The CHSH-type inequalities for infinite-dimensional quantum systems

Abstract

By establishing CHSH operators and CHSH-type inequalities, we show that any entangled pure state in infinite-dimensional systems is entangled in a $2\otimes 2$ subspace. We find that, for infinite-dimensional systems, the corresponding properties are similar to that of the two-qubit case: (i) The CHSH-type inequalities provide a sufficient and necessary condition for separability of pure states; (ii) The CHSH operators satisfy the Cirel'son inequalities; (iii) Any state which violates one of these Bell inequalities is distillable.

9 pages. arXiv admin note: text overlap with arXiv:1006.3557 by other authors

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• Quantum entanglement
• Entanglement detection
• Gisin's Theorem for Arbitrary Dimensional Multipartite States
• A characterization of positive linear maps and criteria of entanglement for quantum states
• When different entanglement witnesses detect entangled states simultaneously
• Verifying continuous-variable entanglement in finite spaces
• Teleportation capability, distillability, and nonlocality on three-qubit states