Bound Nonlocality and Activation

Brunner, Nicolás; Cavalcanti, Daniel; Salles, A.; Skrzypczyk, Paul

doi:10.1103/physrevlett.106.020402

Cited by 50 publications

(48 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…These results demonstrate the activation of quantum nonlocality, which was also discussed in the multipartite case [15,16]. Other works showed the activation of general nonlocal non-signaling correlations via local wirings, a process termed nonlocality distillation [17][18][19].…”

Section: Introductionsupporting

confidence: 74%

Superactivation of quantum steering

2016

Self Cite

View full text Add to dashboard Cite

We consider Einstein-Podolsky-Rosen steering in the regime where the parties can perform collective measurements on many copies of a given shared entangled state. We derive a simple and efficient condition for guaranteeing that an entangled state is k-copy steerable. In particular we show that any two-qubit and qubit-qutrit entangled states is k-copy steerable. This allows us to discuss the effect of super-activation of steering, whereby an entangled state that is unsteerable (i.e., admits a local hidden state model) in the one-copy regime becomes k-copy steerable. We provide examples with few copies and low dimensions. Our results give evidence that entanglement and steering could become equivalent in the multi-copy regime.

show abstract

Section: Introductionsupporting

confidence: 74%

Superactivation of quantum steering

2016

Self Cite

View full text Add to dashboard Cite

show abstract

“…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

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…In this sense it may be considered similar to entanglement distillation. We have gained some understanding of when nonlocality can be distilled [17,18,20,9,2,1,23,19], when it cannot [33] and when it appears in bound form [8]. In general, the results suggest that distillation is only possible under special favorable circumstances and that large classes of nonlocal boxes are not distillable.…”

Section: Nonlocality Distillationmentioning

confidence: 99%

Quantum Nonlocal Boxes Exhibit Stronger Distillability

Hoyer

Rashid

2013

Mod. Phys. Lett. A

View full text Add to dashboard Cite

The hypothetical nonlocal box (NLB) proposed by Popescu and Rohrlich allows two spatially separated parties, Alice and Bob, to exhibit stronger than quantum correlations. If the generated correlations are weak, they can sometimes be distilled into a stronger correlation by repeated applications of the NLB. Motivated by the limited distillability of NLBs, we initiate here a study of the distillation of correlations for nonlocal boxes that output quantum states rather than classical bits (qNLBs). We propose a new protocol for distillation and show that it asymptotically distills a class of correlated quantum nonlocal boxes to the value 1 2 (3 √ 3 + 1) ≈ 3.098076, whereas in contrast, the optimal non-adaptive parity protocol for classical nonlocal boxes asymptotically distills only to the value 3.0. We show that our protocol is an optimal non-adaptive protocol for 1, 2 and 3 qNLB copies by constructing a matching dual solution for the associated primal semidefinite program (SDP). We conclude that qNLBs are a stronger resource for nonlocality than NLBs. The main premise that develops from this conclusion is that the NLB model is not the strongest resource to investigate the fundamental principles that limit quantum nonlocality. As such, our work provides strong motivation to reconsider the status quo of the principles that are known to limit nonlocal correlations under the framework of qNLBs rather than NLBs. Nonlocality distillationConsider two parties, Alice and Bob, spatially separated and isolated, interested in jointly computing some boolean function f (·, ·). A third party, David, provides Alice with an input x (unbeknown to Bob) and Bob with an input y (unbeknown to Alice) and challenges them to compute the bit f (x, y). David allows Alice and Bob to communicate, but charges for each and every bit communicated between them. Alice and Bob therefore pre-agree upon a protocol that minimizes the amount of communication required for them to compute the bit f (x, y). This is what we know as communication complexity [25].It seems entirely impossible to jointly compute a non-trivial function if no information can be interchanged between Alice and Bob, and it is indeed one of the first results typically shown in any introduction to communication complexity. But as soon as one tweaks the models ever so slightly, surprising results are possible. The nonlocal box is one such tweaking.A nonlocal box (NLB) is a device shared between two parties that, in itself is incapable of transferring any information from Alice to Bob, or vice-versa. A nonlocal box takes two bits as input, a bit x from Alice and a bit y from Bob, and outputs two bits, a bit a provided to Alice (and only Alice) and a bit b provided to Bob (and only Bob). If the two input bits x and y from Alice and Bob equal (0, 0), (0, 1), or (1, 0), the box (by definition) provides Alice and Bob with identical bits. That is, either both of them receive 0 or both of them receive 1, each case happening with probability 1 2 . If the two parties both give the box ...

show abstract

Bound Nonlocality and Activation

Cited by 50 publications

References 25 publications

Superactivation of quantum steering

Superactivation of quantum steering

All quantum states useful for teleportation are nonlocal resources

Quantum Nonlocal Boxes Exhibit Stronger Distillability

Contact Info

Product

Resources

About