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arXiv:1311.6062

Wigner function description of entanglement swapping using parametric down conversion: the role of vacuum fluctuations in teleportation

Alberto Casado, S. Guerra, J. Plácido

Published Nov 23, 2013• 0 citations
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Abstract

We apply the Wigner formalism of quantum optics 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 nonlinear crystal and the Bell-state analyser is emphasized.

DOI
10.48550/arxiv.1311.6062

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We apply the Wigner formalism of quantum optics 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 nonlinear crystal and the Bell-state analyser is emphasized.
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.
The Wigner formalism in the Heisenberg picture constitutes a bridge that connects Quantum Optics to Stochastic Optics. The vacuum field appears explicitly in the formalism, and the wavelike aspects of light are emphasised. In addition, the zeropoint intensity as a threshold for detection is a common denominator in both theories. In this paper, after summarising the basic rules of the Wigner approach and its application to parametric down-conversion, some new results are presented that delve into the physical meaning of the zeropoint field in optical quantum communication. Specifically, the relationship between Bell-state distinguishability and the number of sets of zeropoint modes that take part in the experiment is analysed in terms of the coupling between the phases of the different fields involved and the subtraction of the zeropoint intensity at the detectors. Additionally, the connection between the compatibility theorem in quantum cryptography and zeropoint field is stressed.
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.
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