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arXiv:1509.04011 · Physical Review A

Reexamination of decoy-state quantum key distribution with biased bases

Zong‐Wen Yu, Yi-Heng Zhou, Xiang‐Bin Wang

Published Mar 7, 2016• 29 citations
arXivHTMLPDF

Abstract

In order to improve the key rate of the decoy-state method, we need to jointly study yields of different bases. Given the delicate fact that pulses of the same preparation state can have different counting rates if they are measured in different bases, for example, those vacuum pulses and those single-photon pulses, existing results of decoy-state quantum key distribution using biased bases are actually flawed by assuming that they are equal. We fix this flaw through using the idea that yields of pulses prepared in different bases are the same provided that they are prepared in the same state and also measured in the same basis, for example, those single-photon pulses prepared in different bases but measured in the same basis. Based on this, we present correct formulas for the decoy-state method using biased bases. Taking the effects of statistical fluctuations into account, we then numerically study the key rates of different protocols with all parameters being fully optimized. Our result confirms the prior conclusion that the decoy-state method using biased bases can have an advantage over the symmetric protocol with unbiased bases. We obtain high key rates of our four-intensity protocol without using any vacuum source.

DOI
10.1103/physreva.93.032307

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•Mar 6, 2024•1 citation
In order to improve the key rate of the decoy-state method, we need to jointly study yields of different bases. Given the delicate fact that pulses of the same preparation state can have different counting rates if they are measured in different bases, for example, those vacuum pulses and those single-photon pulses, existing results of decoy-state quantum key distribution using biased bases are actually flawed by assuming that they are equal. We fix this flaw through using the idea that yields of pulses prepared in different bases are the same provided that they are prepared in the same state and also measured in the same basis, for example, those single-photon pulses prepared in different bases but measured in the same basis. Based on this, we present correct formulas for the decoy-state method using biased bases. Taking the effects of statistical fluctuations into account, we then numerically study the key rates of different protocols with all parameters being fully optimized. Our result confirms the prior conclusion that the decoy-state method using biased bases can have an advantage over the symmetric protocol with unbiased bases. We obtain high key rates of our four-intensity protocol without using any vacuum source.
The decoy-state method closes source security loopholes in quantum key distribution (QKD) using a laser source. In this method, accurate estimates of the detection rates of vacuum and single-photon events plus the error rate of single-photon events are needed to give a good enough lower bound of the secret key rate. Nonetheless, the current estimation method for these detection and error rates, which uses three types of photon intensities, is accurate up to about 11%1 relative error. Here I report an experimentally feasible way that greatly improves these estimates and hence increases the one-way key rate of the BB84 QKD protocol with unbiased bases selection by at least 20% on average in realistic settings. The major tricks are the use of more than three types of photon intensities plus the fact that estimating bounds of the above detection and error rates is numerically stable, although these bounds are related to the inversion of a high condition number matrix.
We propose a quantum key distribution scheme that combines a biased basis choice with the decoy-state method. In this scheme, Alice sends all signal states in the Z basis and decoy states in the X and Z basis with certain probabilities, and Bob measures received pulses with optimal basis choice. This scheme simplifies the system and reduces the random number consumption. From the simulation result taking into account of statistical fluctuations, we find that in a typical experimental setup, the proposed scheme can increase the key rate by at least 45% comparing to the standard decoy-state scheme. In the postprocessing, we also apply a rigorous method to upper bound the phase error rate of the single-photon components of signal states.
We show that the three-intensity protocol for measurement device independent quantum key distribution (MDI QKD) can be done with different light intensities in {\em only one} basis. Given the fact that the exact values yields of single-photon pairs in the XXX and ZZZ bases must be the same, if we have lower bound of the value in one basis, we can also use this as the lower bound in another basis. Since in the existing set-up for MDI-QKD, the yield of sources in different bases are normally different, therefore our method can improve the key rate drastically if we choose to only use the lower bound of yield of single-photon pairs in the advantageous basis. Moreover, since our proposal here uses fewer intensities of light, the probability of intensity mismatch will be smaller than the existing protocols do. This will further improve the advantage of our method. The advantage of using Z basis or X basis of our method is studied and significant improvement of key rates are numerically demonstrated.
In the original BB84 quantum key distribution protocol, the states are prepared and measured randomly, which lose the unmatched detection results. To improve the sifting efficiency, biased bases selection BB84 protocol is proposed. Meanwhile, a practical quantum key distribution protocol can only transmit a finite number of signals, resulting in keys of finite length. The previous techniques for finite-key analysis focus mainly on the statistical fluctuations of the error rates and yields of the qubits. However, the prior choice probabilities of the two bases also have fluctuations by taking into account the finite-size effect. In this paper, we discuss the security of biased decoy state BB84 protocol with finite resources by considering all of the statistical fluctuations. The results can be directly used in the experimental realizations.
Abstract Ideal quantum key distribution (QKD) protocols require perfect single photon sources, detectors, and lossless channels. However, the present technology cannot ensure all of the requirements. Among the variants of practical QKD schemes, decoy state QKD in its present form approaches nearly the theoretical security. In any decoy state method, a compromise is made between the security of the key distribution and the rate of key generation by optimizing the two major protocol parameters: the number of decoy states and their relative intensities, and the length of the data string as well. Use of more number of decoy states and higher range of intensities though improve security, their optimization becomes too complex. Therefore, from practical consideration, some restrictions are to be imposed on the choice of decoy states and their intensities. In addition, the treatment of correlations among the laser pulses in security analysis is not fully understood. Normally, lack of correlations or randomness among the signal states is considered to gain security, but, in a different approach, described in the proposed protocol, additional correlation is introduced to improve key generation rate without compromising security. To do that, a one-way function is shared among the legitimate users to provide a semi-random choice of bases depending on the outcome of the receiver’s detector. The initial communication is made through a set of bits with predefined bases and intensity distribution. Then, with the help of the positive outcome of the receiver’s detector, the basis set as well as the length of the bit string for subsequent communications are computed. This results in correlation among the bases and the relative intensities of the signal states and provides a self-checking mechanism to identify eavesdropping. The security analysis of the protocol provides a low error rate and a relatively high key generation rate.