The Exclusivity Principle and Its Consequences

After introducing the graph-approaches to contextuality, we discuss how they lead to important developments in foundations of quantum physics. One of the most thought-provoking scientific challenges in recent times is deriving quantum theory from first principles. The starting point is assuming general probabilistic theories allowing for correlations that go beyond those that arise in quantum theory, and the goal is to find principles that pick out quantum theory from this landscape of possible theories. The exclusivity principle was proposed as a possible answer and many results have been found so far. A detailed review of these results is presented in this chapter.

[1]  Markus P. Mueller,et al.  A derivation of quantum theory from physical requirements , 2010, 1004.1483.

[2]  A. Acín,et al.  A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations , 2008, 0803.4290.

[3]  László Lovász,et al.  On the Shannon capacity of a graph , 1979, IEEE Trans. Inf. Theory.

[4]  T. Fritz,et al.  Local orthogonality as a multipartite principle for quantum correlations , 2012, Nature Communications.

[5]  N. David Mermin,et al.  What's Wrong with these Equations? , 1989 .

[6]  R. Spekkens,et al.  Specker’s parable of the overprotective seer: A road to contextuality, nonlocality and complementarity , 2010 .

[7]  Bin Yan,et al.  Quantum correlations are tightly bound by the exclusivity principle. , 2013, Physical review letters.

[8]  Alexia Auffèves,et al.  Recovering the quantum formalism from physically realist axioms , 2016, Scientific Reports.

[9]  M. T. Cunha,et al.  Exclusivity principle forbids sets of correlations larger than the quantum set. , 2013, 1306.6289.

[10]  Marco T'ulio Quintino,et al.  All noncontextuality inequalities for the n-cycle scenario , 2012, 1206.3212.

[11]  M. Navascués,et al.  A glance beyond the quantum model , 2009, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[12]  H. Buhrman,et al.  Limit on nonlocality in any world in which communication complexity is not trivial. , 2005, Physical review letters.

[13]  Mohamed Bourennane,et al.  Bell inequalities for the simplest exclusivity graph , 2011, 1106.4754.

[14]  Wim van Dam.  Implausible consequences of superstrong nonlocality , 2012, Natural Computing.

[15]  A. Shimony,et al.  Proposed Experiment to Test Local Hidden Variable Theories. , 1969 .

[16]  L. Hardy.  Quantum Theory From Five Reasonable Axioms , 2001, quant-ph/0101012.

[17]  Albert Einstein,et al.  Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? , 1935 .

[18]  A. Winter,et al.  (Non-)Contextuality of Physical Theories as an Axiom , 2010, 1010.2163.

[19]  Proposed experiment to exclude higher-than-quantum violations of the Bell inequality , 2013, 1303.6523.

[20]  G. D’Ariano,et al.  Informational derivation of quantum theory , 2010, 1011.6451.

[21]  A. Winter,et al.  Information causality as a physical principle , 2009, Nature.

[22]  Donald E. Knuth.  The Sandwich Theorem , 1994, Electron. J. Comb..

[23]  Christopher A. Fuchs,et al.  Some Negative Remarks on Operational Approaches to Quantum Theory , 2014, 1401.7254.

[24]  Alexander Schrijver,et al.  Relaxations of vertex packing , 1986, J. Comb. Theory B.

[25]  E. Specker.  DIE LOGIK NICHT GLEICHZEITIG ENTSC HEIDBARER AUSSAGEN , 1960 .

[26]  Charles H. Bennett,et al.  Teleporting an unknown quantum state via dual classical and EPR channels , 1993 .

[27]  Tamás Vértesi,et al.  Maximal violation of a bipartite three-setting, two-outcome Bell inequality using infinite-dimensional quantum systems , 2010 .

[28]  N. Mermin,et al.  Physics: QBism puts the scientist back into science , 2014, Nature.

[29]  S. Popescu,et al.  Quantum nonlocality as an axiom , 1994 .

[30]  Charles H. Bennett,et al.  Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. , 1993, Physical review letters.

[31]  M. A. Can,et al.  Simple test for hidden variables in spin-1 systems. , 2007, Physical review letters.

[32]  L. Hardy.  Reformulating and Reconstructing Quantum Theory , 2011, 1104.2066.

[33]  Ron Wright.  THE STATE OF THE PENTAGON A NONCLASSICAL EXAMPLE , 1978 .

[34]  A. J. Short,et al.  Quantum nonlocality and beyond: limits from nonlocal computation. , 2007, Physical review letters.

[35]  Harry Buhrman,et al.  The European Quantum Technologies Roadmap , 2017, 1712.03773.

[36]  A. Acín,et al.  Almost quantum correlations , 2014, Nature Communications.

[37]  M. Lewenstein,et al.  Quantum Entanglement , 2020, Quantum Mechanics.

[38]  Philip Ball,et al.  Physics: Quantum quest , 2013, Nature.

[39]  Lars Eirik Danielsen,et al.  Basic exclusivity graphs in quantum correlations , 2012, 1211.5825.

[40]  S. Massar,et al.  Bell inequalities for arbitrarily high-dimensional systems. , 2001, Physical review letters.

[41]  A. Cabello.  Simple explanation of the quantum violation of a fundamental inequality. , 2012, Physical review letters.

[42]  T. Fritz,et al.  A Combinatorial Approach to Nonlocality and Contextuality , 2012, Communications in Mathematical Physics.