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

Casado, Alberto; Guerra, S.; Plácido, J.

doi:10.1088/0953-4075/41/4/045501

Cited by 19 publications

(44 citation statements)

References 24 publications

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“…The distinguishing feature of the above Equations is that the momentum at Alice's detectors is correlated to the momentum of Bob's photon. For a given detector DX± (X = {T, R}), there are two cross-correlations, F (27) are similar to the cross-correlations of the light field before Alice's station, which are given in Equations (13) to (16). Nevertheless, the information contained in the electromagnetic field before Alice's station is divided into the autocorrelations (Equations (11) and (12)) and the crosscorrelations (Equations (13) to (16)).…”

Section: The One-photon Polarization-momentum Bell-state Analysermentioning

confidence: 99%

“…Nevertheless, the information contained in the electromagnetic field before Alice's station is divided into the autocorrelations (Equations (11) and (12)) and the crosscorrelations (Equations (13) to (16)). In contrast, once we have considered the action of the different optical devices placed at Alice's station, we can state that the total information about the preparation is contained into the eight cross-correlations given Equations (24) to (27).…”

Section: The One-photon Polarization-momentum Bell-state Analysermentioning

confidence: 99%

“…The cross-correlation functions concerning the polarization components of F (24) to (27), by making the exchange F…”

Section: Bob's Stationmentioning

confidence: 99%

“…• On the one hand, in order to transform the cross-correlation properties concerning the momentum of Bob's photon (see Equations (24) to (27)) into the cross-correlations involving the polarization (see Equations (32) to (35)), there must be a transfer from momentum to polarization. The excess of noise at Bob's station is eliminated through one of the outgoing channels of PBS Bob (see Equation (30)).…”

Section: Zpf and Complete Bsm In The Rome Experimentsmentioning

confidence: 99%

“…In contrast, in the Rome teleportation experiment only two entangled photons are used, and the qubit to be teleported is encoded in one of two ZPF inputs in experiments on quantum cryptography [27], partial BSM [28], hyperentanglement and complete BSM [29], and entanglement swapping [30]. Two features of the ZPF constitute the common denominator in these works.…”

Section: Introductionmentioning

confidence: 99%

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

Casado

Guerra

Plácido

2018

Journal of Modern Optics

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AcknowledgementsThe authors would like to thank Prof. E. Santos for revising the manuscript, and for helpful suggestions and comments on the work. We are grateful for the insights gained in conversations with R. Risco-Delgado. AbstractThe 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 setup. 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 whith certainty. arXiv:1707.09624v1 [quant-ph] 30 Jul 2017 degrees of freedom (polarization or momentum) of Alice's photon [15]. The other photon of the down converted pair is sent to Bob. The advantage of this teleportation scheme is that a complete BSM of one-photon polarizationmomentum Bell-states is possible. Nevertheless, the input state cannot be supplied by an external system, and this presents some limitations, such as the inability to teleport entangled or mixed states [2]. The result obtained by Alice is communicated to Bob, who uses this information to apply one out of four unitary transformations, in order to reproduce the original state. This experiment was proposed by Popescu [20] and performed in Rome [15] by using two-photon momentum entanglement, and polarization coding for preparing the qubit to be teleported. The Innsbruck and Rome experiments omitted the final stage of teleportation, the unitary transformations applied by Bob after the classical communication in order to reconstruct the unknown state. This was accomplished using nuclear magnetic resonance [21], and later the first long-distance optical quantum teleportation experiment with active feed-forward in real time was accomplished [22].The Wigner representation of quantum optics in the Heisenberg picture (WRHP) has been applied in recent years to the study of experiments on quantum communication using photons generated via parametric down conversion. The WRHP formalism of PDC resembles nonlinear classical optics, by taking into consideration the vacuum inputs at the nonlinear crystal and the different linear optical devices placed between the source of down converted photons and the detectors. The zeropoint field (ZPF) appears as a stochastic field that couples with the laser beam into the crystal, giving rise to the down converted beams [23,24]. In this way, the signals emitted by the crystal constitute needles of radiation generated by the amplification of vacuum fluctuations [25]. These signals propagate according to the classical Maxwell equations, so that the WRHP formalism of PDC emphasizes the wave-like aspects in the generation and propagation of light [26]. The Wigner function of PDC is positive, and corresponds to the Gaussian Wi...

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Section: The One-photon Polarization-momentum Bell-state Analysermentioning

confidence: 99%

Section: The One-photon Polarization-momentum Bell-state Analysermentioning

confidence: 99%

“…The cross-correlation functions concerning the polarization components of F (24) to (27), by making the exchange F…”

Section: Bob's Stationmentioning

confidence: 99%

Section: Zpf and Complete Bsm In The Rome Experimentsmentioning

confidence: 99%