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arXiv:1904.08403

Round robin differential phase shift quantum key distribution with yes-no detectors only

Cong, Jiang, Zong‐Wen Yu, Xiang‐Bin Wang

Published Apr 17, 2019• 1 citation
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Abstract

In the original round-robin differential-phase-shift (RRDPS) quantum key distribution and its improved method, the photon-number-resolving detectors are must for the security. We present a RRDPS protocol with yes-no detectors only. We get the upper bounds of mutual information of Alice and Eve, and Bob and Eve, and the formula of key rate. Our main idea is to divide all counts into two classes, the counts due to the odd number photons of incident detectors and the counts due to the even number photons of incident detectors. The fact that the bit-flip error rate of the later class is certainly $50\%$ makes it possible for us to perform a tightened estimation of the upper bound of the leakage information. The robustness of original RRDPS against source flaws such as side-channel attacks still holds for the RRDPS with yes-no detectors. The simulation results show that the key rate of RRDPS with yes-no detectors is close to that of RRDPS with photon-number-resolving detectors. Our results make the RRDPS protocol much more practical.

DOI
10.48550/arxiv.1904.08403

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In the original round-robin differential-phase-shift (RRDPS) quantum key distribution and its improved method, the photon-number-resolving detectors are must for the security. We present a RRDPS protocol with yes-no detectors only. We get the upper bounds of mutual information of Alice and Eve, and Bob and Eve, and the formula of key rate. Our main idea is to divide all counts into two classes, the counts due to the odd number photons of incident detectors and the counts due to the even number photons of incident detectors. The fact that the bit-flip error rate of the later class is certainly 50%50\%50% makes it possible for us to perform a tightened estimation of the upper bound of the leakage information. The robustness of original RRDPS against source flaws such as side-channel attacks still holds for the RRDPS with yes-no detectors. The simulation results show that the key rate of RRDPS with yes-no detectors is close to that of RRDPS with photon-number-resolving detectors. Our results make the RRDPS protocol much more practical.
The round-robin-differential-phase-shift (RRDPS) quantum key distribution (QKD) protocol has attracted intensive study due to its distinct security characteristics; e.g., information leakage is bounded without learning the error rate of key bits. Nevertheless, its practicality and performance are still not satisfactory. Here, by observing the phase randomization of the encoding states and its connection with eavesdropper's attack, we develop an improved bound on information leakage. Interestingly, our theory is especially useful for implementations with short trains of pulses, and running without monitoring signal disturbance is still available. As a result, the practicality and performance of RRDPS are improved. Furthermore, we realize a proof-of-principle experiment with up to 140 km of fiber, which has been the longest achievable distance of RRDPS until now, whereas the original theory predicted that no secret key could be generated in our experiment. Our results will help in bringing practical RRDPS closer to practical implementations.
Among many quantum key distribution protocols, the round-robin differential-phase-shift (RRDPS) protocol is unique in that it can upper-bound the amount of information leakage without monitoring signal disturbance. To expedite implementation of the protocol, however, the number of pulses forming a single block should be kept small, which significantly decreases the key rates in the original security proof. In the present paper, we refine the security proof of the RRDPS protocol in the finite-sized regime and achieve a tighter estimation for the information leakage with neither monitoring signal disturbance nor changing the original experimental setups. As a consequence, we obtain better key rates in both asymptotic and finite-sized cases while keeping the preferable features of the protocol, such as omission of phase randomization.
Quantum key distribution (QKD) offers the possibility for two individuals to communicate a securely encrypted message. A common technical requirement is the monitoring of signal disturbance in a QKD system to bound the information leakage toward an unwanted eavesdropper. Recently, the round-robin differential-phase-shift (RRDPS) protocol, which encodes bits of information in a high-dimensional state space, was proposed to introduce an upper bound on the amount of Eve's information based on dimensionality of prepared quantum states and randomized measurement settings. Since its introduction, many realizations of the RRDPS protocol were demonstrated using trains of coherent pulses (time bin encoding). Given that this realization of the protocol requires active and random choice of many delays in a delayed Mach-Zehnder interferometer, its implementation can be technically demanding. Here, we propose and experimentally demonstrate an implementation of the RRDPS protocol using the photonic orbital angular momentum degree of freedom in dimensions L=3L=3L=3--8, 16, 32, and 64. In particular, we show that Alice's generation stage and Bob's detection stage can each be reduced to a single phase element, greatly simplifying the implementation. Our scheme offers a practical path to using RRDPS protocol in free-space quantum channels.
By introducing four-phase modulations into round-robin-differential-phase-shift (RRDPS) quantum key distribution (QKD) protocol, the round-robin-differential-quadrature-phase-shift (RRDQPS) protocol is proposed. According to the security proof of RRDQPS protocol, it is able to tolerate a higher error rate of key bits. However, its performance with a practical weak coherent source is still unknown since that security proof only applies to a single photon source. In this article, we give the security proof for the general nnn-photon RRDQPS protocol, by which RRDQPS with a practical weak coherent source becomes feasible in the experiment. Through numerical simulation, it is verified that RRDQPS protocol has an advantage over RRDPS protocol on transmission distance, especially when the pulse number is small.
We give a security proof of the ‘round-robin differential phase shift’ (RRDPS) quantum key distribution scheme, and we give a tight bound on the required amount of privacy amplification. Our proof consists of the following steps. We construct an EPR variant of the scheme. We show that the RRDPS protocol is equivalent to RRDPS with basis permutation and phase flips performed by Alice and Bob; this causes a symmetrization of Eve’s state. We identify Eve’s optimal way of coupling an ancilla to an EPR qudit pair under the constraint that the bit error rate between Alice and Bob should not exceed a value β\beta β . As a function of β\beta β , we derive, for non-asymptotic key size, the trace distance between the real state and a state in which no leakage exists. We invoke post-selection in order to go from qudit-wise attacks to general attacks. For asymptotic key size, we obtain a bound on the trace distance based on the von Neumann entropy. Our asymptotic result for the privacy amplification is sharper than existing bounds. At low qudit dimension, even our non-asymptotic result is sharper than existing asymptotic bounds.
Recently, a novel protocol named round-robin differential phase-shift (RRDPS) quantum key distribution [Nature 509, 475(2014)] has been proposed. It can estimate information leakage without monitoring bit error rate. In this paper, we study the performance of RRDPS using heralded single photon source (HSPS) without and with decoy-state method, then compare it with the performance of weak coherent pulses (WCPs). From numerical simulation, we can see that HSPS performs better especially for shorter packet and higher bit error rate. Moreover, we propose a general theory of decoy-state method for RRDPS protocol based on only three decoy states and one signal state. Taking WCPs as an example, the three-intensity decoy-state protocol can distribute secret keys over a distance of 128 km when the length of pulses packet is 32, which confirms great practical interest of our method.