Kochen-Specker theorem as a precondition for secure quantum key distribution

Abstract

We show that (1) the violation of the Ekert 91 inequality is a sufficient condition for certification of the Kochen-Specker (KS) theorem, and (2) the violation of the Bennett-Brassard-Mermin 92 (BBM) inequality is, also, a sufficient condition for certification of the KS theorem. Therefore the success in each QKD protocol reveals the nonclassical feature of quantum theory, in the sense that the KS realism is violated. Further, it turned out that the Ekert inequality and the BBM inequality are depictured by distillable entanglement witness inequalities. Here, we connect the success in these two key distribution processes into the no-hidden-variables theorem and into witness on distillable entanglement. We also discuss the explicit difference between the KS realism and Bell's local realism in the Hilbert space formalism of quantum theory.

4 pages, To appear in Phys. Rev. A

References in corpus (10)

• Simple Proof of Security of the BB84 Quantum Key Distribution Protocol
• Information and Computation: Classical and Quantum Aspects
• Entanglement as precondition for secure quantum key distribution
• Secure quantum key distribution with an uncharacterized source
• Configuration of separability and tests for multipartite entanglement in Bell-type experiments
• Quantum correlations and secret bits
• All quantum observables in a hidden-variables model must commute simultaneously
• Equivalence between two-qubit entanglement and secure key distribution
• Observables suitable for restricting the fidelity to multipartite maximally entangled states
• Classification of mixed high-dimensional multiparticle systems

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• Bell's Inequalities: Foundations and Quantum Communication
• Comment on ``All quantum observables in a hidden-variable model must commute simultaneously"
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