Contextuality of Identical Particles

Abstract

A generalisation of quantum contextuality to the case of many indentical particles is presented. The model consists of a finite collection of modes that can be occupied by N particles, either bosons or fermions. Measurement scenarios allow one to measure occupation of each mode in at least two different measurement contexts. The system is said to be non-contextual if the occupation numbers can be assigned to modes in each measurement scenario. The assignment is done under the non-contextuality assumption, i.e., an occupation number assigned to a mode does not depend on a scenario in which this mode is measured. In addition, the total number of particles has to be conserved, therefore the sum of occupation numbers in each measurement context is equal to N. For N=1 the model does not differ from the standard contextuality scenario. However, for N>1 the problem reveals new complex features. In particular, it is shown that a type of contextuality exhibited by the system (state-dependent, state-independent, or non-contextual) depends on the type and the number of particles. Further properties of this model and open problems are also discussed.