If a physical system contains a single particle, and if two distant detectors test the presence of linear superpositions of one-particle and vacuum states, a violation of classical locality can occur, due to the creation of a two-particle component by the detecting process itself.
Abstract We generalize Gisin’s theorem on the relation between the entanglement of pure states and Bell non-classicality to the case of mode entanglement of separated groups of modes of quantum fields extending the theorem to cover also states with undefined particle number. We show that any pure state of the field which contains entanglement between two groups of separated modes violates some Clauser–Horne (CH) inequality. In order to construct the observables leading to a violation in the first step, we show an isomorphism between the Fock space built from a single-particle space involving two separated groups of modes and a tensor product of two abstract separable Hilbert spaces spanned by formal monomials of creation operators. In the second step, we perform a Schmidt decomposition of a given entangled state mapped to this tensor product space and then we map back the obtained Schmidt decomposition to the original Fock space of the system under consideration. Such obtained Schmidt decomposition in Fock space allows for construction of observables leading to a violation of the CH inequality. We also show that our generalization of Gisin’s theorem holds for the case of states on non-separable Hilbert spaces, which physically represent states with actually infinite number of particles. Such states emerge, for example, in the discussion of quantum phase transitions. Finally, we discuss the experimental feasibility of constructed Bell test and provide a necessary condition for realizability of this test within the realm of passive linear optics.
Nonlocal effects associated with quantum-mechanical states have been theoretically interesting because they emphasize the differences between classical and quantum mechanics. We describe a system in which a single input photon causes a nonlocal influence on two spatially separated homodyne detectors, as evidenced by a violation of Bell's inequalities. Unlike previous configurations for violating Bell's inequalities, the correlation is not imposed on a pair of particles that spatially separate before being detected. Rather, the correlation arises from the interaction of the local oscillators at each homodyne detector with the spatially extended field of the input photon. The above effect is only one of a class of situations in which nonlocal correlations can be imposed on separated homodyne detectors by quantum mechanical fields. By deriving the conditions for violating Bell's inequality with phase-sensitive detectors, new tests can be developed that relate to squeezed light and other nonclassical fields.
Recently, Danielson, Satishchandran, and Wald have proposed a novel source of decoherence of charges and masses in a spatial superposition state when placed in a spacetime with Killing horizons. They argued that the effect is primarily caused by the emission of soft particles through these horizons, which will eventually occur even if the process is assumed to be adiabatic. It turns out this decoherence is intimately related to the presence of low-frequency quanta in the thermal radiation, as described by stationary observers in the Schwarzschild and Rindler spaces, which arises depending on the choice of vacuum state. We investigate this claim in a rather different setting, with a gapless detector interacting with a massive scalar field. We introduce how such interaction is described and how to quantify the resulting decoherence. Then, we investigate our proposed model in two seminal cases: We consider that the components of the spatial superposition are inertial and that they are uniformly accelerating in the Minkowski space. We highlight the similarities and differences between our results and those of previous studies when the system is tuned in an analogous regime. Finally, we discuss what we sought to improve with our model and how it might clarify some questions left open in the original work.