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arXiv This work extends a bottom-up, statistics-first linear-algebraic framework previously developed for prepare-measure scenarios to operational scenarios with sequential transformations of an arbitrary number of stages, provides a full decision procedure for contextuality in such scenarios together with a complexity analysis (linearly exponential in the minimum generalized probabilistic theory dimension and polynomial in the number of procedures), demonstrates the approach through multiple examples including Spekkens' toy theory and the 8-state single-qubit stabilizer theory, and constructs an operational theory in which contextuality manifests itself only in the sequential structure of the transformations.
This work extends a bottom-up, statistics-first linear-algebraic framework previously developed for prepare-measure scenarios to operational scenarios with sequential transformations of an arbitrary number of stages, provides a full decision procedure for contextuality in such scenarios together with a complexity analysis (linearly exponential in the minimum generalized probabilistic theory dimension and polynomial in the number of procedures), demonstrates the approach through multiple examples including Spekkens' toy theory and the 8-state single-qubit stabilizer theory, and constructs an operational theory in which contextuality manifests itself only in the sequential structure of the transformations.
This work extends a bottom-up, statistics-first linear-algebraic framework previously developed for prepare-measure scenarios to operational scenarios with sequential transformations of an arbitrary number of stages, provides a full decision procedure for contextuality in such scenarios together with a complexity analysis (linearly exponential in the minimum generalized probabilistic theory dimension and polynomial in the number of procedures), demonstrates the approach through multiple examples including Spekkens' toy theory and the 8-state single-qubit stabilizer theory, and constructs an operational theory in which contextuality manifests itself only in the sequential structure of the transformations.
This work extends a bottom-up, statistics-first linear-algebraic framework previously developed for prepare-measure scenarios to operational scenarios with sequential transformations of an arbitrary number of stages, provides a full decision procedure for contextuality in such scenarios together with a complexity analysis (linearly exponential in the minimum generalized probabilistic theory dimension and polynomial in the number of procedures), demonstrates the approach through multiple examples including Spekkens' toy theory and the 8-state single-qubit stabilizer theory, and constructs an operational theory in which contextuality manifests itself only in the sequential structure of the transformations.