Fundamental limits of repeaterless quantum communications

Abstract

Quantum communications promises reliable transmission of quantum information, efficient distribution of entanglement and generation of completely secure keys. For all these tasks, we need to determine the optimal point-to-point rates that are achievable by two remote parties at the ends of a quantum channel, without restrictions on their local operations and classical communication, which can be unlimited and two-way. These two-way assisted capacities represent the ultimate rates that are reachable without quantum repeaters. Here, by constructing an upper bound based on the relative entropy of entanglement and devising a dimension-independent technique dubbed ‘teleportation stretching', we establish these capacities for many fundamental channels, namely bosonic lossy channels, quantum-limited amplifiers, dephasing and erasure channels in arbitrary dimension. In particular, we exactly determine the fundamental rate-loss tradeoff affecting any protocol of quantum key distribution. Our findings set the limits of point-to-point quantum communications and provide precise and general benchmarks for quantum repeaters.

General bounds for sender-receiver capacities in multipoint quantum communications

“…[31] proved that D 2 = Q 2 = K = − log 2 (1 − η) corresponding to ≃ 1.44η bits per channel use at high loss. The latter result completely characterizes the fundamental rate-loss scaling that affects any point-to-point protocol of QKD through a lossy communication line, such as an optical fiber or free-space link.…”

“…Only recently, after about 20 years [30], Ref. [31] finally addressed this problem and established the two-way capacities at which two remote parties can distribute entanglement (D 2 ), transmit quantum information (Q 2 ), and generate secret keys (K) over a number of fundamental quantum channels at both finite and infinite dimension, including erasure channels, dephasing channels, bosonic lossy channels and quantum-limited amplifiers. For a review of these results, see also Ref.…”

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

“…Specifically, we first calculate the secret key rate with the assumption that ideal quantum memories, meaning those that feature no limitations in performance, are employed. We compare the secret key rate per pulse of both schemes with the maximum rate achievable over a lossy channel, as obtained in [51]. We refer to this bound by the PLOB acronym.…”

“…In section 3, we study the performance of these setups by calculating their secret key rates. In section 4, we present our numerical results by comparing the key rate with the fundamental rate bounds for the distribution of secure keys over a lossy channel found in [51]. We also determine the secret key rate of the quasi-EPR-based setup for different types of ensemble-based quantum memories and we compare the rate with that of no-memory systems.…”

Gaussian one-way thermal quantum cryptography with finite-size effects

“…The increasing attention received by CV-QKD in recent years is justified by the relative simplicity of the experimental setup, and the very high key-rate achievable, which can be close to the secret-key capacity of an optical communication channel, also known as PLOB bound [39,42,43]. Moreover, the possibility of implementing communications exploiting all the electromagnetic spectrum represents an additional appealing feature of CV systems.…”