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Physical Review A

Spectral effects in quantum teleportation

Travis S. Humble, Warren P. Grice

Published Feb 8, 2007• 40 citations
Publisher

Abstract

We use a multimode description of polarization-encoded qubits to analyze the quantum teleportation protocol. Specifically, we investigate how the teleportation fidelity depends on the spectral correlations inherent to polarization-entangled photons generated by type-II spontaneous parametric down conversion. We find that the maximal obtainable fidelity depends on the spectral entanglement carried by the joint probability amplitude, a result which we quantify for the case of a joint spectrum approximated by a correlated Gaussian function. We contrast these results with a similar analysis of the visibility obtained in a polarization-correlation experiment.

DOI
10.1103/physreva.75.022307

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We use a multimode description of polarization-encoded qubits to analyze the quantum teleportation protocol. Specifically, we investigate how the teleportation fidelity depends on the spectral correlations inherent to polarization-entangled photons generated by type-II spontaneous parametric down conversion. We find that the maximal obtainable fidelity depends on the spectral entanglement carried by the joint probability amplitude, a result which we quantify for the case of a joint spectrum approximated by a correlated Gaussian function. We contrast these results with a similar analysis of the visibility obtained in a polarization-correlation experiment.
Polarization-entangled photon pairs can be efficiently prepared into pure Bell states with a high fidelity via type-II spontaneous parametric down-conversion (SPDC) of narrow-band pump light. However, the use of femtosecond pump pulses to generate multiphoton states with precise timing often requires spectral filtering to maintain a high quality of polarization entanglement. This typically reduces the efficiency of photon pair collection. We experimentally map the polarization correlations of photon pairs from such a source over a range of down-converted wavelengths with a high spectral resolution and find strong polarization correlations everywhere. A spectrally dependent imbalance between contributions from the two possible decay paths of SPDC is identified as the reason for a reduction in entanglement quality observed with femtosecond pump pulses. Our spectral measurements allow us to predict the polarization correlations for arbitrary filter profiles when the frequency degree of freedom of the photon pairs is ignored.
We examine how spectral entanglement in polarization-entangled photon states generated from bulk-crystal, spontaneous parametric down-conversion affects the success of entanglement swapping and type-I fusion gates. We quantify the success of the entanglement swapping and fusion gates by calculating the bipartite concurrence and residual tangle, respectively, in terms of the joint spectral probability amplitudes of the initial broad-bandwidth polarization-entangled states. We find that both polarization-entanglement measures depend strongly on the initial spectral entanglement, as well as on the configuration of the independent sources. Specifically, when spectral differences correlate with polarization, the optimal source configuration is different for the two protocols. We conclude that this distinction is founded in how the underlying Bell-state measurement and quantum-erasure techniques respond differently to distinguishing spectral information.
The twin photons produced by a type‐II spontaneous parametric down conversion are well know as a potential source of photons for quantum teleportation due to the strong entanglement in polarization. This strong entanglement in polarization, however, depends on the spectral composition of the pump photon and the nature of optical isotropy of the crystal. By exact numerical calculation of the concurrence, we have shown that how pump photons spectral width and the birefringence nature of the crystal directly affect the degree of polarization entanglement of the twin photons.
Recent demonstrations of teleportation have transferred quantum information encoded into either polarization or field-quadrature degrees of freedom (DOFs), but an outstanding question is how to simultaneously teleport quantum information encoded into multiple DOFs. We describe how the transverse-spatial, spectral and polarization states of a single photon can be simultaneously teleported using a pair of multimode, polarization-entangled photons derived from spontaneous parametric down-conversion. Furthermore, when the initial photon pair is maximally entangled in the spatial, spectral, and polarization DOFs then the photon’s full quantum state can be reliably teleported using a Bell-state measurement based on sum-frequency generation.
Spectral properties of entangled photons generated via type-I frequency-nondegenerate spontaneous parametric down-conversion are studied theoretically and experimentally. For monochromatic pumping, the joint spectral intensity function for the photon pair is found to be symmetric even though each photon has a different central wavelength. The single-photon (first-order) interference shows the familiar triangular interferogram, usually associated with the cw-pumped frequency-degenerate type-II spontaneous parametric down-conversion. For broadband (ultrafast) pumping, on the other hand, the joint spectral intensity function is shown to be asymmetric, similar to the case of ultrafast-pumped frequency-degenerate type-II spontaneous parametric down-conversion. The spectral studies reported here are expected to play an important role in developing ultrabright two-color entangled photon sources.
Spectrally correlated photon pairs can be used to improve performance of long range fiber based quantum communication protocols. We present a source based on spontaneous parametric down-conversion producing polarization entangled photons without spectral filtering. In addition, the spectral correlation within the photon pair can be controlled by changing the pump pulse duration or coupled spatial modes characteristics. The spectral and polarization correlations were characterized. The generated photon pairs feature both positive spectral correlations, no correlations, or negative correlations and polarization entanglement with the fidelity as high as 0.97 (no background subtraction) with the expected Bell state. © 2014 Optical Society of America OCIS codes: 190.4410,300.6190,270.4180,270.5565 Controlling the spectral correlations of a polariza-tion entangled photon pair produced via spontaneous parametric down-conversion (SPDC) could have impor-tant benefits to applications in optical quantum infor-mation. Photonic quantum gates require pure states, which can be created by heralded sources producing pairs of spectrally decorrelated photons [1–11]. On the other