High-dimensional decoy-state quantum key distribution over multicore telecommunication fibers

Multiplexing is a strategy to augment the transmission capacity of a communication system. It consists of combining multiple signals over the same data channel and it has been very successful in classical communications. However, the use of enhanced channels has only reached limited practicality in quantum communications (QC) as it requires the manipulation of quantum systems of higher dimensions. Considerable effort is being made towards QC using high-dimensional quantum systems encoded into the transverse momentum of single photons, but so far no approach has been proven to be fully compatible with the existing telecommunication fibers. Here we overcome such a challenge and demonstrate a secure high-dimensional decoy-state quantum key distribution session over a 300-m-long multicore optical fiber. The high-dimensional quantum states are defined in terms of the transverse core modes available for the photon transmission over the fiber, and theoretical analyses show that positive secret key rates can be achieved through metropolitan distances.

Figure 1

(a) Experimental setup: Alice encodes the four-dimensional BB84 QKD states using a deformable mirror (DM1). The communication link consists of a 300-m-long four-core multicore fiber. Bob uses a deformable mirror (DM2) and a SPD to implement his measurements. See main text. (b) The multicore fiber's cross section. (c) The deformable mirror is composed of a 6 $\times$ 6 mirror matrix. Light coming from each MCF's core is mapped to an individual mirror. As an example, in (c) cores $|1\rangle ,|3\rangle$, and $|4\rangle$ have a relative phase of 0 applied, while $|2\rangle$ has a $\pi$ relative phase shift. (d) Simulated FF distribution with the pinhole area indicated by red circle. The first case is when Bob's projection is performed on the same state as the one Alice sent. It displays constructive interference. The second case is with an orthogonal projection, leading to no detection. The last case is when Alice and Bob use different MUBs. HWP (QWP): half (quarter) wave plate. PBS: polarizing beamsplitter.

Figure 2

(a) Mean QKD fidelity of the four-dimensional BB84 states transmitted through the 300-m-long multicore fiber. With the control system off, the fidelity slowly degrades. With the control on, the fidelity remains above the threshold, enabling stable QKD sessions. (b) Two examples of measured fidelities after 1.08 hours, for the states $|{\phi }_2^{\left(1\right)}\rangle$ and $|{\phi }_3^{\left(2\right)}\rangle$.

Figure 3

(a) Measured QBER over time (blue dots). The brown line is the average QBER of $10.25\%$. The dashed black and cyan lines are the bounds to achieve positive key rate against individual ($25\%$) and coherent ($18.93\%$) attacks, respectively. (b) Secret key rate (R) as a function of distance for the weak decoy + vacuum protocol. The point is the actual key generation rate in our QKD session.

Figure 4

Secret key rate for $d$-dimensional Hilbert spaces when considering a single-detector and a $d$-detector scheme configuration. Here we perform secret key rate simulations considering the infinite decoy case, while using as input parameters the experimental data from [42]. In the $d$-detector case, as expected, the rate increases for shorter distances and the cutoff point in the secret rate versus distance curve occurs for shorter distances, as $d$ increases. In the single-detector case, the probability of correctly projecting the transmitted state onto itself decreases linearly with $d$, while the information gain per transmitted photon only increases with $O\left[\text{log}\right(d\left)\right]$. Thus, the case of $d=8$ always generates a lower secret key rate when compared to $d=4$. Nonetheless, as shown on the inset, our implementation (i.e., the $d=4$ case) is capable of beating the $d=2$ case.

Figure 5

Schematic setup of a $d$ detector integrated detection scheme for HD-QKD based on MCFs. See text for details.