Bell's Inequalities: Foundations and Quantum Communication
arXiv:0909.2611
Abstract
Efforts to construct deeper, realistic, level of physical description, in which individual systems have, like in classical physics, preexisting properties revealed by measurements are known as hidden-variable programs. Demonstrations that a hidden-variable program necessarily requires outcomes of certain experiments to disagree with the predictions of quantum theory are called "no-go theorems". The Bell theorem excludes local hidden variable theories. The Kochen-Specker theorem excludes noncontextual hidden variable theories. In local hidden-variable theories faster-that-light-influences are forbidden, thus the results for a given measurement (actual, or just potentially possible) are independent of the settings of other measurement devices which are at space-like separation. In noncontextual hidden-variable theories the predetermined results of a (degenerate) observable are independent of any other observables that are measured jointly with it. It is a fundamental doctrine of quantum information science that quantum communication and quantum computation outperforms their classical counterparts. If this is to be true, some fundamental quantum characteristics must be behind better-than-classical performance of information processing tasks. This chapter aims at establishing connections between certain quantum information protocols and foundational issues in quantum theory. After a brief discusion of the most common misinterpretations of Bell's theorem and a discussion of what its real meaning is, it will be demonstrated how quantum contextuality and violations of local realism can be used as useful resources in quantum information applications.
43 pages, 3 figures. to be published in "Handbook of Natural Computing", Editors: G. Rozenberg, T.H.W. Baeck, J.N. Kok (Springer, 2010) (http://www.springer.com/computer/foundations/book/978-3-540-92911-6)
References in corpus (29)
- Violation of Bell's inequality under strict Einstein locality conditions
- Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
- All multipartite Bell correlation inequalities for two dichotomic observables per site
- Simulating quantum computation by contracting tensor networks
- Bell's theorem for general N-qubit states
- Substituting Quantum Entanglement for Communication
- A limit on nonlocality in any world in which communication complexity is not trivial
- Bell-Kochen-Specker theorem: A proof with 18 vectors
- Violation of local realism with freedom of choice
- Most quantum states are too entangled to be useful as computational resources
- Preparation contextuality powers parity-oblivious multiplexing
- Nonlocality of cluster states of qubits
- Four Photon Entanglement from Down Conversion
- Measurement-based quantum computer in the gapped ground state of a two-body Hamiltonian
- Are random pure states useful for quantum computation?
- Multiparty Quantum Communication Complexity
- Relations between Entanglement Witnesses and Bell Inequalities
- Bound entanglement maximally violating Bell inequalities: quantum entanglement is not equivalent to quantum security
- Quantum codewords contradict local realism
- Two-setting Bell Inequalities for Graph States
- Quantum advantages in classically defined tasks
- Information-theoretic temporal Bell inequality and quantum computation
- Bell inequalities and distillability in N-quantum-bit systems
- A feasible quantum communication complexity protocol
- Foundations of quantum theory and quantum information applications
- Kochen-Specker theorem as a precondition for secure quantum key distribution
- Proposed direct test of a certain type of noncontextuality in quantum mechanics
- Is Communication Complexity Physical?
- Communication Complexity Protocol for Q-trits