Local Hidden Variables Models Resting Upon the Wigner Function of Quantum Optics

G. S. Agarwal, Dipankar Home, W. P. Schleich

Alberto Casado, Trevor W. Marshall, Ramón Risco +1 more

In previous articles we have developed a theory of down conversion in nonlinear crystals, based on the Wigner representation of the radiation field. Taking advantage of the fact that the Wigner function is always positive in parametric down conversion experiments, we construct a local hidden variables model where the amplitudes of the field modes are taken as random variables whose probability distribution is the Wigner function. In order to achieve our goal we give a model of detection which is fully local but departs from quantum theory. In our model the zeropoint (vacuum) level of radiation lies below a threshold of the detectors and only signals above the threshold are detectable. The predictions of the model agree with those of quantum mechanics if the signal intensities surpase some level and the efficiency is low. This is consistent with the known fact that quantum mechanics is compatible with local realism in that case (a fact called the ``efficiency loophole''). Our model gives a number of constraints which do not follow from the quantum theory of detection and are experimentally testable.

I. Földesi, József Janszky, Петер Адам +3 more

Stanley Gudder

Danko Dimchev Georgiev, Eliahu Cohen

Although regarded today as an important resource in quantum information, nonlocality has yielded over the years many conceptual conundrums. Among the latter are nonlocal aspects of single particles which have been of major interest. In this paper, the nonlocality of single quanta is studied in a square nested Mach–Zehnder interferometer with spatially separated detectors using a delayed choice modification of quantum measurement outcomes that depend on the complex-valued weak values. We show that if spacelike separated Bob and Alice are allowed to freely control their quantum devices, the geometry of the setup constrains the local hidden variable models. In particular, hidden signaling and a list of contextual instructions are required to split a quantum state characterized by a positive Wigner function into two quantum states with nonpositive Wigner functions. This implies that local hidden variable models could rely neither on only two hidden variables for position and momentum, nor on simultaneous factorizability of both the hidden probability densities and weights of splitting to reproduce the correct quantum distributions. While our analysis does not fully exclude the existence of nonfactorizable local hidden variable models, it demonstrates that the recently proposed weak values of quantum histories necessitate contextual splitting of prior commitments to measurement outcomes, due to functional dependence on the total Feynman sum that yields the complex-valued quantum probability amplitude for the studied quantum transition. This analysis also highlights the quantum nature of weak measurements.

Trevor W. Marshall, Emilio Santos