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Physical Review A

Interfering-or-not-interfering quantum key distribution

Yang Yu, Wei Li, Le Wang, Shengmei Zhao

Published May 6, 2024• 9 citations
Publisher

Abstract

Single-photon interference is the essential key for the recently well-known twin-field quantum key distribution (TF-QKD) to break the linear rate-distance limit and requires beams with identical polarizations. Inspired by this fact and aiming to improve the secret key rate, we propose a hybrid high-dimensional QKD named the interfering-or-not-interfering QKD (INI-QKD), in which both the polarization and phase degrees of freedom (DOFs) are adopted as information carriers. The protocol's security proof is analyzed based on entanglement distillation and three defined effective events, ${X}_{1}$, ${X}_{2}$, and ${X}_{3}$. The simulation shows that the ${X}_{1}$ event, from which only the phase information is extracted, exceeds TF-QKD's variants, while the ${X}_{2}$ and ${X}_{3}$ events, in which both types of information are decoded, can achieve twice the secret key rate as measurement-device-independent QKD (MDI-QKD). It is also proven that by adding the polarization DOF, INI-QKD obtains more resistance to phase mismatch than TF-QKD. Remarkably, these can all be achieved by simply altering the TF-QKD's measurement setup to that of MDI-QKD.

DOI
10.1103/physreva.109.052609

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Single-photon interference is the essential key for the recently well-known twin-field quantum key distribution (TF-QKD) to break the linear rate-distance limit and requires beams with identical polarizations. Inspired by this fact and aiming to improve the secret key rate, we propose a hybrid high-dimensional QKD named the interfering-or-not-interfering QKD (INI-QKD), in which both the polarization and phase degrees of freedom (DOFs) are adopted as information carriers. The protocol's security proof is analyzed based on entanglement distillation and three defined effective events, X1{X}_{1}X1​, X2{X}_{2}X2​, and X3{X}_{3}X3​. The simulation shows that the X1{X}_{1}X1​ event, from which only the phase information is extracted, exceeds TF-QKD's variants, while the X2{X}_{2}X2​ and X3{X}_{3}X3​ events, in which both types of information are decoded, can achieve twice the secret key rate as measurement-device-independent QKD (MDI-QKD). It is also proven that by adding the polarization DOF, INI-QKD obtains more resistance to phase mismatch than TF-QKD. Remarkably, these can all be achieved by simply altering the TF-QKD's measurement setup to that of MDI-QKD.
The twin-field quantum key distribution (TF-QKD) protocol has led to extensive investigation for its capacity of overcoming the rate-distance limit. One variant for TF-QKD named sending-or-not-sending (SNS) TF-QKD has also been proposed. The SNS-TF-QKD encodes the classical keys 0 and 1 in sending or not sending the phase-randomized coherent states, which helps it to tolerate large misalignment errors due to optical phase fluctuations. Nevertheless, the original SNS-TF-QKD scheme utilizes only single-photon interference in generating secret keys, which seems quite different from other TF-QKD protocols. In this paper, we prove that multiphoton interference in the SNS TF-QKD protocol can also contribute to key generation. Accordingly, an improved SNS-TF-QKD scheme with higher key rate is proposed, where events of not only single-photon but also two-photon emissions are considered as effective events.
The ultimate aim of quantum key distribution (QKD) is improving the transmission distance and key generation speed. Unfortunately, it is believed to be limited by the secret-key capacity of quantum channel without quantum repeater. Recently, a novel twin-field QKD (TF-QKD) is proposed to break through the limit, where the key rate is proportional to the square-root of channel transmittance. Here, by using the vacuum and one-photon state as a qubit, we show that the TF-QKD can be regarded as a measurement-device-independent QKD (MDI-QKD) with single-photon Bell state measurement. Therefore, the MDI property of TF-QKD can be understood clearly. Importantly, the universal security proof theories can be directly used for TF-QKD, such as BB84 encoding, six-state encoding and reference-frame-independent scheme. Furthermore, we propose a feasible experimental scheme for the proof-of-principle experimental demonstration.
Twin field quantum key distribution (TF-QKD) has attracted the attention of the research community thanks to its higher secure key rate which scales as square root of the channel transmittance. The twin field secure key rate thus crosses the repeaterless secure key rate distance bound, showing that the protocol can cater to large channel lengths. Here, we present a twin-field-like QKD protocol based on single photon interference of differential phase shift (DPS) encoded states and prove the security of the scheme. Our protocol builds upon an existing measurement device independent (MDI) QKD system that has a DPS encoding and modifies the sifting step to one based on single photon interference. We demonstrate security of our DPS-twin-field (DPS-TF) protocol against collective attacks and quantify the secure key rate. We find that with the current state-of-the-art technology, both TF-QKD and MDI-QKD protocols with the DPS encoding work almost identically in terms of the channel length, although the achievable secure key rate of the DPS-TF QKD is higher compared to MDI-QKD.
Two time-reversal quantum key distribution (QKD) schemes are the quantum entanglement based device-independent (DI)-QKD and measurement-device-independent (MDI)-QKD. The recently proposed twin field (TF)-QKD, also known as phase-matching (PM)-QKD, has improved the key rate bound from O(η) to O[Formula: see text] with η the channel transmittance. In fact, TF-QKD is a kind of MDI-QKD but based on single-photon detection. In this paper, we propose a different PM-QKD based on single-photon entanglement, referred to as single-photon entanglement-based phase-matching (SEPM)-QKD, which can be viewed as a time-reversed version of the TF-QKD. Detection loopholes of the standard Bell test, which often occur in DI-QKD over long transmission distances, are not present in this protocol because the measurement settings and key information are the same quantity which is encoded in the local weak coherent state. We give a security proof of SEPM-QKD and demonstrate in theory that it is secure against all collective attacks and beam-splitting attacks. The simulation results show that the key rate enjoys a bound of O[Formula: see text] with respect to the transmittance. SEPM-QKD not only helps us understand TF-QKD more deeply, but also hints at a feasible approach to eliminate detection loopholes in DI-QKD for long-distance communications.
Based on the novel idea of twin-field quantum key distribution [TF-QKD; Lucamarini et al., Nature (London) 557, 400 (2018)], we present a protocol named the ``sending or not sending TF-QKD'' protocol, which can tolerate large misalignment error. A revolutionary theoretical breakthrough in quantum communication, TF-QKD changes the channel-loss dependence of the key rate from linear to square root of channel transmittance. However, it demands the challenging technology of long-distance single-photon interference, and also, as stated in the original paper, the security proof was not finalized there due to the possible effects of the later announced phase information. Here we show by a concrete eavesdropping scheme that the later phase announcement does have important effects and the traditional formulas of the decoy-state method do not apply to the original protocol. We then present our ``sending or not sending'' protocol. Our protocol does not take postselection for the bits in ZZZ-basis (signal pulses), and hence the traditional decoy-state method directly applies and automatically resolves the issue of security proof. Most importantly, our protocol presents a negligibly small error rate in ZZZ-basis because it does not request any single-photon interference in this basis. Thus our protocol greatly improves the tolerable threshold of misalignment error in single-photon interference from the original a few percent to more than 4545%45. As shown numerically, our protocol exceeds a secure distance of 700, 600, 500, or 300 km even though the single-photon interference misalignment error rate is as large as 1515%, 25%, 35%15, or 4545%45.
Abstract Twin-Field quantum key distribution (TF-QKD) and its variants, e.g. phase-maching 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, in this paper, we propose passive-decoy based TF-QKD, in which we combine TF-QKD with the passive-decoy method. And we present a simulation comparing the key generation rate with that in active-decoy, the result shows our scheme performs as good as active decoy TF-QKD, and our scheme could reach satisfactory secret key rates with just a few photon detectors. This shows our work is meaningful in practice.