Entanglement swapping of noisy states: A kind of superadditivity in nonclassicality

Sen, Aditi; Sen, Ujjwal; Brukner, Časlav; Bužek, Vladimír; Żukowski, Marek

doi:10.1103/physreva.72.042310

Cited by 64 publications

(55 citation statements)

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“…Celebrated examples of activation were demonstrated in entanglement theory [9] and quantum channel theory [10]. In the case of nonlocality, some forms of activation in specific contexts were demonstrated, for instance, when postselection is considered [11][12][13][14], when several copies of the quantum state are distributed in a quantum network [15][16][17][18], when the number of measurements considered are restricted [19], when taking the amount of violation of a Bell inequality as a figure of merit [20], or in the case of general nonsignaling probability distributions [21]. However, the first example of superactivation of quantum nonlocality in the most natural scenario consisting of two parties who do not perform any local preprocessing of their quantum state is due to Palazuelos [22].…”

Section: Introductionmentioning

confidence: 99%

All quantum states useful for teleportation are nonlocal resources

et al. 2013

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Understanding the relation between the different forms of inseparability in quantum mechanics is a longstanding problem in the foundations of quantum theory and has implications for quantum information processing. Here we make progress in this direction by establishing a direct link between quantum teleportation and Bell nonlocality. In particular, we show that all entangled states which are useful for teleportation are nonlocal resources, i.e., lead to deterministic violation of Bell's inequality. Our result also extends the phenomenon of superactivation of quantum nonlocality, recently proven by C. Palazuelos [Phys. Rev. Lett. 109, 190401 (2012)], and suggests that the latter might in fact be more general than initially thought.

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Section: Introductionmentioning

confidence: 99%

All quantum states useful for teleportation are nonlocal resources

et al. 2013

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“…which is the bound in (9). A third remark: With minor modification following [21], we can involve non-full correlation terms in our inequalities.…”

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confidence: 94%

Bell-type inequalities for arbitrary noncyclic networks

Tavakoli

2016

Phys. Rev. A

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Bell inequalities bound the strength of classical correlations between observers measuring on a shared physical system. However, studies of physical correlations can be considered beyond the standard Bell scenario by networks of observers sharing some configuration of many independent physical systems. Here, we show how to construct Bell-type inequalities for correlations arising in any tree-structured network i.e. networks without cycles. This is achieved by an iteration procedure that in each step allows one to add a branch to the tree-structured network and construct a corresponding Bell-type inequality. We explore our inequalities in several examples, in all of which we demonstrate strong violations from quantum theory.Introduction.-The milstone work of John Bell showed that quantum correlations arising between spatially separated observers can break the limitations of classical physics [1]. Studies of correlations predicted by quantum theory has been a key to understanding fundamental properties of the theory and has led to applications in information processing including random number generation [2], device-independent cryptography [3] and reduction of communication complexity [4].A Bell experiment considers a source emitting a physical system shared between a set of observers who can randomly chose to apply some local measurements. The standard two-particle Bell experiment is illustrated in Figure 1 a). The properties of the correlations arising between the outcomes of the observers in Bell experiments have been thoroughly studied [5] and may be considered fairly well understood. However, much less is known about the nature of correlations arising in more sophisticated network configurations beyond the Bell experiments. A network could in general involve many independent sources each emitting a physical system that is shared between some set of observers. Importantly, a single observer could be receiving subsystems of many independent physical systems originating from different sources.There are both conceptual and applied motivations for studying classical and quantum correlations in networks. Networks naturally generalize Bell experiments which makes them conceptually attractive. Also, the notion of classical correlations on a network leads to stronger constraints than those associated to standard Bell inequalities. However, these constraints also influence the strength of quantum correlations, which makes it interesting to study their comparative strength as opposed to standard Bell inequalities. Furthermore, networks are relevant in a variety of applications involving entanglement swapping experiments [6], entanglement percolation [7] and quantum repeaters protocols [8,9]. Quantum correlations in networks are interesting for the practical implementation of large scale quantum communication networks which is arguably one of the main goals of applied quantum information.

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“…This effect does not occur for all mixed states. For example it was shown that if one performs entanglement swapping with mixtures of two Bell states or Werner states, then the final state has always the singlet fraction less than the initial states [13,14]. We will also consider maximization of the fidelity of quantum teleportation.…”

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confidence: 99%

Increasing singlet fraction with entanglement swapping

Modławska

Grudka

2008

Phys. Rev. A

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We consider entanglement swapping for certain mixed states. We assume that the initial states have the same singlet fraction and show that the final state can have singlet fraction greater than the initial states. We also consider two quantum teleportations and show that entanglement swapping can increase teleportation fidelity. Finally, we show how this effect can be demonstrated with linear optics.PACS numbers: 03.67. Lx, 42.50.Dv Maximally entangled states are crucial for quantum information processing. If two parties share a pair of qubits in the maximally entangled state then they can perform quantum teleportation. However, usually the parties share nonmaximally entangled state ̺. One can define the singlet fraction F of the state ̺ as the maximal overlap of the state ̺ with the maximally entangled state, i.e.,where the maximum is taken over all maximally entangled states |Ψ . If one performs quantum teleportation with the state ̺ preprocessed by local unitary operations [1] then the optimal teleportation fidelity isIf F > 1 2 then the parties can perform quantum teleportation with the average fidelity of the teleported qubit exceeding classical limit 2 3 . However, it is well known that there are two-qubit entangled states which have F < 1 2 . The Horodecki family has proved that one can increase the singlet fraction of any two-qubit entangled state above 1 2 by non-trace preserving local operations and classical communication (LOCC) [2]. Verstraete and Verschelde have proved that one can do it even with trace preserving LOCC [3]. Moreover, they have found how to obtain optimal teleportation with any two-qubit state, i.e., how to find an LOCC protocol which gives the highest average fidelity of the teleported qubit. Let us now consider a string of nodes connected by nonmaximally entangled pairs of qubits. The first set of entangled pairs is distributed between nodes A and B, the second one is distributed between B and C and so on. In order to perform quantum teleportation from the first to the last node one first distills entanglement between A and B, then between B and C and so on [4]. Next, one performs entanglement swapping [5,6] at each node which creates entanglement between the first and the last node. Notice that usually many entangled pairs are needed between two nodes in order to distill entanglement. Finally, one performs quantum teleportation between the first and the last node. This strategy is crucial ingredient of quantum repeaters [7]. However, for pure nonmaximally entangled states there exists another strategy. Instead of distilling maximally entangled state between each pair of neighboring nodes and then performing entanglement swapping one first performs entanglement swapping and then distills entanglement between the first and the last node [8,9,10,11,12]. If each pair of neighboring nodes is connected by a single nonmaximally entangled pure state this strategy gives higher probability of obtaining maximally entangled state between the first and the last node.In this paper we conside...

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Entanglement swapping of noisy states: A kind of superadditivity in nonclassicality

Cited by 64 publications

References 48 publications

All quantum states useful for teleportation are nonlocal resources

All quantum states useful for teleportation are nonlocal resources

Bell-type inequalities for arbitrary noncyclic networks

Increasing singlet fraction with entanglement swapping

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