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Physical Review A

Effects of spectral entanglement in polarization-entanglement swapping and type-I fusion gates

Travis S. Humble, Warren P. Grice

Published Feb 11, 2008• 38 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.77.022312

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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.
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.
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.
The quantum state of the photon pair generated from type-II spontaneous parametric down-conversion pumped by a ultrafast laser pulse exhibits strong decoherence in its polarization entanglement, an effect which can be attributed to the clock effect of the pump pulse or, equivalently, to distinguishing spectral information in the two-photon state. Here, we propose novel temporal and spectral engineering techniques to eliminate these detrimental decoherence effects. The temporal engineering of the two-photon wavefunction results in a universal Bell-state synthesizer that is independent of the choice of pump source, crystal parameters, wavelengths of the interacting photons, and the bandwidth of the spectral filter. In the spectral engineering technique, the distinguishing spectral features of the two-photon state are eliminated through modifications to the two-photon source. In addition, spectral engineering also provides a means for the generation of polarization-entangled states with novel spectral characteristics: the frequency-correlated state and the frequency-uncorrelated state.