Alberto Casado

Type II parametric downconversion in the Wigner-function formalism: entanglement and Bell’s inequalities

We continue the analysis of our previous papers that were devoted to type I parametric downconversion, the extension to type II being straightforward. We show that entanglement, in the Wigner representation, is merely a correlation that involves both signals and vacuum fluctuations. An analysis of the detection process opens the way to a complete description of parametric downconversion in terms of pure Maxwell electromagnetic waves.

Parametric Down-Conversion Experiments in the Wigner Representation

The Wigner representation is developed in the Heisenberg picture for the study of experiments involving photon pairs created in the process of parametric down conversion. After the general description of a light beam and the theory of detection (restricted here to single count probabilities in the Wigner formalism) the theory of parametric downconversion is developed to the point of calculating the autocorrelations of the signal and idler beams. Two recent experiments are analyzed in detail: frustrated two-photon creation by interference, and induced coherence and indistinguishability.

Wigner representation for experiments on quantum cryptography using two-photon polarization entanglement produced in parametric down-conversion

In this paper, the theory of parametric down-conversion in the Wigner representation is applied to Ekerts quantum cryptography protocol. We analyse the relation between two-photon entanglement and (non-secure) quantum key distribution within the Wigner framework in the Heisenberg picture. Experiments using two-qubit polarization entanglement generated in nonlinear crystals are analysed in this formalism, along with the effects of eavesdropping attacks in the case of projective measurements.

Partial Bell-State Analysis with Parametric down Conversion in the Wigner Function Formalism

We apply the Wigner function formalism to partial Bell-state analysis using polarization entanglement produced in parametric down conversion. Two-photon statistics at a beam-splitter are reproduced by a wave-like description with zeropoint fluctuations of the electromagnetic field. In particular, the fermionic behaviour of two photons in the singlet state is explained from the invariance on the correlation properties of two light beams going through a balanced beam-splitter. Moreover, we show that a Bell-state measurement introduces some fundamental noise at the idle channels of the analyzers. As a consequence, the consideration of more independent sets of vacuum modes entering the crystal appears as a need for a complete Bell-state analysis.

Wigner representation for entanglement swapping using parametric down conversion: the role of vacuum fluctuations in teleportation

We apply the Wigner formalism of quantum optics in the Heisenberg picture to study the role of the zeropoint field fluctuations in entanglement swapping produced via parametric down conversion. It is shown that the generation of mode entanglement between two initially non-interacting photons is related to the quadruple correlation properties of the electromagnetic field, through the stochastic properties of the vacuum. The relationship between the process of transferring entanglement and the different zeropoint inputs at the non-linear crystal and the Bell-state analyser is emphasized.

Local Realistic Theory for PDC Experiments Based on the Wigner Formalism

Abstract In this article we present a local hidden variables model for all experiments involving photon pairs produced in parametric down conversion, based on the Wigner representation of the radiation field. A modification of the standard quantum theory of detection is made in order to give a local realistic explanation of the counting rates in photodetectors. This model involves the existence of a real zeropoint field, such that the vacumm level of radiation lies below the threshold of the detectors.

Rome teleportation experiment analysed in the Wigner representation: the role of the zeropoint fluctuations in complete one-photon polarization-momentum Bell-state analysis

ABSTRACT The Wigner representation of parametric down conversion in the Heisenberg picture is applied to the study of the Rome teleportation experiment. We investigate the physical meaning of the zeropoint inputs at the different areas of the experimental set-up. In particular, we establish a quantitative relationship between the zeropoint sets of modes that are needed for the preparation of the quantum state to be teleported, the idle channels inside the one-photon polarization-momentum Bell-state analyser, and the possibility of performing teleportation of a polarization state with certainty.