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arXiv:0711.3526 · Physical Review A

Unconditionally secure quantum key distribution with relatively strong signal pulse

Kiyoshi Tamaki

Published Mar 26, 2008• 12 citations
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Abstract

We propose an unconditionally secure quantum key distribution protocol, which uses a relatively strong signal pulse. While our protocol shares similar security bases as the Bennett 1992 protocol with a strong reference pulse, our scheme uses a smaller number of detectors and it is robust against Rayleigh scattering in an optical fiber. We derive a lower bound of secret key generation rate of our protocol and show that our protocol can cover relatively long distances, assuming precise phase modulations and stable interferometers.

DOI
10.1103/physreva.77.032341

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We propose an unconditionally secure quantum key distribution protocol, which uses a relatively strong signal pulse. While our protocol shares similar security bases as the Bennett 1992 protocol with a strong reference pulse, our scheme uses a smaller number of detectors and it is robust against Rayleigh scattering in an optical fiber. We derive a lower bound of secret key generation rate of our protocol and show that our protocol can cover relatively long distances, assuming precise phase modulations and stable interferometers.
We prove the unconditional security of the original Bennett 1992 protocol with strong reference pulse. We show that we may place a projection onto suitably defined qubit spaces before the receiver, which makes the analysis as simple as qubit-based protocols. Unlike the single-photon-based qubits, the qubits identified in this scheme are almost surely detected by the receiver even after a lossy channel. This leads to the key generation rate that is proportional to the channel transmission rate for proper choices of experimental parameters.
In the BB84 protocol with a perfect single photon source, the key rate decreases linearly with the transmission η of the channel. If we simply replace this source with a weak coherent-state pulse, the key rate drops more rapidly (as O(η2)) since the presence of multiple photons favors the eavesdropper. Here we discuss the unconditional security of a quantum key distribution protocol in which bit values are encoded in the phase of a weak coherent-state pulse relative to a strong reference pulse, which is essentially the one proposed by Bennett in 1992 (the B92 scheme). We show that in the limit of high loss in the transmission channel, we can construct a secret key with a rate proportional to the transmission η of the channel.
Quantum key distribution provides a promising solution for sharing secure keys between two distant parties with unconditional security. Nevertheless, quantum key distribution is still severely threatened by the imperfections of devices. In particular, the classical pulse correlation threatens security when sending decoy states. To address this problem and simplify experimental requirements, we propose a phase-matching quantum key distribution protocol without intensity modulation. Instead of using decoy states, we propose an alternative method to estimate the theoretical upper bound on the phase error rate contributed by even-photon-number components. Simulation results show that the transmission distance of our protocol could reach 305 km in telecommunication fiber. Furthermore, we perform a proof-of-principle experiment to demonstrate the feasibility of our protocol, and the key rate reaches 22.5 bit/s under a 45-dB channel loss. Addressing the security loophole of pulse intensity correlation and replacing continuous random phase with a six- or eight-slice random phase, our protocol provides a promising solution for constructing quantum networks.
We discuss the unconditional security of a quantum key distribution protocol in which bit values are encoded in the phase of a weak coherent-state pulse relative to a strong reference pulse, which is essentially the one proposed by Bennett in 1992 (the B92 scheme). In the BB84 protocol with a perfect single photon source, the key rate decreases linearly with the transmission T of the channel. If we simply replace this source with a weak coherent-state pulse, the key rate drops more rapidly (as O(η2)) since the presence of multiple photons favors the eavesdropper, Eve. The B92 protocol, if modified to be encoded on the polarization of a single photon, also shows O(η2) dependence. This comes from Eve's option of sending the vacuum state, which is always registered as an inconclusive result and never causes bit errors. In the original B92 scheme with phase coding, Eve has no such option--replacing the weak pulse by the vacuum cannot avoid errors completely, thanks to the strong reference pulse. This should make the scheme stronger against the loss in the channel even coherent-state pulses from conventional lasers are used. We have obtained an unconditional security proof allowing the presence of small bit errors, and confirmed the above observation in a rigorous way. The key rate is found to drop linearly with the transmission η, and it is lower than the BB84 with a perfect single-photon source only by a constant.