2013/06/16 by Paweł Kurzyński, Pawel Kurzynski, Akihito Soeda +2
Computer Science · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Bounded function #Identical particles #Kochen–Specker theorem #Mathematical analysis #Mathematics #Pairwise comparison #Physics #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum entanglement #Quantum mechanics #Quantum nonlocality #Statistical physics #Statistics #Theoretical physics #quant-ph
paper · pdf · doi:10.1103/physrevlett.112.020403
4 pages, 1 figure, extended version of arXiv:1211.6907, discussion includes response to arXiv:1212.5502
arxiv created 2013/06/16 · openalex publication_date 2014/01/14 · arxiv updated 2015/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.