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- W4320561207 abstract "Quantum mechanics describes seemingly paradoxical relations between the outcomes of measurements that cannot be performed jointly. In Hilbert space, the outcomes of such incompatible measurements are represented by non-orthogonal states. In this paper, we investigate how the relation between outcomes represented by non-orthogonal quantum states differs from the relations suggested by a joint assignment of measurement outcomes that do not depend on the actual measurement context. The analysis is based on a well-known scenario where three statements about the impossibilities of certain outcomes would seem to make a specific fourth outcome impossible as well, yet quantum theory allows the observation of that outcome with a non-vanishing probability. We show that the Hilbert space formalism modifies the relation between the four measurement outcomes by defining a lower bound of the fourth probability that increases as the total probability of the first three outcomes drops to zero. Quantum theory thus makes the violation of non-contextual consistency between the measurement outcomes not only possible, but actually requires it as a necessary consequence of the Hilbert space inner products that describe the contextual relation between the outcomes of different measurements." @default.
- W4320561207 created "2023-02-15" @default.
- W4320561207 creator A5063245104 @default.
- W4320561207 creator A5064295131 @default.
- W4320561207 date "2022-11-03" @default.
- W4320561207 modified "2023-09-30" @default.
- W4320561207 title "Characterization of the non-classical relation between measurement outcomes represented by non-orthogonal quantum states" @default.
- W4320561207 doi "https://doi.org/10.48550/arxiv.2211.02199" @default.
- W4320561207 hasPublicationYear "2022" @default.
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