Contextuality in Bosonic Bunching
Abstract
In the classical probability theory a sum of probabilities of three pairwise exclusive events is always bounded by one. This is also true in quantum mechanics if these events are represented by pairwise orthogonal projectors. However, this might not be true if the three events refer to a system of indistinguishable particles. We show that one can find three pairwise exclusive events for a system of three bosonic particles whose corresponding probabilities sum to 3/2. This can be done under assumptions of realism and noncontextuality, i.e., that it is possible to assign outcomes to events before measurements are performed and in a way that does not depend on a particular measurement setup. The root of this phenomenon comes from the fact that for indistinguishable particles there are events that can be deduced to be exclusive under the aforementioned assumptions, but at the same time are complementary because the corresponding projectors are not orthogonal.
 Publication:

Physical Review Letters
 Pub Date:
 January 2014
 DOI:
 10.1103/PhysRevLett.112.020403
 arXiv:
 arXiv:1306.3700
 Bibcode:
 2014PhRvL.112b0403K
 Keywords:

 03.65.Ud;
 03.65.Ta;
 Entanglement and quantum nonlocality;
 Foundations of quantum mechanics;
 measurement theory;
 Quantum Physics
 EPrint:
 4 pages, 1 figure, extended version of arXiv:1211.6907, discussion includes response to arXiv:1212.5502