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Physical Review A

Realistic and general model for quantum key distribution with entangled-photon sources

Zhen-Qiu Zhong, Shuang Wang, Xiao-Hai Zhan, Zhen−Qiang Yin, Wei Chen, Guang‐Can Guo, Zheng‐Fu Han

Published Nov 14, 2022• 16 citations
Publisher

Abstract

Entanglement-based quantum key distribution (EB-QKD) has several advantages over prepare-and-measure protocols, such as eliminating the need for decoy states and active modulators. At present, entanglement sources based on the spontaneous parametric down-conversion process have been widely used in EB-QKD experiments. Most of the existing models regard the photon-number distribution of pulse-pumped entanglement sources as thermal. However, doing so ignores any effects of spectral modes, which will lead to the overestimation of the secure key rate. In this paper, we analyze the correlation between the photon-number distribution and the joint spectral distribution and rewrite the quantum state of the photon pairs. Then we apply the results to EB-QKD and present a general model which can be used to calculate the secure key rate not only for any pulse-pumped systems but even for cw-pumped systems.

DOI
10.1103/physreva.106.052606

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Entanglement-based quantum key distribution (EB-QKD) has several advantages over prepare-and-measure protocols, such as eliminating the need for decoy states and active modulators. At present, entanglement sources based on the spontaneous parametric down-conversion process have been widely used in EB-QKD experiments. Most of the existing models regard the photon-number distribution of pulse-pumped entanglement sources as thermal. However, doing so ignores any effects of spectral modes, which will lead to the overestimation of the secure key rate. In this paper, we analyze the correlation between the photon-number distribution and the joint spectral distribution and rewrite the quantum state of the photon pairs. Then we apply the results to EB-QKD and present a general model which can be used to calculate the secure key rate not only for any pulse-pumped systems but even for cw-pumped systems.
Abstract The paper analyzes security aspects of practical entanglement-based quantum key distribution (QKD), namely, BBM92 or entanglement-based BB84 protocol. Similar to prepare-and-measure QKD protocols, practical implementations of the entanglement-based QKD have to rely upon non-ideal photon sources. A typical solution for entanglement generation is the spontaneous parametric down-conversion. However, this process creates not only single photon pairs, but also quantum states with more than two photons, which potentially may lead to security deterioration. We show that this effect does not impair the security of entanglement-based QKD systems. We also review the available security proofs and show that properties of the entanglement source have nothing to do with security degradation.
A workflow for evaluation of entanglement source quality is proposed. Based on quantum state density matrices obtained from theoretical models and experimental data, we make an estimate of a potential performance of a quantum entanglement source in quantum key distribution protocols. This workflow is showcased for continuously pumped spontaneous parametric down-conversion (SPDC) source, where it highlights the trade-off between entangled pair generation rate and entanglement quality caused by multiphoton nature of the generated quantum states. We employ this characterization technique to show that secure key rate of down-converted photon pairs is limited to 0.029 bits per detection window due to intrinsic multiphoton contributions. We also report that there exists one optimum gain for continuous-wave down-conversion sources. We find a bound for secure key rate extracted from SPDC sources and make a comparison with perfectly single-pair quantum states, such as those produced by quantum dots.
Quantum cryptography or quantum key distribution (QKD) applies fundamental laws of quantum physics to guarantee secure communication. The security of quantum cryptography was proven in the last decade. Many security analyses are based on the assumption that QKD system components are idealized. In practice, inevitable device imperfections may compromise security unless these imperfections are well investigated.\n\nA highly attenuated laser pulse which gives a weak coherent state is widely used in QKD experiments. A weak coherent state has multi-photon components, which opens up a security loophole to the sophisticated eavesdropper. With a small adjustment of the hardware, we will prove that the decoy state method can close this loophole and substantially improve the QKD performance. We also propose a few practical decoy state protocols, study statistical fluctuations and perform experimental demonstrations. Moreover, we will apply the methods from entanglement distillation protocols based on two-way classical communication to improve the decoy state QKD performance. Furthermore, we study the decoy state methods for other single photon sources, such as triggering parametric down-conversion (PDC) source. Note that our work, decoy state protocol, has attracted a lot of scientific and media interest. The decoy state QKD becomes a standard technique for prepare-and-measure QKD schemes.\n\nAside from single-photon-based QKD schemes, there is another type of scheme based on entangled photon sources. A PDC source is commonly used as an entangled photon source. We propose a model and post-processing scheme for the entanglement-based QKD with a PDC source. Although the model is proposed to study the entanglement-based QKD, we emphasize that our generic model may also be useful for other non-QKD experiments involving a PDC source. By simulating a real PDC experiment, we show that the entanglement-based QKD can achieve longer maximal secure distance than the single-photon-based QKD schemes.\n\nWe propose a time-shift attack that exploits the efficiency mismatch of two single photon detectors in a QKD system. This eavesdropping strategy can be realized by current technology. We will also discuss counter measures against the attack and study the security of a QKD system with efficiency mismatch detectors.
Quantum key distribution (QKD) enables two parties to establish a secret key over a potentially hostile channel by exchanging photonic quantum states, relying on the fact that it is impossible for an eavesdropper to tap the quantum channel without disturbing these photons in a way that can be detected [1]. Here we introduce a large-alphabet QKD protocol that makes optimal use of temporal and spectral correlations of entangled photons, reaching the maximum number of inde- pendent basis states (the Schmidt number) and enabling extremely high information content per photon together with an optimal rate of secret key generation. This protocol, which we call 'Dense Wavelength Division Multiplexed Quantum Key Distribution' (DWDM-QKD), derives its security by the conjugate nature of the temporal and spectral entanglement of photon pairs generated by spontaneous parametric down conversion. By using a combination of spectral and temporal bases, we can adjust the protocol to be resource efficient. We show that DWDM-QKD is well suited to approach the optimal key generation rate using present-day sources, detectors, and DWDM opti- cal networks from classical communications, as well as emerging optical interconnect and photonic integrated chip (PIC) systems.
Quantum key distribution (QKD) protocols utilize single photons for key exchanging. Heralded single-photon sources (HSPSs) with spontaneous parametric down-conversion (SPDC) is a practical and effective way of producing single photons of high fidelity, bringing extra performance especially at long distances. A pulsed laser is usually used as the pump for HSPS QKD, but it has disadvantages in operational stability and practicality compared to a cw one. On the other hand, a precise model describing the performance of HSPS with a cw pump is still missing. It is inaccurate and unsafe to apply the key rate model of the pulse-pumped HSPS QKD directly to the cw one, and it also overlooks the timing jitter and dead time of the single-photon detectors. In this paper, we study the cw case in detail, including practical imperfections of the experimental instruments. Our model shows that a cw-pumped setup can reach a much longer transmission distance (31 % longer) than the fastest pulsed HSPS QKD system at present, together with other advantages such as higher operational stability and better spectral characteristics.
Quantum key distribution (QKD) allows unconditionally secure communication based on the laws of quantum mechanics rather than assumptions about computational hardness. Optimizing the operation parameters of a given QKD implementation is indispensable in order to achieve high secure key rates. So far, there exists no model that accurately describes entanglement-based QKD with continuous-wave pump lasers. We analyze the underlying mechanisms for QKD with temporally uniform pair-creation probabilities and develop a simple but accurate model to calculate optimal tradeoffs for maximal secure key rates. In particular, we find an optimization strategy of the source brightness for given losses and detection-time resolution. All experimental parameters utilized by the model can be inferred directly in standard QKD implementations, and no additional assessment of device performance is required. Comparison with experimental data shows the validity of our model. Our results yield a tool to determine optimal operation parameters for already existing QKD systems, to plan a full QKD implementation from scratch, and to determine fundamental key rate and distance limits of given connections.