## Wigner-PDC description of photon entanglement as a local theory    [PDF]

David Rodriguez
The Wigner description of PDC-generated (Parametric Down Conversion)
photon-entanglement [2] can (contrary to widespread belief) be formulated as
entirely local-realistic: a formalism that is one-to-one with a quantum
(field-theoretical) model of the experimental setup can be cast, thanks to an
additional manipulation (also one-to-one) into a form that respects all
axiomatic laws of probability. Moreover, such manipulation seems reasonable
(though it would need refinement) from the point of view of the physical
behaviour of the detectors.
Seeking for the maximum generality, we adopted a non-factorizable expression
of joint detection probabilities (we know that it is possibly a necessary
condition to match quantum correlations, an issue we will examine elsewhere):
in respect to former versions, we now realize that non-factorability on \alpha
(the vacuum amplitudes) is simply an indicator of the need to introduce other
(vector of) additional variables \mu in the model. An interpretation for this
is simple: we could not expect to obtain a model on \alpha's alone, we need
other variables related to the laser and the state of the crystal.
Also as a correction on former versions, such additional \mu-dependence is
now introduced directly within the intensities I_i(\alpha) \rightarrow
I_i(\alpha,\mu) at each (the i-th) detector: this makes no conceptual
difference with our previous picture but preserves, as it seems more
reasonable, a dependence of the probability of detection only on the incoming
intensity: P_i(det|\alpha,\mu) \equiv f(I(\alpha,\mu)) instead of our former
P_i(det|\alpha,\mu) \equiv f(I(\alpha),\mu).
View original: http://arxiv.org/abs/1111.3898