Quantitative relations between different measurement contexts

Abstract

In quantum theory, a measurement context is defined by an orthogonal basis in a Hilbert space, where each basis vector represents a specific measurement outcome. The precise quantitative relation between two different measurement contexts can thus be characterized by the inner products of nonorthogonal states in that Hilbert space. Here, we use measurement outcomes that are shared by different contexts to derive specific quantitative relations between the inner products of the Hilbert space vectors that represent the different contexts. It is shown that the probabilities that describe the paradoxes of quantum contextuality can be derived from a very small number of inner products, revealing details of the fundamental relations between measurement contexts that go beyond a basic violation of noncontextual limits. The application of our analysis to a product space of two systems reveals that the nonlocality of quantum entanglement can be traced back to a local inner product representing the relation between measurement contexts in only one system. Our results thus indicate that the essential nonclassical features of quantum mechanics can be traced back to the fundamental difference between quantum superpositions and classical alternatives.

arXiv comment12 pages, 4 figures, accepted for publication in Quantum

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Cited by in corpus (6)

• Properties and Applications of the Kirkwood-Dirac Distribution
• Counterfactuality, back-action, and information gain in multi-path interferometers
• Tracing quantum correlations back to collective interferences
• Statistical signatures of quantum contextuality
• Quantum coherence and negative quasi probabilities in a contextual three-path interferometer
• Almost no experiments have classical Kirkwood-Dirac representations