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arXiv:quant-ph/0612121

Unconditional Security Proof of Decoy-State Quantum Key Distribution with Arbitrary Intensity Error Pattern of Light Pulses

Cheng-Zhi Peng

Published Dec 14, 2006• 0 citations
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Abstract

We show the unconditional security of decoy-state method with whatever intensity error pattern if the intensity upper bound of decoy pulses and intensity lower bound of signal pulses are known. Our result immediately applies to the existing experimental data.

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The decoy-state quantum-key-distribution method(based on a heralded single photon source) is frequently used in experiments serves as an object of study.Using the finite data,it is possible to derive the formula of the lower limit of the single-photon state and the upper limit of the error rate and to obtain the lower limit of key generation rate with unconditional security and the range of secure transmission distance.According to the conclusion drawn from the research,the unconditional security boundary of decoy-state quantum key distribution will be obtained if the number of data-set size is known.The number of transmitted data can also be decided according to the demands for quantum key distribution.In this way,the loop holes in security which are created by finite data can be avoided so as to improve the security and efficiency of quantum key distribution.
The existing theory of decoy-state quantum cryptography assumes the exact control of each state from Alice's source. Such exact control is impossible in practice. We develop the theory of decoy-state method so that it is unconditionally secure even if there are state errors of sources, if the range of a few parameters in the states are known. This theory simplifies the practical implementation of the decoy-state quantum key distribution because the unconditional security can be achieved with a slightly shortened final key, even though the small errors of pulses are not corrected.
The method of decoy-state quantum key distribution requests different intensities of light pulses. Existing theory has assumed exact control of intensities. Here the authors propose a simple protocol which is secure and efficient even there are errors in intensity control. In their protocol, decoy pulses and signal pulses are generated from the same father pulses with a two-value attenuation. Given the upper bound of fluctuation of the father pulses, their protocol is secure provided that the two-value attenuation is done exactly. They propose to use unbalanced beam splitters for a stable attenuation.
We show how to do decoy-state quantum key distribution efficiently with large random errors in the intensity control. We present a theorem for efficiently calculating the lower bound of single-photon counts with many undetermined parameters. In the calculation of the single-photon counts of our protocol, the linear terms of the intensity fluctuation disappear and only the quadratic terms take effect. Given that the intensity fluctuation is upper bounded by $\ifmmode\pm\else\textpm\fi{}5%$, $\ifmmode\pm\else\textpm\fi{}10%$, and $\ifmmode\pm\else\textpm\fi{}15%$, the verified lower bound of the percentage of untagged bits from our protocol is as large as 99.7%, 99.0%, and 97.9% of that from an ideal protocol where the light intensity is exactly controlled.
The use of decoy states in quantum key distribution (QKD) has provided a method for substantially increasing the secret key rate and distance that can be covered by QKD protocols with practical signals. The security analysis of these schemes, however, leaves open the possibility that the development of better proof techniques or better classical postprocessing methods might further improve their performance in realistic scenarios. In this paper, we derive upper bounds on the secure key rate for decoy-state QKD. These bounds are based basically only on the classical correlations established by the legitimate users during the quantum communication phase of the protocol. The only assumption about the possible postprocessing methods is that double click events are randomly assigned to single click events. Further, we consider only secure key rates based on the uncalibrated device scenario which assigns imperfections such as detection inefficiency to the eavesdropper. Our analysis relies on two preconditions for secure two-way and one-way QKD. The legitimate users need to prove that there exists no separable state (in the case of two-way QKD) or that there exists no quantum state having a symmetric extension (one-way QKD) that is compatible with the available measurements results. Both criteria have been previously applied to evaluate single-photon implementations of QKD. Here we use them to investigate a realistic source of weak coherent pulses. The resulting upper bounds can be formulated as a convex optimization problem known as a semidefinite program which can be efficiently solved. For the standard four-state QKD protocol, they are quite close to known lower bounds, thus showing that there are clear limits to the further improvement of classical postprocessing techniques in decoy-state QKD.
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.