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Quantum probabilities as Dempster-Shafer probabilities in the lattice of subspaces. (English) Zbl 1303.81041

The Dempster-Shafer probabilities as quantum probabilities have been used in the lattice of finite subspaces. This indicates the difficulty when using Kolmogorov theories as quantum probabilities. An example of these difficulties is that they lead to various Bell-like inequalities, that are violated by an experiments.
It is further shown that the proof of the inequalities of Clauser, Horne, Shimony and Holt for a system of two spin-\(1/2\) particles is valid for Kolmogorov probabilities, but is not valid for Dempster-Shafer probabilities. Their violation in experiments supports the use of the Dempster-Shafer theory for quantum probabilities.

MSC:

81P45 Quantum information, communication, networks (quantum-theoretic aspects)
81P40 Quantum coherence, entanglement, quantum correlations
81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
81P15 Quantum measurement theory, state operations, state preparations
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