Quantum communication improved by spectral entanglement and supplementary chromatic dispersion

Implementations of many quantum communication protocols require sources of photon pairs. However, optimization of the properties of these photons for specific applications is an open problem. We theoretically demonstrate the possibility of extending the maximal distance of secure quantum communication when a photon pair source and standard fibers are used in a scenario where Alice and Bob do not share a global time reference. It is done by manipulating the spectral correlation within a photon pair and by optimizing chromatic dispersion in transmission links. Contrary to typical expectations, we show that in some situations the secure communication distance can be increased by introducing some extra dispersion.

Figure 1

Sketch of the asymmetric QKD scheme with the source of photon pairs located outside of the laboratories of the legitimate participants of the protocol.

Figure 2

The lower bound of the key generation rate $K$ that can be obtained by Alice and Bob when using the QKD setup pictured in Fig. 1, plotted as a function of Bob's link length $L_B$ for $\xi =12$ (yellow, solid line), $\xi =6$ (red, dashed line), $\xi =3$ (green, dotted line), $\xi =1$ (blue, dot-dashed line), and for the numerically optimized $\xi$ (black, solid line). All of the plots were made for $\rho =0.9$ and $L_A=1\mathrm{km}$.

Figure 3

The lower bound of the key generation rate $K$ that can be obtained by Alice and Bob when using the QKD setup pictured in Fig. 1. It is plotted as a function of Alice's link length $L_A$. The plots show simulation results for fixed correlation coefficient $\rho =0.9$ and five different lengths of Bob's link $L_B$, as indicated in the picture.

Figure 4

Maximal length $L_B$ of Bob's link plotted as a function of the length $L_A$ of Alice's link and the spectral correlation coefficient $\rho$ for which it is possible for the trusted parties to generate a secure key using the setup pictured in Fig. 1. The values displayed in the figure are given in kilometers.

Figure 5

Logarithm of key generation rate, ${log}_{10}K$, plotted as a function of dispersion and losses introduced in Alice's link, calculated for $\rho =0.9$ and (a) $L_B=202\mathrm{km}$, (b) $L_B=210\mathrm{km}$, and (c) $L_B=217\mathrm{km}$. $K$ is nonzero only in the colored area. Blue solid (dashed) line denotes pairs of values of dispersion, ${\beta }_A{L}_A$, and losses, ${\alpha }_A{L}_A$, introduced by a standard SMF fiber (high-dispersion fiber) of different lengths (see text). Black dots correspond to the dispersion-introducing module [28]. For the typical telecommunication photons with wavelength centered around $1550\mathrm{nm}$, the dispersion value of ${10}^{-21}{\mathrm{s}}^2$ on the horizontal scale corresponds to approximately $784\mathrm{ns}/\mathrm{nm}$.

Figure 6

The lower bound of the key generation rate $K$ that can be obtained by Alice and Bob when using the QKD setup pictured in Fig. 1, assuming that there is $e=5\%$ for getting opposite results from their measurements of a given pair of SPDC photons in the right basis. The key generation rate is plotted as a function of Alice's link length $L_A$. The plots show simulation results for a fixed correlation coefficient $\rho =0.9$ and five different lengths of Bob's link $L_B$, as indicated in the picture.