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Register a new userQuantum Measurements Are Noncontextual
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Added by
Robert B. Griffiths
Publication date
2013
fields
Physics
and research's language is
English
Authors
Robert B. Griffiths
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Quantum measurements are noncontextual, with outcomes independent of which other commuting observables are measured at the same time, when consistently analyzed using principles of Hilbert space quantum mechanics rather than classical hidden variables.
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Contextuality is a fundamental feature of quantum theory and is necessary for quantum computation and communication. Serious steps have therefore been taken towards a formal framework for contextuality as an operational resource. However, the most important component for a resource theory - a concrete, explicit form for the free operations of contextuality - was still missing. Here we provide such a component by introducing noncontextual wirings: a physically-motivated class of contextuality-free operations with a friendly parametrization. We characterize them completely for the general case of black-box measurement devices with arbitrarily many inputs and outputs. As applications, we show that the relative entropy of contextuality is a contextuality monotone and that maximally contextual boxes that serve as contextuality bits exist for a broad class of scenarios. Our results complete a unified resource-theoretic framework for contextuality and Bell nonlocality.
We discuss chromatic constructions on orthogonality hypergraphs which are classical set representable or have a faithful orthogonal representation. The latter ones have a quantum mechanical realization in terms of intertwined contexts or maximal observables. Structure reconstruction of these hypergraphs from their table of two-valued states is possible for a class of hypergraphs, namely perfectly separable hypergraphs. Some examples from exempt categories that either cannot be reconstructed by two-valued states or whose set of two-valued states does not yield a coloring are presented.
One implication of Bells theorem is that there cannot in general be hidden variable models for quantum mechanics that both are noncontextual and retain the structure of a classical probability space. Thus, some hidden variable programs aim to retain noncontextuality at the cost of using a generalization of the Kolmogorov probability axioms. We generalize a theorem of Feintzeig (2015) to show that such programs are committed to the existence of a finite null cover for some quantum mechanical experiments, i.e., a finite collection of probability zero events whose disjunction exhausts the space of experimental possibilities.
We show that, for any n, there are m-outcome quantum correlations, with m>n, which are stronger than any nonsignaling correlation produced from selecting among n-outcome measurements. As a consequence, for any n, there are m-outcome quantum measurements that cannot be constructed by selecting locally from the set of n-outcome measurements. This is a property of the set of measurements in quantum theory that is not mandatory for general probabilistic theories. We also show that this prediction can be tested through high-precision Bell-type experiments and identify past experiments providing evidence that some of these strong correlations exist in nature. Finally, we provide a modified version of quantum theory restricted to having at most n-outcome quantum measurements.
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