This paper addresses multi-user quantum key distribution networks, in which any two users can mutually exchange a secret key without trusting any other nodes. The same network also supports conventional classical communications by assigning two diffe
rent wavelength bands to quantum and classical signals. Time and code division multiple access (CDMA) techniques, within a passive star network, are considered. In the case of CDMA, it turns out that the optimal performance is achieved at a unity code weight. A listen-before-send protocol is then proposed to improve secret key generation rates in this case. Finally, a hybrid setup with wavelength routers and passive optical networks, which can support a large number of users, is considered and analyzed.
A feasible route towards implementing long-distance quantum key distribution (QKD) systems relies on probabilistic schemes for entanglement distribution and swapping as proposed in the work of Duan, Lukin, Cirac, and Zoller (DLCZ) [Nature 414, 413 (2
001)]. Here, we calculate the conditional throughput and fidelity of entanglement for DLCZ quantum repeaters, by accounting for the DLCZ self-purification property, in the presence of multiple excitations in the ensemble memories as well as loss and other sources of inefficiency in the channel and measurement modules. We then use our results to find the generation rate of secure key bits for QKD systems that rely on DLCZ quantum repeaters. We compare the key generation rate per logical memory employed in the two cases of with and without a repeater node. We find the cross-over distance beyond which the repeater system outperforms the non-repeater one. That provides us with the optimum inter-node distancing in quantum repeater systems. We also find the optimal excitation probability at which the QKD rate peaks. Such an optimum probability, in most regimes of interest, is insensitive to the total distance.
Memory dephasing and its impact on the rate of entanglement generation in quantum repeaters is addressed. For systems that rely on probabilistic schemes for entanglement distribution and connection, we estimate the maximum achievable rate per employe
d memory for our optimized partial nesting protocol. We show that, for any given distance $L$, the polynomial scaling of rate with distance can only be achieved if quantum memories with coherence times on the order of $L/c$ or longer, with $c$ being the speed of light in the channel, are available. The above rate degrades as a power of $exp[-sqrt{(L/c)/ tau_c}]$ with distance when the coherence time $tau_c ll L/c$.
Any characterization of a single-photon source is not complete without specifying its second-order degree of coherence, i.e., its $g^{(2)}$ function. An accurate measurement of such coherence functions commonly requires high-precision single-photon d
etectors, in whose absence, only time-averaged measurements are possible. It is not clear, however, how the resulting time-averaged quantities can be used to properly characterize the source. In this paper, we investigate this issue for a heralded source of single photons that relies on continuous-wave parametric down-conversion. By accounting for major shortcomings of the source and the detectors--i.e., the multiple-photon emissions of the source, the time resolution of photodetectors, and our chosen width of coincidence window--our theory enables us to infer the true source properties from imperfect measurements. Our theoretical results are corroborated by an experimental demonstration using a PPKTP crystal pumped by a blue laser, that results in a single-photon generation rate about 1.2 millions per second per milliwatt of pump power. This work takes an important step toward the standardization of such heralded single-photon sources.
Single-photon sources (SPSs) are mainly characterized by the minimum value of their second-order coherence function, viz. their $g^{(2)}$ function. A precise measurement of $g^{(2)}$ may, however, require high time-resolution devices, in whose absenc
e, only time-averaged measurements are accessible. These time-averaged measures, standing alone, do not carry sufficient information for proper characterization of SPSs. Here, we develop a theory, corroborated by an experiment, that allows us to scrutinize the coherence properties of heralded SPSs that rely on continuous-wave parametric down-conversion. Our proposed measures and analysis enable proper standardization of such SPSs.
