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.
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.
The decoy-state method in quantum key distribution (QKD) is a popular technique to approximately achieve the performance of ideal single-photon sources by means of simpler and practical laser sources. In high-speed decoy-state QKD systems, however, intensity correlations between succeeding pulses leak information about the users' intensity settings, thus invalidating a key assumption of this approach. Here, we solve this pressing problem by developing a general technique to incorporate arbitrary intensity correlations to the security analysis of decoy-state QKD. This technique only requires to experimentally quantify two main parameters: the correlation range and the maximum relative deviation between the selected and the actually emitted intensities. As a side contribution, we provide a non-standard derivation of the asymptotic secret key rate formula from the non-asymptotic one, in so revealing a necessary condition for the significance of the former.
The passive decoy scheme represents a quantum key distribution protocol that employs a photon number resolving detector to selectively extract the decoy states from the signal states during post-processing. This selection process ensures resilience against attacks capable of distinguishing between these two states, thereby enhancing the security of the protocol. Previous research has emphasized the good performance of the protocol under optimal conditions. However, our study focuses on numerically evaluating the protocol performance in various practical scenarios. We aim to understand the implications of these scenarios in terms of the maximum attainable attenuation and bit rate per second, considering the number of photons per pulse sent under specific experimental conditions. Our findings demonstrate that opting for a low average photon number value ensures high tolerance to attenuation during communication, albeit at the cost of a reduced bit rate per second. Conversely, for lower attenuations, it is more advantageous to increase the average number of photons, even if it deviates from the ideal behaviour of a single-photon source. The benefit of selecting the decoy states at the end of the transmission remains consistent across different configurations. This research signifies an advancement in assessing the viability of incorporating the protocol within a practical QKD network.
Abstract Quantum key distribution (QKD) protocols allow for information theoretically secure distribution of (classical) cryptographic key material. However, due to practical limitations the performance of QKD implementations is somewhat restricted. For this reason, it is crucial to find optimal protocol parameters, while guaranteeing information theoretic security. The performance of a QKD implementation is determined by the tightness of the underlying security analysis. In particular, the security analyses determines thekey-rate, i.e., the amount of cryptographic key material that can be distributed per time unit. Nowadays, the security analyses of various QKD protocols are well understood. It is known that optimal protocol parameters, such as the number of decoy states and their intensities, can be found by solving a nonlinear optimization problem. The complexity of this optimization problem is typically handled by making a number of heuristic assumptions. For instance, the number of decoy states is restricted to only one or two, with one of the decoy intensities set to a fixed value, and vacuum states are ignored as they are assumed to contribute only marginally to the secure key-rate. These assumptions simplify the optimization problem and reduce the size of search space significantly. However, they also cause the security analysis to be non-tight, and thereby result in sub-optimal performance. In this work, we follow a more rigorous approach using both linear and nonlinear programs describing the optimization problem. Our approach, focusing on the decoy-state BB84 protocol, allows heuristic assumptions to be omitted, and therefore results in a tighter security analysis with better protocol parameters. We show an improved performance for the decoy-state BB84 QKD protocol, demonstrating that the heuristic assumptions typically made are too restrictive. Moreover, our improved optimization frameworks shows that the complexity of the performance optimization problem can also be handled without making heuristic assumptions, even with limited computational resources available.
Decoy-state quantum key distribution (QKD) is the most widely adopted approach for overcoming the limitations of imperfect single-photon sources. However, existing security proofs typically either neglect important device imperfections or rely on assumptions that are difficult to justify in realistic high-speed implementations, such as the independent and identically distributed nature of the emitted signals. In this work, we combine and extend several recent theoretical advances to provide a comprehensive analytical finite-key security proof for decoy-state QKD that simultaneously incorporates multiple practically relevant transmitter and receiver imperfections, including state-preparation flaws, bit and basis side-channel leakage and correlations, setting-independent intensity fluctuations, and detection-efficiency mismatches.
With the potential of quantum computers to compromise current public-key cryptosystems, Quantum Key Distribution (QKD), which is based on the physical laws of quantum mechanics, has garnered significant attention. However, while QKD security proofs typically assume ideal single-photon sources, realistic implementations rely on Weak Coherent Pulses (WCP) due to the difficulties associated with commercializing true single-photon sources. Unfortunately, the multi-photon components inherent in WCPs are vulnerable to Photon Number Splitting (PNS) attacks, which limits the secure transmission distance to a few tens of kilometers. This article introduces the Decoy State method, which effectively resolves this issue. Proposed by W.-Y. Hwang in 2003 and further advanced by H.-K. Lo and X.-B. Wang, this technique utilizes the random interleaving of pulses with different mean photon numbers during transmission. By doing so, it enables the accurate estimation of single-photon yield and error rates, thereby effectively detecting PNS attacks. Because it can be implemented using standard commercial lasers and intensity modulators, the Decoy State method has become the standard technology in most modern QKD systems. It serves as a core component for long-distance quantum communication, enabling major milestones reported recently. This article reviews the principles, mathematical analysis, and latest applications of the Decoy State method.
Practical quantum key distribution (QKD) modulators inevitably introduce correlations, causing the state emitted in a given round to depend on the setting choices made in previous rounds. These correlations break the round-by-round independence structure on which many widely used security proof techniques rely, leaving a significant gap between available theoretical guarantees and the reality of practical implementations. In this work, we develop a fully analytical finite-key security proof for decoy-state BB84 against general coherent attacks that rigorously incorporates correlations introduced by Alice's bit-and-basis encoder, while requiring only partial characterization of such correlations. Crucially, it does so without requiring the round partitioning of the data used for phase-error estimation introduced in previous works, showing that this technique is not indispensable for dealing with correlated encoders, and resulting in improved finite-key performance. Moreover, we also analyze the case of ideal single-photon sources, and our results reveal a counterintuitive effect: in the presence of strong encoding correlations, decoy-state BB84 can outperform single-photon implementations.