classes, however, turn out to be extremely robust against local noise. Theoretical results and recent experiments regarding the difference between local and global decoherence are summarized. Control and robustness-enhancement techniques, scaling laws, statistical and geometrical aspects of multipartite-entanglement decay are also reviewed; all in order to give a broad picture of entanglement dynamics in open quantum systems addressed to both theorists and experimentalists inside and outside the field of quantum information.

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Scalability of Greenberger-Horne-Zeilinger and random-state entanglement in the presence of decoherence

Cited by 38 publications

References 48 publications

Entanglement dynamics in three-qubitXstates

Entanglement dynamics in three-qubitXstates

Entanglement and communication-reducing properties of noisyN-qubit states

Open-system dynamics of entanglement:a key issues review

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