Bosonic fields in states with undefined particle numbers possess detectable non-contextuality features, plus more

The paradoxical features of quantum theory are usually formulated for fixed number of particles. While one can now find a formulation of Bell's theorem for quantum fields, a Kochen-Specker-type reasoning is usually formulated for just one particle, or like in the case of Peres-Mermin square for two. Is it possible to formulate a contextuality proof for situation in which the numbers of particles are fundamentally undefined? We introduce a representation of the su(2) algebra in terms of boson number states in two modes that allows us to assess nonclassicality of states of bosonic fields. This representation allows to show contextuality, and is efficient to reveal violation of local realism, and to formulate entanglement indicators. A form of an non-contextuality inequality is derived, giving a bosonic Peres-Mermin square. The entanglement indicators are built with Pauli-like field observables. The non-clasicality indicators are effective. This is shown for the 2 x 2 bright squeezed vacuum state, and a recently discussed bright-GHZ state resulting from multiple three photon emissions in a parametric process.

Automated summary

This article discusses the paradoxical features of quantum theory in fixed number of particles in quantum fields. The authors introduce a representation of the su(2) algebra using boson number states in two modes to assess nonclassicality of bosonic fields states. They show contextuality, violation of local realism, and formulate entanglement indicators using this representation. They further derive a non-contextuality inequality, revealing a bosonic Peres-Mermin square. The effectiveness of non-classicality indicators is demonstrated using the 2 x 2 bright squeezed vacuum state and the bright-GHZ state resulting from multiple three photon emissions in a parametric process.