Abstract
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 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 × 2 bright squeezed vacuum state, and a recently discussed bright-GHZ state resulting from multiple three photon emissions in a parametric process.
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