Quantum key distribution session with 16-dimensional photonic states

Abstract

The secure transfer of information is an important problem in modern telecommunications. Quantum key distribution (QKD) provides a solution to this problem by using individual quantum systems to generate correlated bits between remote parties, that can be used to extract a secret key. QKD with D-dimensional quantum channels provides security advantages that grow with increasing D. However, the vast majority of QKD implementations has been restricted to two dimensions. Here we demonstrate the feasibility of using higher dimensions for real-world quantum cryptography by performing, for the first time, a fully automated QKD session based on the BB84 protocol with 16-dimensional quantum states. Information is encoded in the single-photon transverse momentum and the required states are dynamically generated with programmable spatial light modulators. Our setup paves the way for future developments in the field of experimental high-dimensional QKD.

Figure 1. Detection procedure.

(a) Detection apparatus. See the main text for details. (b) Numerical simulation showing the single-photon spatial distribution in the case that Alice and Bob have both chosen the same state in the same MUB α. We have arbitrarily chosen states 13 from MUBs α and α′ and state 7 from α to illustrate the distributions. The dashed blue dotted lines indicate the boundaries of the 10 μm circular pinhole used in front of the detector in the experiment. In this case, the probability of detecting the single-photon is maximum. (c) Alice and Bob choose different states and from the same MUB α. In this case the detection probability is null. (d) The detection probability when two vectors are chosen, from the two distinct MUBs. In this case a detection probability of 1/16 is obtained.

Figure 2. Experimental setup.

The laser light source is followed by an acousto-optic modulator (AOM) which defines the optical pulses repetition frequency and width, see text for details. A FPGA unit is used by Alice to trigger the AOM and randomly project phase-masks in the SLM2 to encode the states required in the 16-dimensional BB84 protocol. Bob has a different FPGA unit to randomly perform the MUBs states projections and to count the single-photon detections at the avalanche photo-detector (APD). The FPGAs are connected between themselves for synchronization. Each FPGA is connected to a personal computer (PC1 and PC2) who perform the basis reconciliation procedure while communicating through an Ethernet cable, which acts as the public channel. The single-photons are transmitted from Alice to Bob through free-space with a telescope system forming the transmission channel (Trans. Channel).

Figure 3. Experimental results.

(a) Number of detections as a function of the number of elapsed hours for the QKD session with μ_a = 0.60 photons per pulse. The detections are broken down into raw key (total detections), sifted key (sum of the detections when Alice and Bob choose the same MUB), N_c (sum of all the detections when the same state from the same MUB is chosen by both Alice and Bob) and N_i (sum of all the detections when different states from the same MUB are chosen). Each row sums up the results of 12 hours of continuous measurements. (b) The measured QBER as a function of continuous elapsed hours of the QKD session with μ_a. Error bars show the statistical error in the calculation of the QBER. The two security thresholds for general collective (D^coh) and individual attacks (D^ind) are also plotted with dotted lines. The average QBER is 13.4 ± 4% with an average sifted key rate of 27.0 bits/hour. (c) The same as part (a) but with μ_b = 0.18 photons per pulse. (d) Same as (b) but with μ_b. The average QBER in this case is 15.6 ± 7% and an average sifted key rate of 11.1 bits/hour. Note, that in both cases the QBER is well below the security thresholds of individual attacks as well as collective attacks.