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An upper bound for the fidelity of quantum teleportation explainable by local hidden variables is derived. This bound is larger than the fidelity corresponding to product states, i.e. to local quantum states. This is relevant for the study of mixed states. In particular, the fidelity of Werner's mixed state, known to be larger than the fidelity of product states, is found to be smaller than the fidelity explainable by local hidden variables. Hence the fidelity of Werner's mixed state does not exhibit nonclassical aspects.
Any Bell test consists of a sequence of measurements on a quantum state in spacelike separated regions. Thus, a state is better than others for a Bell test when, for the optimal measurements and the same number of trials, the probability of existence of a local model for the observed outcomes is smaller. The maximization over states and measurements defines the optimal nonlocality proof. Numerical results show that the required optimal state does not have to be maximally entangled.
