Detector Efficiency Mismatch Research Articles

Imperfect Measurement Devices Impact the Security of Tomography‐Based Source‐Independent Quantum Random Number Generator

AbstractSource‐independent quantum random number generators (SI‐QRNGs) can generate secure random numbers with untrusted and uncharacterized sources. Recently, a tomography‐based SI‐QRNG protocol has garnered significant attention for its higher randomness generation rate[Phys. Rev. A 99, 022328 (2019)], achieved through measurements utilizing three mutually unbiased bases. However, imperfect and inadequately characterized measurement devices would impact the security and performance of this protocol. In this work, considering the imperfect basis modulation, afterpulse effect and detection efficiency mismatch, it is demonstrated that the imperfect measurement devices would reduce the extractable randomness and lead to the incorrect estimation of the conditional min‐entropy. Additionally, the influences of the finite‐size effect and the performances of the protocol based on different parameter estimation methods are investigated and compared. To guarantee the security of generated random numbers, accurate conditional min‐entropy estimation methods that are compatible with imperfect factors are also developed. The work emphasizes the significance of considering the imperfections in measurement devices and establishing tighter bounds for parameter estimation, especially in high‐speed systems, thereby enhancing the robustness and performance of the protocol.

Eurasian-scale experimental satellite-based quantum key distribution with detector efficiency mismatch analysis.

The Micius satellite is the pioneering initiative to demonstrate quantum teleportation, entanglement distribution, quantum key distribution (QKD), and quantum-secured communications experiments at the global scale. In this work, we report on the results of the 600-mm-aperture ground station design which has enabled the establishment of a quantum-secured link between the Zvenigorod and Nanshan ground stations using the Micius satellite. As a result of a quantum communications session, an overall sifted key of 2.5 Mbits and a total final key length of 310 kbits have been obtained. We present an extension of the security analysis of the realization of satellite-based QKD decoy-state protocol by taking into account the effect of the detection-efficiency mismatch for four detectors. We also simulate the QKD protocol for the satellite passage and by that validate our semi-empirical model for a realistic receiver, which is in good agreement with the experimental data. Our results pave the way to the considerations of realistic imperfection of the QKD systems, which are important in the context of their practical security.

Security of quantum key distribution with detection-efficiency mismatch in the multiphoton case

Detection-efficiency mismatch is a common problem in practical quantum key distribution (QKD) systems. Current security proofs of QKD with detection-efficiency mismatch rely either on the assumption of the single-photon light source on the sender side or on the assumption of the single-photon input of the receiver side. These assumptions impose restrictions on the class of possible eavesdropping strategies. Here we present a rigorous security proof without these assumptions and, thus, solve this important problem and prove the security of QKD with detection-efficiency mismatch against general attacks (in the asymptotic regime). In particular, we adapt the decoy state method to the case of detection-efficiency mismatch.

Security proof of practical quantum key distribution with detection-efficiency mismatch

Quantum key distribution (QKD) protocols with threshold detectors are driving high-performance QKD demonstrations. The corresponding security proofs usually assume that all physical detectors have the same detection efficiency. However, the efficiencies of the detectors used in practice might show a mismatch depending on the manufacturing and setup of these detectors. A mismatch can also be induced as the different spatial-temporal modes of an incoming signal might couple differently to a detector. Here we develop a method that allows to provide security proofs without the usual assumption. Our method can take the detection-efficiency mismatch into account without having to restrict the attack strategy of the adversary. Especially, we do not rely on any photon-number cut-off of incoming signals such that our security proof is directly applicable to practical situations. We illustrate our method for a receiver that is designed for polarization encoding and is sensitive to a number of spatial-temporal modes. In our detector model, the absence of quantum interference between any pair of spatial-temporal modes is assumed. For a QKD protocol with this detector model, we can perform a security proof with characterized efficiency mismatch and without photon-number cut-off assumption. Our method also shows that in the absence of efficiency mismatch in our detector model, the key rate increases if the loss due to detection inefficiency is assumed to be outside of the adversary's control, as compared to the view where for a security proof this loss is attributed to the action of the adversary.

Generic security analysis framework for quantum secure direct communication

Quantum secure direct communication provides a direct means of conveying secret information via quantum states among legitimate users. The past two decades have witnessed its great strides both theoretically and experimentally. However, the security analysis of it still stays in its infant. Some practical problems in this field to be solved urgently, such as detector efficiency mismatch, side-channel effect and source imperfection, are propelling the birth of a more impeccable solution. In this paper, we establish a new framework of the security analysis driven by numerics where all the practical problems may be taken into account naturally. We apply this framework to several variations of the DL04 protocol considering real-world experimental conditions. Also, we propose two optimizing methods to process the numerical part of the framework so as to meet different requirements in practice. With these properties considered, we predict the robust framework would open up a broad avenue of the development in the field.

Practical source-independent quantum random number generation with detector efficiency mismatch

Quantum random number generators (QRNGs) are widely used in information processing tasks. The quality of the random numbers obtained from QRNGs relies on the accurate characterization of the physical implementations. In practice, realistic devices are difficult to characterize, resulting in incorrect entropy estimations of the output random numbers. Recently, a novel quantum random number generation (QRNG) scheme, referred to as source-independent QRNG (SIQRNG), has attracted a lot of interest. The scheme can provide certified randomness by using untrusted and uncharacterized sources, under the assumption that the measurement devices are trusted. However, realistic devices inevitably feature imperfections. Here, we show that the output randomness of SIQRNG is compromised in the presence of detection imperfection , by constructing an attack based on a time-domain detection efficiency mismatch between two practical detectors. More importantly, we provide an unconditional security proof of SIQRNG that takes detection efficiency mismatch into account. In addition, we provide a parameter optimization method to effectively improve the final random number generation rate. Our work demonstrates that SIQRNG is highly practical and that randomness can be extracted even in the presence of a detection efficiency mismatch.

Operational interpretation of coherence in quantum key distribution

Quantum coherence was recently formalized as a physical resource to measure the strength of superposition. Based on the resource theory, we present a systematic framework that connects a coherence measure to the security of quantum key distribution. By considering a generic entanglement-based key distribution protocol under the collective attack scenario, we show that the key rate can be quantified by the coherence of the shared bipartite states. This framework allows us to derive the key rate of the BB84 and six-state protocols. By utilizing fine-grained parameters, we also derive the improved key rates of both protocols within the coherence-based framework. Furthermore, we apply it to a practical issue, detection efficiency mismatch, and obtain an improved result. In conclusion, this framework demonstrates the interplay among coherence, entanglement, and quantum key distribution at a fundamental level.

Security of quantum key distribution with detection-efficiency mismatch in the single-photon case: Tight bounds

One of the challenges in practical quantum key distribution is dealing with efficiency mismatch between different threshold single-photon detectors. There are known bounds for the secret key rate for the BB84 protocol with detection-efficiency mismatch provided that the eavesdropper sends no more than one photon to the legitimate receiver. Here we improve these bounds and give tight bounds for the secret key rate with a constant detection-efficiency mismatch under the same single-photon assumption. We propose a method based on the analytical minimization of the relative entropy of coherence, which can be used in other problems in quantum key distribution. Also we propose an adaptation of the decoy state method to proof the security in the case of weak coherent pulses on the source side.

Practical decoy state quantum key distribution with detector efficiency mismatch

Decoy state method is widely used in practical quantum key distribution (QKD) systems to substantially extend the secure communication distance. Detector efficiency mismatch (DEM), which exists between practical detectors, effects the security of practical QKD systems seriously. Security of single photon QKD with DEM has been analyzed. However, estimate of the phase error rate still remains difficult in practice. Here, using a simple equivalent detection model, the mutual information between legitimate users and the eavesdropper for single photon state in QKD with DEM is analyzed. Then we improve the security analysis to cover the situation of weak coherent QKD with DEM. A general theory of the decoy state QKD with DEM is proposed to calculate the lower bound of count rate and the upper bound of error rate of single photon state signals. The numerical simulations show that secure key can also be generated, but the existing of DEM will reduce the secure key of practical decoy state QKD systems. The experiment parameter related security bound of DEM is also given out.

Exploiting wavelength-dependent beam splitter to attack the calibration of practical quantum key distribution systems

We propose a modified attack on the calibration stage of polarized-based passive-basis-choice BB84 quantum key distribution (QKD) systems, where the activation windows of the detectors are scanned independently, by exploiting the wavelength-dependent defect of practical beam splitters. The eavesdropper may induce large basis dependent detector efficiency mismatch (BEM) in every attempt without failure. Moreover, the coupling radios of practical beam splitters at different wavelengths do not need to be close to 0 or 1, which makes our attack more applicative in practical QKD systems. Theoretical analysis and numerical simulation of BEM-based faked states attack on decoy-state QKD are also given out, which indicates that the eavesdropper can steal information about the final key if legitimate users are not aware of the induced BEM and re-emphasizes the inappropriate design of independently scanned activation windows of gated single photon detectors should be treated strictly. Countermeasures are also discussed.

Quantum man-in-the-middle attack on the calibration process of quantum key distribution

Quantum key distribution (QKD) protocol has been proved to provide unconditionally secure key between two remote legitimate users in theory. Key distribution signals are transmitted in a quantum channel which is established by the calibration process to meet the requirement of high count rate and low error rate. All QKD security proofs implicitly assume that the quantum channel has been established securely. However, the eavesdropper may attack the calibration process to break the security assumption of QKD and provide precondition to steal information about the final key successfully. In this paper, we reveal the security risk of the calibration process of a passive-basis-choice BB84 QKD system by launching a quantum man-in-the-middle attack which intercepts all calibration signals and resends faked ones. Large temporal bit-dependent or basis-dependent detector efficiency mismatch can be induced. Then we propose a basis-dependent detector efficiency mismatch (BEM) based faked states attack on a single photon BB84 QKD to stress the threat of BEM. Moreover, the security of single photon QKD systems with BEM is studied simply and intuitively. Two effective countermeasures are suggested to remove the general security risk of the calibration process.

Realistic Device Imperfections Affect the Performance of Hong-Ou-Mandel Interference With Weak Coherent States

Measurement-device-independent quantum key distribution (MDI QKD) is a promising and practical protocol for remote secret sharing, where the Hong-Ou-Mandel (HOM) type interference in the measurement side provides a simple and economic way to resist malicious attacks on the measurement devices. Because the HOM interference greatly indicates the performance of MDI QKD system, its interferential behavior in practical situations deserve to be studied. In this work, we analyzed HOM visibility with several practical imperfections, such as the deviation of the beam splitting ratio, detection efficiency mismatch of detectors, inconsistent intensities of two incident pulses. In particular, we discussed the afterpulse effect of InGaAs avalanche photodiode detectors with a non-Markovian model, where we take the avalanche history into consideration and provide a new and more accurate perspective for afterpulse analysis. Simulation results indicate that the afterpulse effect in practical situation has a greater impact on the HOM performance than other imperfections. The results exhibit its value in realistic high-speed MDI QKD systems as well as other fiber-based HOM applications.

Trustworthiness of devices in a quantum random number generator based on a symmetric beam splitter

Quantum random number generators (QRNGs) based on a symmetric beam splitter have attracted a great deal of interest, and the commercial version can be found in the marketplace. However, practical implementations of this QRNG may be imperfect. Here, we propose two attacks for this kind of QRNG, based on some imperfections existing in devices. The first attack exploits the imperfection that the transmission-reflection ratio of a symmetric beam splitter varies with different wavelengths. The second attack can be successful because of the detection efficiency mismatch in two single-photon detectors. With our attacks, Eve can easily break the inherent randomness of the QRNG without being detected. A key point of our paper is to raise awareness of such security loopholes in existing QRNG schemes.

Entanglement verification with detection-efficiency mismatch

The security analysis of quantum key distribution is difficult to perform when there is efficiency mismatch between various threshold detectors involved in an experimental setup. Even the verification that the device actually performs in the quantum domain, referred to as the task of entanglement verification, is hard to perform. In this article we provide such an entanglement-verification method for characterized detection-efficiency mismatch. Our method does not rely on a cut-off of photon numbers in the optical signal. It can be applied independently of the degrees of freedom involved, thus covering, for example, efficiency mismatch in polarization and time-bin modes, but also in spatial modes. The evaluation of typical experimental scenarios suggests that an increase of detection-efficiency mismatch will drive the performance of a given setup out of the quantum domain.

Security loophole in free-space quantum key distribution due to spatial-mode detector-efficiency mismatch

In free-space quantum key distribution (QKD), the sensitivity of the receiver's detector channels may depend differently on the spatial mode of incoming photons. Consequently, an attacker can control the spatial mode to break security. We experimentally investigate a standard polarization QKD receiver, and identify sources of efficiency mismatch in its optical scheme. We model a practical intercept-and-resend attack and show that it would break security in most situations. We show experimentally that adding an appropriately chosen spatial filter at the receiver's entrance is an effective countermeasure.

Practical attacks on decoy-state quantum-key-distribution systems with detector efficiency mismatch

To the active basis choice decoy state quantum key distribution systems with detector efficiency mismatch, we present a modified attack strategy, which is based on faked states attack, with quantum nondemolition measurement ability to restress the threat of detector efficiency mismatch. Considering that perfect quantum nondemolition measurement ability dose not exist in real life, we also propose a practical attack strategy using photon number resolving detectors. Theoretical analysis and numerical simulation results show that, without changing the channel, our attack strategies are serious threats to decoy state quantum key distribution systems. The eavesdropper may get some information ab out the secret key without causing any alarms. Besides, the lower bound of detector efficiency mismatch to run our modified faked states attack successfully with perfect quantum nondemolition measurement ability is also given out, which provides the producers of quantum key distribution systems with a reference and can be treated as the approximate secure bound of detector efficiency mismatch in decoy state quantum key distribution systems.

Device Calibration Impacts Security of Quantum Key Distribution

Characterizing the physical channel and calibrating the cryptosystem hardware are prerequisites for establishing a quantum channel for quantum key distribution (QKD). Moreover, an inappropriately implemented calibration routine can open a fatal security loophole. We propose and experimentally demonstrate a method to induce a large temporal detector efficiency mismatch in a commercial QKD system by deceiving a channel length calibration routine. We then devise an optimal and realistic strategy using faked states to break the security of the cryptosystem. A fix for this loophole is also suggested.

Secure gated detection scheme for quantum cryptography

Several attacks have been proposed on quantum key distribution systems with gated single-photon detectors. The attacks involve triggering the detectors outside the center of the detector gate, and/or using bright illumination to exploit classical photodiode mode of the detectors. Hence a secure detection scheme requires two features: The detection events must take place in the middle of the gate, and the detector must be single-photon sensitive. Here we present a technique called bit-mapped gating, which is an elegant way to force the detections in the middle of the detector gate by coupling detection time and quantum bit error rate. We also discuss how to guarantee single-photon sensitivity by directly measuring detector parameters. Bit-mapped gating also provides a simple way to measure the detector blinding parameter in security proofs for quantum key distribution systems with detector efficiency mismatch, which up until now has remained a theoretical, unmeasurable quantity. Thus if single-photon sensitivity can be guaranteed within the gates, a detection scheme with bit-mapped gating satisfies the assumptions of the current security proofs.

Security of quantum key distribution with bit and basis dependent detector flaws

We consider the security of the Bennett-Brassard 1984 (BB84) protocol for Quantum Key Distribution (QKD), in the presence of bit and basis dependent detector flaws. We suggest a powerful attack that can be used in systems with detector efficiency mismatch, even if the detector assignments are chosen randomly by Bob. A security proof is provided, valid for any basis dependent, possibly lossy, linear optical imperfections in the channel/receiver/detectors. The proof does not assume the so-called squashing detector model.

Security proof of quantum key distribution with detection efficiency mismatch

In theory, quantum key distribution (QKD) offers unconditional security based on the laws of physics. However, as demonstrated in recent quantum hacking theory and experimental papers, detection efficiency loophole can be fatal to the security of practical QKD systems. Here, we describe the physical origin of detection efficiency mismatch in various domains including spatial, spectral, and time domains and in various experimental set-ups. More importantly, we prove the unconditional security of QKD even with detection efficiency mismatch. We explicitly show how the key generation rate is characterized by the maximal detection efficiency ratio between the two detectors. Furthermore, we prove that by randomly switching the bit assignments of the detectors, the effect of detection efficiency mismatch can be completely eliminated.