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Journal of Naval University of Engineering

Unconditional security boundary of decoy-state quantum key distribution with finite data

Yingjian Wang

Published Jan 1, 2012• 0 citations
OpenAlex

Abstract

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.

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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 quantum key distribution (QKD) allows two parties to share a secret key by typically making use of a one-way quantum channel. However, the two-way QKD has its own unique advantages, which means the two-way QKD has become a focus recently. To improve the practical performance of the two-way QKD, we present a security analysis of a two-way QKD protocol based on the decoy method with heralded single-photon sources (HSPSs). We make use of two approaches to calculate the yield and the quantum bit error rate of single-photon and two-photon pulses. Then we present the secret key generation rate based on the GLLP formula. The numerical simulation shows that the protocol with HSPSs has an advantage in the secure distance compared with weak coherent state sources. In addition, we present the final secret key generation rate of the LM05 protocol with finite resources by considering the statistical fluctuation of the yield and the error rate.
Abstract: The quantum key distribution (QKD) technique establishes secret keys shared between two communicating parties. Theoretically, unconditional security provided by QKD is guaranteed by the fundamental laws of quantum physics. in the real life, it is still possible to obtain unconditionally secure QKD, even with (phase randomized) attenuated laser pulses, as theoretically demonstrated by Gottesman-Lo-L¨utkenhaus-Preskill (GLLP). However, one must pay a steep price by placing severe limits on the distance and the key generation rate. These problems were solved using the decoy state method introduced by Hwang. In this paper, we have proposed a method to estimate parameters of the decoy state method based on two decoy state protocol for both BB84 and SARG04. The vacuum and weak decoy state protocol has been introduced as a special case of two decoy states protocol. This method has given different lower bound of the fraction of single-photon counts (y1), the fraction of two-photon counts (y2), the upper bound QBER of single-photon pulses (e1), the upper bound QBER of two-photon pulses (e2) and the lower bound of key generation rate for both BB84 and SARG04. The fiber based QKD systems also have been simulated using the proposed method for BB84 and SARG04. The numerical simulation has shown that the fiber based QKD systems using the proposed method for BB84 are able to achieve both a higher secret key rate and greater secure distance than that of SARG04. Key words: Quantum cryptography Quantum key distribution Decoy state protocol and optical communications
To increase dramatically the distance and the secure key generation rate of quantum key distribution (QKD), the idea of quantum decoys--signals of different intensities--has recently been proposed. Here, we present the first experimental implementation of decoy state QKD. By making simple modifications to a commercial quantum key distribution system, we show that a secure key generation rate of 165 bit/s, which is 1/4 of the theoretical limit, can be obtained over 15 km of a telecommunication fiber. We also show that with the same experimental parameters, not even a single bit of secure key can be extracted with a non-decoy-state protocol. Compared to building single photon sources, decoy state QKD is a much simpler method for increasing the distance and key generation rate of unconditionally secure QKD.
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.
Nonorthogonal coded agreements and decoy state method can effectively protect the photon number against splitting attack. Owing to the fact that the component of single-photon in the coherent-state superposition (CSS) is as high as 90%, CSS has recently emerged as an alternative to single-photon qubits for quantum information processing and metrology. The approximate CSS of small amplitudes is generated by the subtraction of photons from a squeezed vacuum state, and the approximate CSS of large amplitude is generated from Fock state by using a single homodyne detection. Here, we combine both of the methods and propose a new protocol by using the CSS as a light source. We derive the secure key generation rate, the lower bound of count rate and upper bound of error rate of single-photon. We simulate the curves relationship between secure key generation rate and safety transmission distance in the case of an infinite number of decoy states by using matlab. The parameters are given according to the Gobby-Yuan-Shields (GYS) experiment. We infer that the safety transmission distance achieves 147.4 km and the secure key generation rate is much higher than those of other schemes. We also simulate the relationship between key generation rate and safety transmission distance in the case of a limited number of decoy states by using matlab. The parameters are given according to the GYS experiment too. When the N is 1010, the safety transmission distance achieves 144 km; when the N is 109, the safety transmission distance achieves 139 km; when the N is 108, the safety transmission distance achieves 125.9 km. In this paper, we propose the use of CSS as the light source. Combining SARG04 agreements and decoy state, the scheme has the following advantages: first, the scheme which combines SARG04 agreements and decoy state method can effectively resist PNS; second, nonorthogonal decoy-state quantum key distribution based on coherent-state superpositions has a longer safety transmission distance and higher secure key generation rate than nonorthogonal decoy-state quantum key distribution based on weak coherent pulse and nonorthogonal decoy-state quantum key distribution based on conditionally prepared down-conversion source; third, nonorthogonal decoy-state quantum key distribution based on coherent-state superpositions is easier to prepare, which just needs one decoy state, than other schemes that require several decoy states. Obviously, our scheme can enhance the performance of quantum key distribution. Nonorthogonal decoy-state quantum key distribution based on coherent-state superpositions will have a very good application with the further development of preparation technology of CSS.