Bell Inequalities for Arbitrarily High-Dimensional Systems

Collins, Daniel; Gisin, Nicolas; Linden, Noah; Massar, Serge; Popescu, Sandu

doi:10.1103/physrevlett.88.040404

Cited by 929 publications

(1,175 citation statements)

References 8 publications

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“…Fidelity decreases as the state dimension increases, however, the recovered fidelity for d ¼ 4 lies above the threshold states, which are defined by the minimum probability for which a high-dimensional Bell inequality is violated 39 .…”

Section: Article Nature Communications | Doi: 101038/ncomms4248mentioning

confidence: 99%

Self-healing of quantum entanglement after an obstruction

et al. 2014

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Quantum entanglement between photon pairs is fragile and can easily be masked by losses in transmission path and noise in the detection system. When observing the quantum entanglement between the spatial states of photon pairs produced by parametric downconversion, the presence of an obstruction introduces losses that can mask the correlations associated with the entanglement. Here we show that we can overcome these losses by measuring in the Bessel basis, thus once again revealing the entanglement after propagation beyond the obstruction. We confirm that, for the entanglement of orbital angular momentum, measurement in the Bessel basis is more robust to these losses than measuring in the usually employed Laguerre-Gaussian basis. Our results show that appropriate choice of measurement basis can overcome some limitations of the transmission path, perhaps offering advantages in free-space quantum communication or quantum processing systems.

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Section: Article Nature Communications | Doi: 101038/ncomms4248mentioning

confidence: 99%

Self-healing of quantum entanglement after an obstruction

et al. 2014

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“…We use a software, which can give experimence expression given enough points, to find a expression that describes the curve in Fig.1 Note added: While completing this work we learn a similar result obtained in Ref. [13], which based on the CGLMP inequality [12].…”

Section: Bell Inequality For Multi-component Correlation Functionsmentioning

confidence: 84%

“…When squeezing parameter goes to infinity, i.e., original EPR state gotten, we can find the bound of the violation of multi-component correlation-function Bell inequality [12].…”

Section: Bell Inequality For Multi-component Correlation Functionsmentioning

confidence: 99%

Multicomponent Bell inequality and its violation for continuous-variable systems

Chen

Kwek

et al. 2005

Phys. Rev. A

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Multi-component correlation functions are developed by utilizing d-outcome measurements. Based on the multi-component correlation functions, we propose a Bell inequality for bipartite d-dimensional systems. Violation of the Bell inequality for continuous variable (CV) systems is investigated. The violation of the original Einstein-Podolsky-Rosen state can exceed the Cirel'son bound, the maximal violation is 2.96981. For finite value of squeezing parameter, violation strength of CV states increases with dimension d. Numerical results show that the violation strength of CV states with finite squeezing parameter is stronger than that of original EPR state.

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“…In contrast, a two qubit Werner state is classical, i.e., it admits a GLHV description -unless it is the Bell state. In view of the increased interest in quantum correlations with qudits [10,11], it is not without interest to extend the investigation to higher dimensional systems. We study 3 × N systems in this paper.…”

Section: Introductionmentioning

confidence: 99%

Super-quantum states in SU(2) invariant 3×N level systems

2017

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Nonclassicality of quantum states is expressed in many shades, the most stringent of them being a new standard introduced recently in [1]. This is accomplished by expanding the notion of local hidden variables (LHV) to generalised local hidden variables (GLHV), which renders many nonlocal states also classical. We investigate these super-quantum states (called exceptional in [1]) in the family of SU (2) invariant 3 × N level systems. We show that all super-quantum states admit a universal geometrical description, and that they are most likely to lie on a line segment in the manifold, irrespective of the value of N . We also show that though the super -quantum states can be highly mixed, its relative rank with respect to the uniform state is always less than that of a state which admits a GLHV description.

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Bell Inequalities for Arbitrarily High-Dimensional Systems

Cited by 929 publications

References 8 publications

Self-healing of quantum entanglement after an obstruction

Self-healing of quantum entanglement after an obstruction

Multicomponent Bell inequality and its violation for continuous-variable systems

Super-quantum states in SU(2) invariant 3×N level systems

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