Odd-parity error rejection (OPER) can drastically improve the asymptotic key rate of sending-or-not-sending twin-field (SNS-TF) quantum key distribution (QKD). However, in practice, the finite key effects have to be considered for security. Here, we propose a zigzag approach to verify the phase-flip error of the survived bits after OPER. Based on this, we can take all the finite key effect efficiently in calculating the non-asymptotic key rate. Numerical simulation shows that our method here produces the highest key rate over all distances among all existing methods, improving the key rate by more than $100\%$ to $3000\%$ in comparison with different prior art methods with typical experimental setting. Also, we show that with the method here, the SNS-TF QKD can by far break the the absolute bound of repeater-less key rate with whatever detection efficiency. We can even reach a non-asymptotic key rate more than $40$ times of the practical bound and $13$ times of the absolute bound with $10^{12}$ pulses. Besides, we apply the McDiarmid inequality to estimate the phase flip error rate, further improving the key rate by more than $20\%$.
Based on the novel idea of twin-field quantum key distribution, we present a sending-or-not-sending twin-field fault tolerant quantum key distribution protocol. Our protocol can access a secure distance longer than 700 km even though the misalignment error rate is $15\%$. In the case of zero alignment error, our protocol can exceeds a secure distance of 800 km. Thanks to the novel idea of TF-QKD !
The sending-or-not-sending (SNS) protocol of the twin-field quantum key distribution (TFQKD) can tolerant large misalignment error and its key rate can exceed the bound of repeaterless QKD. But the original SNS protocol requires the two users to use the same source parameters. Here we propose a general protocol with asymmetric source parameters and give the security proof of this protocol. Our general protocol has a much better performance than that of the original SNS protocol when the channel of the system is asymmetric.
The Sending-or-Not-Sending protocol of the twin-field quantum key distribution (TF-QKD) has its advantage of unconditional security proof under any coherent attack and fault tolerance to large misalignment error. So far this is the only coherent-state based TF-QKD protocol that has considered finite-key effect, the statistical fluctuations. Here we consider the complete finite-key effects for the protocol and we show by numerical simulation that the protocol with typical finite number of pulses in practice can produce unconditional secure final key under general attack, including all coherent …
We present the method of decoy-state analysis after bit-flip error correction and using confidential observed numbers. Taking this tool we then construct a universal approach to sending-or-not-sending (SNS) protocol of twin-field quantum key distribution. In this improved protocol, the code bits are not limited to heralded events in time windows participated by pulses of intensity $μ_z$ and vacuum. All kinds of heralded events can be used for code bits to distill the final keys. The number of intensities (3 or 4) and the kinds of heralded events for code bits are automatically chosen by the ke…
Quantum key distribution (QKD) offers a secret way to share keys between legitimate users which is guaranteed by the law of quantum mechanics. Most recently, the limitation of transmission distance without quantum repeaters was broken through by twin-field QKD [Nature (London) 557, 400 (2018)]. Based on its main idea, sending or not-sending (SNS) QKD protocol was proposed [Phys. Rev. A 98, 062323 (2018)], which filled the remaining security loopholes and can tolerate large misalignment errors. In this paper, we give a more general model for SNS QKD, where the two legitimate users, Alice and Bo…
We study the sending-or-not-sending (SNS) protocol with discrete phase modulation of coherent states. We first make the security of the SNS protocol with discrete phase modulation. We then present analytic formulas for key rate calculation. We take numerical simulations for the key rate through discrete phase modulation of both the original SNS protocol and the SNS protocol with two way classical communications of active-odd-parity pairing (AOPP). Our numerical simulation results show that only with $6$ phase values, the key rates of the SNS protocol can exceed the linear bound, and with $12$ …
We present improved method of sending-or-not-sending twin-field quantum key distribution (SNS TF-QKD) based on its structure and the application of error rejection. %And we present iteration formula for bit-flip error rate of the survived bits after error rejection. Taking the finite key effect into consideration with only $10^{11}$ total pulses, we show that the method here exceeds the absolute limit of repeater-less key rate with whatever detection efficiency. We also make comparative study of different protocols numerically. It shows that the method here presents advantageous results at lon…
The sending-or-not-sending (SNS) protocol is one of the most major variants of the twin-field (TF) quantum key distribution (QKD) protocol and has been realized in a 511 km field fiber, the farthest field experiment to date. In practice, however, all decoy-state methods have unavoidable source errors, and the source errors may be non-random, which compromises the security condition of the existing TF-QKD protocols. In this study, we present a general approach for efficiently calculating the SNS protocol's secure key rate with source errors, by establishing the equivalent protocols through virt…
Quantum key distribution endows people with information-theoretical security in communications. Twin-field quantum key distribution (TF-QKD) has attracted considerable attention because of its outstanding key rates over long distances. Recently, several demonstrations of TF-QKD have been realized. Nevertheless, those experiments are implemented in the laboratory, remaining a critical question about whether the TF-QKD is feasible in real-world circumstances. Here, by adopting the sending-or-not-sending twin-field QKD (SNS-TF-QKD) with the method of actively odd parity pairing (AOPP), we demonst…
Twin-field quantum key distribution (TF-QKD) and its variants can overcome the fundamental rate-distance limit of QKD which has been demonstrated in the laboratory and field while their physical implementations with side channels remains to be further researched. We find the external modulation of different intensity states through the test, required in those TF-QKD with post-phase compensation, shows a side channel in frequency domain. Based on this, we propose a complete and undetected eavesdropping attack, named passive frequency shift attack, on sending or not-sending (SNS) TF-QKD protocol…
We present results of practical sending-or-not quantum key distribution. In real-life implementations, we need consider the following three requirements, a few different intensities rather than infinite number of different intensities, a phase slice of appropriate size rather than infinitely small size and the statistical fluctuations. We first show the decoy-state method with only a few different intensities and a phase slice of appropriate size. We then give a statistical fluctuation analysis for the decoy-state method. Numerical simulation shows that, the performance of our method is compar…
Twin field quantum key distribution promises high key rates at long distance to beat the rate distance limit. Here, applying the sending or not sending TF QKD protocol, we experimentally demonstrate a secure key distribution breaking the absolute key rate limit of repeaterless QKD over 509 km, 408 km ultra-low loss optical fibre and 350 km standard optical fibre. Two independent lasers are used as the source with remote frequency locking technique over 500 km fiber distance; Practical optical fibers are used as the optical path with appropriate noise filtering; And finite key effects are consi…
Channel loss seems to be the most severe limitation on the practical application of long distance quantum key distribution. The idea of twin-field quantum key distribution can improve the key rate from the linear scale of channel loss in the traditional decoy-state method to the square root scale of the channel transmittance. However, the technical demanding is rather tough because it requests single photon level interference of two remote independent lasers. Here, we adopt the technology developed in the frequency and time transfer to lock two independent lasers' wavelengths and utilize addit…
Digital signature is a key technique in information security, especially for identity authentications. Compared with classical correspondence, quantum digital signatures (QDSs) provide a considerably higher level of security, i.e., information-theoretic security. At present, its performance is limited by key generation protocols (e.g., BB84 or measurement-device-independent protocols), which are fundamentally limited in terms of channel capacity. Fortunately, the recently proposed twin-field quantum key distribution can overcome this limit. This paper presents a twin-field QDS protocol and det…
Twin-field quantum key distribution (TF-QKD) and its variant protocols are highly attractive due to the advantage of overcoming the rate-loss limit for secret key rates of point-to-point QKD protocols. For variations of TF-QKD, the key point to ensure security is switching randomly between a code mode and a test mode. Among all TF-QKD protocols, their code modes are very different, e.g. modulating continuous phases, modulating only two opposite phases, and sending or not sending signal pulses. Here we show that, by discretizing the number of global phases in the code mode, we can give a unifie…
Twin-field quantum key distribution (TF-QKD) protocol and its variants, e.g. phase-matching (PM) QKD and TF-QKD based on sending or not sending, are highly attractive since they are able to overcome the well-known rate-loss limit for QKD protocols without repeater: $R=O(η)$ with $η$ standing for the channel transmittance. However, all these protocols require active phase randomization and post-selection that play an essential role together in their security proof. Counterintuitively, we find that in TF-QKD, beating the rate-loss limit is still possible even if phase randomization and post-sele…
Twin-Field quantum key distribution (TF-QKD) and its variants, e.g. Phase-Matching QKD, Sending-or-not-sending QKD, and No Phase Post-Selection TFQKD promise high key rates at long distance to beat the rate distance limit without a repeater. The security proof of these protocols are based on decoy-state method, which is usually performed by actively modulating a variable optical attenuator together with a random number generator in practical experiments, however, active-decoy schemes like this may lead to side channel and could open a security loophole. To enhance the source security of TF-QKD…
The basic principle of quantum mechanics guarantee the unconditional security of quantum key distribution (QKD) at the cost of inability of amplification of quantum state. As a result, despite remarkable progress in worldwide metropolitan QKD networks over the past decades, long haul fiber QKD network without trustful relay has not been achieved yet. Here, through sending-or-not-sending (SNS) protocol, we complete a twin field QKD (TF-QKD) and distribute secure keys without any trusted repeater over a 511 km long haul fiber trunk linking two distant metropolitans. Our secure key rate is around…
Twin-Field Quantum Key Distribution(TF-QKD) protocol and its variants, such as Phase-Matching QKD(PM-QKD), sending or not QKD(SNS-QKD) and No Phase Post-Selection TF-QKD(NPP-TFQKD), are very promising for long-distance applications. However, there are still some gaps between theory and practice in these protocols. Concretely, a finite-key size analysis is still missing, and the intensity fluctuations are not taken into account. To address the finite-key size effect, we first give the key rate of NPP-TFQKD against collective attack in finite-key size region and then prove it can be against cohe…
We show that a side-channel-free (SCF) source does not have to be an ideal source by introducing the idea of mapping from ideal source. We propose a 3-state no-touch protocol for quantum key distribution (QKD) where Alice and Bob does not modulate any light sent out, the only thing the do is to send (or not send, in sending-or-not protocol). The reference light are from independent Lasers. We show that, the protocol is side-channel-free (i.e., both source side channel free and measurement device independent) and there is no modulation to the weak beams for QKD coding, except for sending or not…
We present methods to strictly calculate the finite-key effects in quantum key distribution (QKD) with error rejection through two-way classical communication (TWCC) for the sending-or-not-sending twin-field protocol. Unlike the normal QKD without TWCC, here the probability of tagging or untagging for each two-bit random group is not independent. We rigorously solve this problem by imagining a virtual set of bits where every bit is independent and identical. We show the relationship between the outcome starting from this imagined set containing independent and identical bits and the outcome st…
As an essential ingredient of quantum networks, quantum conference key agreement (QCKA) provides unconditional secret keys among multiple parties, which enables only legitimate users to decrypt the encrypted message. Recently, some QCKA protocols employing twin-field was proposed to promote transmission distance. These protocols, however, suffer from relatively low conference key rate and short transmission distance over asymmetric channels, which demands a prompt solution in practice. Here, we consider a tripartite QCKA protocol utilizing the idea of sending-or-not-sending twin-field scheme a…
Twin-field quantum key distribution can overcome the secret key capacity of repeaterless quantum key distribution via single-photon interference. However, to compensate for the channel fluctuations and lock the laser fluctuations, the techniques of phase tracking and phase locking are indispensable in experiment, which drastically increase experimental complexity and hinder free-space realization. Inspired by the duality in entanglement, we herein present an asynchronous measurement-device-independent quantum key distribution protocol that can surpass the secret key capacity even without phase…
Quantum key distribution (QKD) is an important branch of quantum information science as it holds promise for unconditionally secure communication. For QKD research, a central issue is to improve the final secure key rate (SKR) and the maximal transmission distance. To address this issue, most works focused on reducing the information leakage of QKD. In this paper, we propose a novel approach to further reduce the information leakage by specially considering the overlap between the information leakage of quantum part and post-processing part. The overlap means that the information leakage of po…
Twin-field quantum key distribution (TF-QKD) promises ultra-long secure key distribution which surpasses the rate distance limit and can reduce the number of the trusted nodes in long-haul quantum network. Tremendous efforts have been made towards implementation of TF-QKD, among which, the secure key with finite size analysis can distribute more than 500 km in the lab and in the field. Here, we demonstrate the sending-or-not-sending TF-QKD experimentally, achieving a secure key distribution with finite size analysis over 658 km ultra-low-loss optical fiber, improve the secure distance record b…
Quantum key distribution (QKD) allows for secure communications safe against attacks by quantum computers. QKD protocols are performed by sending a sizeable, but finite, number of quantum signals between the distant parties involved. Many QKD experiments however predict their achievable key rates using asymptotic formulas, which assume the transmission of an infinite number of signals, partly because QKD proofs with finite transmissions (and finite key lengths) can be difficult. Here we develop a robust numerical approach for calculating the key rates for QKD protocols in the finite-key regime…
