A congruence involving products of qq-binomial coefficients

In this paper we establish a $q$-analogue of a congruence of Sun concerning the products of binomial coefficients modulo the square of a prime.Comment: 9 page

Coexistence of continuous variable QKD with intense DWDM classical channels

We demonstrate experimentally the feasibility of continuous variable quantum key distribution (CV-QKD) in dense-wavelength-division multiplexing networks (DWDM), where QKD will typically have to coexist with several co- propagating (forward or backward) C-band classical channels whose launch power is around 0dBm. We have conducted experimental tests of the coexistence of CV-QKD multiplexed with an intense classical channel, for different input powers and different DWDM wavelengths. Over a 25km fiber, a CV-QKD operated over the 1530.12nm channel can tolerate the noise arising from up to 11.5dBm classical channel at 1550.12nm in forward direction (9.7dBm in backward). A positive key rate (0.49kb/s) can be obtained at 75km with classical channel power of respectively -3dBm and -9dBm in forward and backward. Based on these measurements, we have also simulated the excess noise and optimized channel allocation for the integration of CV-QKD in some access networks. We have, for example, shown that CV-QKD could coexist with 5 pairs of channels (with nominal input powers: 2dBm forward and 1dBm backward) over a 25km WDM-PON network. The obtained results demonstrate the outstanding capacity of CV-QKD to coexist with classical signals of realistic intensity in optical networks.Comment: 19 pages, 9 figures. Revised version, to appear in New Journal of Physic