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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Establishing security of quantum key distribution without monitoring disturbance

Masato Koashi

Published Oct 13, 2015• 0 citations
Publisher

Abstract

In conventional quantum key distribution (QKD) protocols, the information leak to an eavesdropper is estimated through the basic principle of quantum mechanics dictated in the original version of Heisenberg's uncertainty principle. The amount of leaked information on a shared sifted key is bounded from above essentially by using information-disturbance trade-off relations, based on the amount of signal disturbance measured via randomly sampled or inserted probe signals. Here we discuss an entirely different avenue toward the private communication, which does not rely on the information disturbance trade-off relations and hence does not require a monitoring of signal disturbance. The independence of the amount of privacy amplification from that of disturbance tends to give it a high tolerance on the channel noises. The lifting of the burden of precise statistical estimation of disturbance leads to a favorable finite-key-size effect. A protocol based on the novel principle can be implemented by only using photon detectors and classical optics tools: a laser, a phase modulator, and an interferometer. The protocol resembles the differential-phase-shift QKD protocol in that both share a simple binary phase shift keying on a coherent train of weak pulses from a laser. The difference lies in the use of a variable-delay interferometer in the new protocol, which randomly changes the combination of pulse pairs to be superposed. This extra randomness has turned out to be enough to upper-bound the information extracted by the eavesdropper, regardless of how they have disturbed the quantum signal.

DOI
10.1117/12.2197813

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In conventional quantum key distribution (QKD) protocols, the information leak to an eavesdropper is estimated through the basic principle of quantum mechanics dictated in the original version of Heisenberg's uncertainty principle. The amount of leaked information on a shared sifted key is bounded from above essentially by using information-disturbance trade-off relations, based on the amount of signal disturbance measured via randomly sampled or inserted probe signals. Here we discuss an entirely different avenue toward the private communication, which does not rely on the information disturbance trade-off relations and hence does not require a monitoring of signal disturbance. The independence of the amount of privacy amplification from that of disturbance tends to give it a high tolerance on the channel noises. The lifting of the burden of precise statistical estimation of disturbance leads to a favorable finite-key-size effect. A protocol based on the novel principle can be implemented by only using photon detectors and classical optics tools: a laser, a phase modulator, and an interferometer. The protocol resembles the differential-phase-shift QKD protocol in that both share a simple binary phase shift keying on a coherent train of weak pulses from a laser. The difference lies in the use of a variable-delay interferometer in the new protocol, which randomly changes the combination of pulse pairs to be superposed. This extra randomness has turned out to be enough to upper-bound the information extracted by the eavesdropper, regardless of how they have disturbed the quantum signal.
We propose a new scheme of quantum key distribution (QKD) called the round-robin differential-phase-shift (RRDPS) protocol, which is based on a principle entirely different from the conventional QKD protocols based on the information-disturbance trade off. In the RRDPS protocol, the amount of privacy amplification is essentially constant and there is no need to change it according to the observed amount of disturbance. This means that it is hard for an eavesdropper to guess the bit value regardless of the amount of disturbance she has caused. The new scheme has a better tolerance on bit errors and is free from the cost of monitoring eavesdropping attempts. In contrast to the conventional QKD schemes, the amount of privacy amplification is the same even if the quality of the transmission channel becomes poorer and the bit error rate increases. This leads to a higher bit error threshold, typically over 30% and with no theoretical bound less than 50%. The fact that the protocol does not require precise estimation of the amount of signal disturbance is advantageous when the finite-key effect is taken into account; the RRDPS protocol can produce a key even when the total number of transmitted bits is small.
Quantum cryptograph exploits the fundamental laws of quantum mechanics to provide a secure way to exchange private information. Such an exchange requires a common random bit sequence, called a key, to be shared secretly between the sender and the receiver. The basic idea behind quantum key distribution (QKD) has widely been understood as the property that any attempt to distinguish encoded quantum states causes a disturbance in the signal. As a result, implementation of a QKD protocol involves an estimation of the experimental parameters influenced by the eavesdropper’s intervention, which is achieved by randomly sampling the signal. If the estimation of many parameters with high precision is required, the portion of the signal that is sacrificed increases, thus decreasing the efficiency of the protocol. Here we propose a QKD protocol based on an entirely different principle. The sender encodes a bit sequence onto non-orthogonal quantum states and the receiver randomly dictates how a single bit should be calculated from the sequence. The eavesdropper, who is unable to learn the whole of the sequence, cannot guess the bit value correctly. An achievable rate of secure key distribution is calculated by considering complementary choices between quantum measurements of two conjugate observables. We found that a practical implementation using a laser pulse train achieves a key rate comparable to a decoy-state QKD protocol, an often-used technique for lasers. It also has a better tolerance of bit errors and of finite-sized-key effects. We anticipate that this finding will give new insight into how the probabilistic nature of quantum mechanics can be related to secure communication, and will facilitate the simple and efficient use of conventional lasers for QKD.
The security of quantum key distribution (QKD) relies on the Heisenberg uncertainty principle, with which legitimate users are able to estimate information leakage by monitoring the disturbance of the transmitted quantum signals. Normally, the disturbance is reflected as bit flip errors in the sifted key; thus, privacy amplification, which removes any leaked information from the key, generally depends on the bit error rate. Recently, a round-robin differential-phase-shift QKD protocol for which privacy amplification does not rely on the bit error rate [Nature 509, 475 (2014)] was proposed. The amount of leaked information can be bounded by the sender during the state-preparation stage and hence, is independent of the behaviour of the unreliable quantum channel. Considering the essence of this protocol, we present a tight bound on the key rate and employ a decoy-state method. The effects of background noise and misalignment are taken into account under practical conditions. Our simulation results show that the protocol can tolerate channel error rates of close to 50% within a typical experiment setting. That is, there is no restriction on the error rate in practice.
The security of quantum key distribution (QKD) relies on the Heisenberg uncertainty principle, with which legitimate users are able to estimate information leakage by monitoring the disturbance of the transmitted quantum signals. Normally, the disturbance is reflected as bit flip errors in the sifted key; thus, privacy amplification, which removes any leaked information from the key, generally depends on the bit error rate. Recently, a round-robin differential-phase-shift QKD protocol for which privacy amplification does not rely on the bit error rate (Sasaki et al 2014 Nature 509 475) was proposed. The amount of leaked information can be bounded by the sender during the state-preparation stage and hence, is independent of the behavior of the unreliable quantum channel. In our work, we apply the tagging technique to the protocol and present a tight bound on the key rate and employ a decoy-state method. The effects of background noise and misalignment are taken into account under practical conditions. Our simulation results show that the protocol can tolerate channel error rates close to 50% within a typical experiment setting. That is, there is a negligible restriction on the error rate in practice.