Fundamental Limits of Repeaterless Quantum Communications

Fundamental Limits of Repeaterless Quantum Communications

24 Jan 2017 | Stefano Pirandola, Riccardo Laurenza, Carlo Ottaviani, Leonardo Banchi
The paper presents the fundamental limits of repeaterless quantum communications, establishing the optimal point-to-point rates achievable by two remote parties without quantum repeaters. By combining the relative entropy of entanglement (REE) with a technique called "teleportation stretching," the authors derive upper bounds for key capacities in various fundamental quantum channels, including bosonic lossy channels, quantum-limited amplifiers, dephasing, and erasure channels. These results provide precise benchmarks for quantum repeaters and characterize the fundamental rate-loss trade-off in quantum key distribution (QKD). The study shows that for the erasure channel, the secret key capacity is $ K = 1 - p $, where $ p $ is the erasure probability. For the dephasing channel, the two-way quantum and secret key capacities are $ Q_2 = K = 1 - H_2(p) $, where $ H_2(p) $ is the binary Shannon entropy. For a quantum-limited amplifier, $ Q_2 = K = -\log_2(1 - g^{-1}) $, where $ g $ is the gain. For a lossy channel, $ Q_2 = K = -\log_2(1 - \eta) $, where $ \eta $ is the transmissivity. These results close a long-standing investigation in quantum communications, providing the ultimate limits for secure quantum optical communications. The study also shows that the secret key capacity of the lossy channel determines the maximum rate achievable in QKD, with a scaling of $ K \simeq 1.44\eta $ secret bits per channel use at high loss. The results are applicable to both discrete-variable (DV) and continuous-variable (CV) systems and provide a general framework for understanding the limits of quantum communications without repeaters.The paper presents the fundamental limits of repeaterless quantum communications, establishing the optimal point-to-point rates achievable by two remote parties without quantum repeaters. By combining the relative entropy of entanglement (REE) with a technique called "teleportation stretching," the authors derive upper bounds for key capacities in various fundamental quantum channels, including bosonic lossy channels, quantum-limited amplifiers, dephasing, and erasure channels. These results provide precise benchmarks for quantum repeaters and characterize the fundamental rate-loss trade-off in quantum key distribution (QKD). The study shows that for the erasure channel, the secret key capacity is $ K = 1 - p $, where $ p $ is the erasure probability. For the dephasing channel, the two-way quantum and secret key capacities are $ Q_2 = K = 1 - H_2(p) $, where $ H_2(p) $ is the binary Shannon entropy. For a quantum-limited amplifier, $ Q_2 = K = -\log_2(1 - g^{-1}) $, where $ g $ is the gain. For a lossy channel, $ Q_2 = K = -\log_2(1 - \eta) $, where $ \eta $ is the transmissivity. These results close a long-standing investigation in quantum communications, providing the ultimate limits for secure quantum optical communications. The study also shows that the secret key capacity of the lossy channel determines the maximum rate achievable in QKD, with a scaling of $ K \simeq 1.44\eta $ secret bits per channel use at high loss. The results are applicable to both discrete-variable (DV) and continuous-variable (CV) systems and provide a general framework for understanding the limits of quantum communications without repeaters.
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[slides and audio] Fundamental limits of repeaterless quantum communications