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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Polarization-entangled light for quantum key distribution: how frequency spectrum and energy affect detection statistics

John M. Myers

Published May 25, 2005• 5 citations
Publisher

Abstract

Light pulses used in quantum key distribution (QKD) designed for polarization entanglement also exhibit frequency entanglement. Although absent from the simplified models that initiated QKD, the degree of frequency entanglement of polarization-entangled light pulses is shown to affect the amount of key that can be distilled from raw light signals. In one example, extreme frequency entanglement generates 4/3 of the amount of distilled key as does no frequency entanglement.

DOI
10.1117/12.603473

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Light pulses used in quantum key distribution (QKD) designed for polarization entanglement also exhibit frequency entanglement. Although absent from the simplified models that initiated QKD, the degree of frequency entanglement of polarization-entangled light pulses is shown to affect the amount of key that can be distilled from raw light signals. In one example, extreme frequency entanglement generates 4/3 of the amount of distilled key as does no frequency entanglement.
With the recognition of a logical gap between experiments and equations of quantum mechanics comes: (1) a chance to clarify such purely mathematical entities as probabilities, density operators, and partial traces-separated out from the choices and judgments necessary to apply them to describing experiments with devices, and (2) an added freedom to invent equations by which to model devices, stemming from the corresponding freedom in interpreting how these equations connect to experiments. Here I apply a few of these clarifications and freedoms to model polarization-entangled light pulses called for in quantum key distribution (QKD). Available light pulses are entangled not only in polarization but also in frequency. Although absent from the simplified models that initiated QKD, the degree of frequency entanglement of polarization-entangled light pulses is shown to affect the amount of key that can be distilled from raw light signals, in one case by a factor of 4/3. Open questions remain, because QKD brings concepts of quantum decision theory, such as measures of distinguishability, mostly worked out in the context of finite-dimensional vector spaces, into contact with infinite-dimensional Hilbert spaces needed to give expression to optical frequency spectra.
We formulate quantum optics to include frequency dependence in the modeling of optical networks. Entangled light pulses available for quantum cryptography are entangled not only in polarization but also, whether one wants it or not, in frequency. We model effects of the frequency spectrum of faint polarization-entangled light pulses on detection statistics. For instance, we show how polarization entanglement combines with frequency entanglement in the variation of detection statistics with pulse energy. Attention is paid not only to single-photon light states but also to multi-photon states. These are needed (1) to analyze the dependence of statistics on energy and (2) to help in calibrating fiber couplers, lasers and other devices, even when their desired use is for the generation of single-photon light.
We formulate quantum optics to include frequency dependence in the modeling of optical networks. Entangled light pulses available for quantum cryptography are entangled not only in polarization but also, whether one wants it or not, in frequency. We model effects of the frequency spectrum of faint polarization-entangled light pulses on detection statistics. For instance, we show how polarization entanglement combines with frequency entanglement in the variation of detection statistics with pulse energy. Attention is paid not only to single-photon light states but also to multi-photon states. These are needed (1) to analyze the dependence of statistics on energy and (2) to help in calibrating fiber couplers, lasers and other devices, even when their desired use is for the generation of single-photon light.
Photon pairs with correlated frequencies from an optical parametric system were generated by a continuous wave pump focused on a type-II nonlinear crystal with polarization entanglement. The polarization entanglement of the frequency resolved photons was measured under several typical configurations. By optimizing a condition, the degree of polarization entanglement was improved substantially. We proposed the application of the system, which can be used as a light source of wavelength division multiplexing quantum key distribution, optimizing the configuration of the photon-pair generation.
Photon pairs with correlated frequencies from an optical parametric system were generated by a continuous wave pump focused on a type-II nonlinear crystal with polarization entanglement. The polarization entanglement of the frequency-resolved photons was measured under several typical configurations. By optimizing the condition, the degree of polarization entanglement was improved substantially. We proposed the application of the system, which can be used as a light source of wavelength division multiplexing quantum key distribution, optimizing the configuration of the photon-pair generation.
Polarization of light has been used extensively in quantum information processing, and quantum entanglement is essential to many areas of research, including quantum computing. Here we investigate the degree of polarization and the entanglement of a family of quantum states known as photon-added entangled coherent states. Such states could serve as means of entanglement distribution and quantum key distribution. Using the quantum Stokes parameters and the QQQ function, we demonstrate that, in general, the degree of polarization of two two-mode photon-added coherent states increases significantly with the number of added photons. And using the concurrence, we show that the amount of entanglement in this kind of superposition presents a behavior that is dependent on whether or not the number of added photons in each mode is the same.