scholarly journals Majorana fermions and non-locality

2014 ◽  
Vol 14 (11&12) ◽  
pp. 981-995
Author(s):  
Earl T. Campbell ◽  
Matty J. Hoban ◽  
Jens Eisert
Keyword(s):  
Quantum Information ◽  
Quantum Computation ◽  
Majorana Fermions ◽  
Variable Theory ◽  
Hidden Variable ◽  
Universal Quantum ◽  
Necessary And Sufficient ◽  
Non Locality ◽  
Local Hidden Variable

Localized Majorana fermions emerge in many topologically ordered systems and exhibit exchange statistics of Ising anyons. This enables noise-resistant implementation of a limited set of operations by braiding and fusing Majorana fermions. Unfortunately, these operations are incapable of implementing universal quantum computation. We show that, regardless of these limitations, Majorana fermions could be used to demonstrate non-locality (correlations incompatible with a local hidden variable theory) in experiments using only topologically protected operations. We also demonstrate that our proposal is optimal in terms of resources, with 10 Majorana fermions shown to be both necessary and sufficient for demonstrating bipartite non-locality. Furthermore, we identify severe restrictions on the possibility of tripartite non-locality. We comment on the potential of such entangled systems to be used in quantum information protocols.

scholarly journals Quantum theory cannot violate a causal inequality

2021 ◽  
Author(s):  
Tom Purves ◽  
Anthony Short
Keyword(s):  
Quantum Theory ◽  
Causal Model ◽  
Bell Inequality ◽  
Variable Model ◽  
Hidden Variable ◽  
Non Locality ◽  
Local Hidden Variable

Abstract Within quantum theory, we can create superpositions of different causal orders of events, and observe interference between them. This raises the question of whether quantum theory can produce results that would be impossible to replicate with any classical causal model, thereby violating a causal inequality. This would be a temporal analogue of Bell inequality violation, which proves that no local hidden variable model can replicate quantum results. However, unlike the case of non-locality, we show that quantum experiments can be simulated by a classical causal model, and therefore cannot violate a causal inequality.

scholarly journals A local hidden variable theory for the GHZ experiment

2002 ◽  
Vol 295 (5-6) ◽  
pp. 229-240 ◽  
Author(s):  
László E. Szabó ◽  
Arthur Fine
Keyword(s):  
Variable Theory ◽  
Hidden Variable ◽  
Ghz Experiment ◽  
Local Hidden Variable

scholarly journals QUANTUM TELEPORTATION WITH PAIR-COHERENT STATES

2007 ◽  
Vol 05 (01n02) ◽  
pp. 17-22 ◽  
Author(s):  
AURÉL GÁBRIS ◽  
GIRISH S. AGARWAL
Keyword(s):  
Coherent State ◽  
Quantum Teleportation ◽  
Coherent States ◽  
Continuous Variable ◽  
Quantum Mechanical ◽  
Variable Theory ◽  
Hidden Variable ◽  
Mechanical Explanation ◽  
Pair Coherent State ◽  
Local Hidden Variable

Recently, it has been argued that all presently performed continuous variable quantum teleportation experiments could be explained using a local hidden variable theory. In this paper, we study a modification of the original protocol which requires a fully quantum mechanical explanation even when coherent states are teleported. Our calculations of the fidelity of teleportation using a pair-coherent state under ideal conditions suggest that fidelity above the required limit of 1/2 may be achievable in an experiment also.

Towards a Local Hidden Variable Theory

2007 ◽  
Vol 37 (10) ◽  
pp. 1461-1469 ◽  
Author(s):  
Peter J. Lewis
Keyword(s):  
Variable Theory ◽  
Hidden Variable ◽  
Local Hidden Variable

scholarly journals Single-copy activation of Bell nonlocality via broadcasting of quantum states

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 499
Author(s):  
Joseph Bowles ◽  
Flavien Hirsch ◽  
Daniel Cavalcanti
Keyword(s):  
Single Copy ◽  
Quantum Correlations ◽  
The State ◽  
Mixed States ◽  
Variable Model ◽  
Variable Theory ◽  
Hidden Variable ◽  
Bell Nonlocality ◽  
Nonlocal Nature ◽  
Local Hidden Variable

Activation of Bell nonlocality refers to the phenomenon that some entangled mixed states that admit a local hidden variable model in the standard Bell scenario nevertheless reveal their nonlocal nature in more exotic measurement scenarios. We present such a scenario that involves broadcasting the local subsystems of a single-copy of a bipartite quantum state to multiple parties, and use the scenario to study the nonlocal properties of the two-qubit isotropic state:ρα=α|Φ+⟩⟨Φ+|+(1−α)14.We present two main results, considering that Nature allows for (i) the most general no-signalling correlations, and (ii) the most general quantum correlations at the level of any hidden variable theory. We show that the state does not admit a local hidden variable description for α>0.559 and α>12, in cases (i) and (ii) respectively, which in both cases provides a device-independent certification of the entanglement of the state. These bounds are significantly lower than the previously best-known bound of 0.697 for both Bell nonlocality and device-independent entanglement certification using a single copy of the state. Our results show that strong examples of non-classicality are possible with a small number of resources.

Sign in / Sign up

Export Citation Format

Share Document