Rate-loss analysis of an efficient quantum repeater architecture

Abstract

We analyze an entanglement-based quantum key distribution (QKD) architecture that uses a linear chain of quantum repeaters employing photon-pair sources, spectral-multiplexing, linear-optic Bell-state measurements, multi-mode quantum memories and classical-only error correction. Assuming perfect sources, we find an exact expression for the secret-key rate, and an analytical description of how errors propagate through the repeater chain, as a function of various loss and noise parameters of the devices. We show via an explicit analytical calculation, which separately addresses the effects of the principle non-idealities, that this scheme achieves a secret key rate that surpasses the TGW bound-a recently-found fundamental limit to the rate-vs.-loss scaling achievable by any QKD protocol over a direct optical link-thereby providing one of the first rigorous proofs of the efficacy of a repeater protocol. We explicitly calculate the end-to-end shared noisy quantum state generated by the repeater chain, which could be useful for analyzing the performance of other non-QKD quantum protocols that require establishing long-distance entanglement. We evaluate that shared state's fidelity and the achievable entanglement distillation rate, as a function of the number of repeater nodes, total range, and various loss and noise parameters of the system. We extend our theoretical analysis to encompass sources with non-zero two-pair-emission probability, using an efficient exact numerical evaluation of the quantum state propagation and measurements. We expect our results to spur formal rate-loss analysis of other repeater protocols, and also to provide useful abstractions to seed analyses of quantum networks of complex topologies.Shared entanglement underlies many quantum information protocols such as quantum key distribution (QKD) [1], teleportation [2] and dense coding [3], and is a fundamental information resource that can boost reliable classical and quantum communication rates over noisy quantum channels [4,5]. Optical photons are arguably the only candidate for distributing entanglement across long distances. They however are susceptible to loss and noise in the channel, which is the bane of practical realizations of long-distance quantum communication. The maximum entanglement-generation rate over a lossy optical channel with no classical-communication assistance is zero when the total loss exceeds 3 dB [6]. With two-way classical-communication assistance, the rates achievable for entanglement generation, as well as those for reliable quantum communication and secretkey generation (i.e., QKD) over a lossy optical channel must decay linearly with the channel's transmittance (i.e., exponentially with optical fiber length), regardless of the specific protocol used, for loss exceeding ∼ 5 dB [7], while the rate plunges to zero at a maximum loss threshold that is determined by the excess noise in the channel and detectors. In order to generate entanglement over long distances at high rates, intermediate nodes equipped with quant...

Entanglement swapping with quantum-memory-compatible photons

“…To improve our result, we therefore have to decrease the probability of generating a photon pair per pulse below our current value of 19%. For instance, reducing the mean photon pair emission probability to 10% would, according to our model [23], result in an increase of the concurrence to 0.53 (keeping all other parameters unchanged). Note that alternative way to reduce the impact of multi-pair emissions are to exploit a quantum Zeno blockade to suppresses multi photons [37] or a quantum non-demolition measurement that reveals the number of simultaneously emitted photon pairs [38], thereby allowing in theory to completely ignore detections stemming from multi pair emissions.…”

“…To independently assess how experimental imperfections limit the amount of entanglement in the final biphoton state, we employ the method described in [23] with measured experimental parameters for heralding efficiency (1.96% at 795 nm and 5.8% at 1533 nm), HOM visibility (89%), mean photon pair number (19%) and fidelities (95%) for the individual sources. This leads to a density matrix having a concurrence of 0.43, i.e.…”

“…To verify successful entanglement swapping, we measure (conditional) two-photon visibility curves. For more complete information, we additionally employ quantum state tomography to derive the concurrence and the fidelity of the swapped state with the nearest maximally entangled state, and we compare the latter with the predictions of a recently developed model [23]. As with the use of quantum state tomography, this has not been done previously for time-bin qubits after entanglement swapping.…”

Entanglement over global distances via quantum repeaters with satellite links

“…Conventional quantum repeaters rely on first creating and storing entanglement for elementary links and then extending the distance of entanglement by entanglement swapping [7,8]. Based on the experimental and theoretical progress in this area over the past few years, it is plausible that this approach will make it possible to extend the distance of entanglement distribution significantly beyond what is possible with direct transmission through optical fibers [8][9][10]. However, truly global distances are still very difficult to envision for repeaters based on fiber links.…”

Memory-assisted quantum key distribution resilient against multiple-excitation effects

“…The limitation in going to further distances is dictated by the exponentially-growing loss factor in optical fibers [3]. Probabilistic quantum repeaters offer a solution to extend the communication distance to over thousands of kilometers [4][5][6][7][8][9][10]. However, such quantum repeaters rely on quantum memory modules [11] with characteristics that are hard to achieve with the current technology.…”