(Non-)Contextuality of Physical Theories as an Axiom
By Adán Cabello, Simone Severini, Andreas J. Winter. 2010
140 citations recorded by the source corpus.
We show that the noncontextual inequality proposed by Klyachko et al. [Phys. Rev. Lett. 101, 020403 (2008)] belongs to a broader family of inequalities, one associated to each compatibility structure of a set of events (a graph), and its independence number. These have the surprising property that the maximum quantum violation is given by the Lovasz theta-function of the graph, which was originally proposed as an upper bound on its Shannon capacity. Furthermore, probabilistic theories beyond quantum mechanics may have an even larger violation, which is given by the so-called fractional packing number. We discuss in detail, and compare, the sets of probability distributions attainable by noncontextual, quantum, and generalized models; the latter two are shown to have semidefinite and linear characterizations, respectively. The implications for Bell inequalities, which are examples of noncontextual inequalities, are discussed. In particular, we show that every Bell inequality can be recast as a noncontextual inequality a la Klyachko et al.
Subfields: Atomic and Molecular Physics, and Optics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/687cb7001e95fa63486b97feec498317638a5ab9
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In Atomic and Molecular Physics, and Optics
- Anthony Leverrier
- Tobias Fritz
- Ana Belén Sainz
- Antonio Acín
- Gilles Pisier
- Eleni Diamanti
- Robin J. Evans
In Computational Theory and Mathematics
Citations in the corpus
- The sheaf-theoretic structure of non-locality and contextuality (2011, unknown): “An important recent contribution in this direction is [8], which studies non-contextual inequalities as a generalization of Bell inequalities.”
- A Combinatorial Approach to Nonlocality and Contextuality (2012, methodology): “Some notable exceptions are the following: (a) The study of test spaces in quantum logic [31,100], (b) Spekkens’ work on measurement and preparation contextuality [65,90], (c) The graph-theoretic approach of Cabello, Severini and Winter (CSW) [26], (d) The sheaf-theoretic approach pioneered by Abram”