Single-photon sources are crucial components for the implementation of quantum communication protocols. However, photons emitted by some of the most popular types of realistic sources are spectrally broadband. Due to this drawback, the signal emitted from such sources is typically affected by the effect of temporal broadening during its propagation through telecommunication fibers which exhibit chromatic dispersion. Such problem can be observed e.g. when using sources based on the process of spontaneous parametric down-conversion (SPDC). In the case of long-distance quantum communication temporal broadening can significantly limit the efficiency of temporal filtering. It is a popular method, which is based on the reduction of the duration time of the detection window, used for decreasing the number of registered errors.
In this work we analyzed the impact of the type of spectral correlation within a pair of photons produced by the SPDC source on the temporal width of those photons during their propagation in dispersive media. We found out that in some situations the width can be decreased by changing the typical negative spectral correlation into positive one or by reducing its strength. This idea can be used to increase the efficiency of the temporal filtering method. Therefore it can be applied in various implementations of quantum communication protocols.
As an example of the application we subsequently analyzed the security of a quantum key distribution (QKD) scheme based on single photons. It was realized in the configuration with the source of photons located in the middle between the legitimate participants of a QKD protocol (called typically Alice and Bob). We demonstrated that when the information about the emission time of the photons produced by the SPDC source is not distributed to Alice and Bob, the maximal security distance can be considerably extended by using positively correlated photons, while in the opposite case strongly (no matter positively or negatively) correlated photons are optimal. We also found out that the results of our calculation may be very sensitive to the spectral widths of the photons produced by the SPDC source. In addition, we concluded that in realistic situation Alice and Bob would have to optimize their source over both the spectral widths of the generated photons and the type of spectral correlation in order to maximally extend the security distance.
The results of our work are, in particular, important for the QKD systems utilizing commercial telecom fibers populated by strong classical signals. In those systems temporal filtering method can be used to reduce not only the dark counts registered by the detection system, but also the channel noise originating from the process of Raman scattering, which is the main factor limiting their performance.
Let us consider the experimental setup where SPDC source generates photon pairs which are subsequently coupled to single-mode fibers (SMFs). We assume that there are three parties involved: 1) Alice, possessing the photon pair source, detection system and the fiber connecting them, 2) Bob, who monitors the output of the second, long-distance fiber and 3) Eve, who can perform the most general collective attacks in order to acquire information which Alice and Bob wish to transfer. Typically, in fiber-based communication the chromatic dispersion is considered to be an obstacle, limiting the maximal distance at which information carrier can be securely transmitted. This phenomenon forces the trusted parties to define longer detection windows to avoid losing signal photons and increases the amount of detection noise that is being registered.
We consider standard BB84 quantum key distribution protocol, based on the SPDC source located in between Alice and Bob. The parameters of standard realistic telecommunication fibers (SMF28e+) are take into account. The source emits photon which apart of being entangled in polarization degree of freedom are entangled in spectral domain. This is the key feature which allows one to reduce detection noise by manipulating the spectral correlation between the produced photons. In this way the maximal security distance can be increased by around 10%.
Single-photon sources are crucial components for the implementation of quantum communication protocols. However, photons emitted by some of the most popular types of realistic sources are spectrally broadband. Due to this drawback, the signal emitted from such sources is typically affected by the effect of temporal broadening during its propagation through telecommunication fibers which exhibit chromatic dispersion. Such problem can be observed e.g. when using sources based on the process of spontaneous parametric down-conversion (SPDC). In the case of long-distance quantum communication temporal broadening can significantly limit the efficiency of temporal filtering. It is a popular method, which relies on the reduction of the duration time of the detection window, used for decreasing the number of registered errors.
In this work we analyzed the impact of the type of spectral correlation within a pair of photons produced by the SPDC source on the temporal width of those photons during their propagation in dispersive media. We found out that in some situations this width can be decreased by changing the typical negative spectral correlation into positive one or by reducing its strength. This idea can be used to increase the efficiency of the temporal filtering method. Therefore, it can be applied in various implementations of quantum communication protocols.
As an example of the application we subsequently analyzed the security of a quantum key distribution (QKD) scheme based on single photons. The investigation was performed for the configuration with the source of photons located in the middle between the legitimate participants of a QKD protocol (called typically Alice and Bob). We demonstrated that when the information about the emission time of the photons produced by the SPDC source is not distributed to Alice and Bob, the maximal security distance can be considerably extended by using positively correlated photons, while in the opposite case strongly (no matter positively or negatively) correlated photons are optimal. We also found out that the results of our calculation may be very sensitive to the spectral widths of the photons produced by the SPDC source. In addition, we concluded that in realistic situation Alice and Bob would have to optimize their source over both the spectral widths of the generated photons and the type of spectral correlation in order to maximally extend the security distance.
The results of our work are, in particular, important for the QKD systems utilizing commercial telecom fibers populated by strong classical signals. In those systems temporal filtering method can be used to reduce not only the dark counts registered by the detection system, but also the channel noise originating from the process of Raman scattering, which is the main factor limiting their performance.
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