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.
Most qubit-based quantum key distribution (QKD) protocols extract the secure key merely from single-photon component of the attenuated lasers. However, with the Scarani-Acin-Ribordy-Gisin 2004 (SARG04) QKD protocol, the unconditionally secure key can be extracted from the two-photon component by modifying the classical post-processing procedure in the BB84 protocol. Employing the merits of SARG04 QKD protocol and six-state preparation, one can extract secure key from the components of single photon up to four photons. In this paper, we provide the exact relations between the secure key rate an…
The technological possibilities of a realistic eavesdropper are discussed. Two eavesdropping strategies taking profit of multiphoton pulses in faint laser QKD are presented. We conclude that, as long as storage of Qubits is technically impossible, faint laser QKD is not limited by this security issue, but mostly by the detector noise.
Multiphoton state in quantum cryptography decreases its security. Key disclosing with universal quantum cloning machine (UQCM) is considered in explicit manner. Although UQCM cannot make perfect clones, there is some invariant quantity between the original photon and the imperfect clones. The invariant quantity, the direction of Stokes parameters, tells us the auxiliary information leading into key information. The attack, then, corresponds to some kind of quantum non-demolition measurement. Its application to recent high-performance quantum cryptography, Y-00 protocol, is also studied.
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 chara…
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 count…
Mistrustful cryptography includes important tasks like bit commitment, oblivious transfer, coin flipping, secure computations, position authentication, digital signatures and secure unforgeable tokens. Practical quantum implementations presently use photonic setups. In many such implementations, Alice sends photon pulses encoding quantum states and Bob chooses measurements on these states. In practice, Bob generally uses single photon threshold detectors, which cannot distinguish the number of photons in detected pulses. Also, losses and other imperfections require Bob to report the detected p…
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. Ou…
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, w…
Security of quantum key distribution with passive basis choice and detection-efficiency mismatch for a realistic satellite setup
Russian Quantum Center（俄罗斯量子中心）；QSpace Technologies（QSpace科技有限公司）；Moscow Institute of Physics and Technology（莫斯科物理技术学院）；National University of Science and Technology MISIS（国立研究技术大学MISIS）；Technische Universität Braunschweig（布伦瑞克工业大学）
We suggest a type of attack on quantum cryptosystems that exploits variations in detector efficiency as a function of a control parameter accessible to an eavesdropper. With gated single-photon detectors, this control parameter can be the timing of the incoming pulse. When the eavesdropper sends short pulses using the appropriate timing so that the two gated detectors in Bob's setup have different efficiencies, the security of quantum key distribution can be compromised. Specifically, we show for the Bennett-Brassard 1984 (BB84) protocol that if the efficiency mismatch between 0 and 1 detector…
In this paper, a photon-number-resolving decoy state quantum key distribution scheme is presented based on recent experimental advancements. A new upper bound on the fraction of counts caused by multiphoton pulses is given. This upper bound is independent of intensity of the decoy source, so that both the signal pulses and the decoy pulses can be used to generate the raw key after verified the security of the communication. This upper bound is also the lower bound on the fraction of counts caused by multiphoton pulses as long as faint coherent sources and high lossy channels are used. We show …
Quantum cryptography or, more precisely, quantum key distribution (QKD), is one of the advanced areas in the field of quantum technologies. The confidentiality of keys distributed with the use of QKD protocols is guaranteed by the fundamental laws of quantum mechanics. This paper is devoted to the decoy state method, a countermeasure against vulnerabilities caused by the use of coherent states of light for QKD protocols whose security is proved under the assumption of single-photon states. We give a formal security proof of the decoy state method against all possible attacks. We compare two wi…
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…
It is the first scheme which allows the detection apparatus to achieve both the photon number of arriving signals and quantum bit error rate of the multiphoton pulses precisely. We show that the upper bound of the fraction of the tagged multiphoton pulses counts is $μ$, which is independent of the channel loss and the intensity of the decoy source. Such upper bound is $inherent$ and cannot be reduced any longer as long as the weak coherent scouces and high lossy channel are used. We show that our scheme can be implemented even if the channel loss is very high. A stronger intensity of the pulse…
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.
The ability of an eavesdropper to compromise the security of a quantum communication system by changing the angle of the incoming light is well-known. Randomizing the role of the detectors has been proposed to be an efficient countermeasure to this type of attack. Here we show that the proposed countermeasure can be bypassed if the attack is generalized by including more attack variables. Using the experimental data from existing literature, we show how randomization effectively prevents the initial attack but fails to do so when Eve generalizes her attack strategy. Our result and methodology …
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. Inspire…
We propose a protocol to perform long-range distribution of near-maximally entangled multiphoton states, allowing versatile applications such as quantum key distribution (QKD) and quantum metrology which can provide alternatives to state-of-the-art protocols. Our scheme uses resources available within the current integrated quantum photonic technology: squeezed vacuum states and photon-number-resolving detectors. The distributed entanglement can be certified by Bell tests which have the potential to be loophole free, and may be directly used in well established QKD protocols. Generally, this p…
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 suggeste…
Spectral Attack on Continuous-Variable Quantum Key Distribution Systems
Shanghai Jiao Tong University（上海交通大学）；Shanghai Research Center for Quantum Sciences（上海量子科学研究中心）；Hefei National Laboratory（合肥国家实验室）；Shanghai XunTai Quantech Co., Ltd（上海迅泰量子科技有限公司）
Loophole-free Bell tests are essential if one wishes to perform device-independent quantum key distribution (QKD), since any loophole could be used by a potential adversary to undermine the security of the protocol. Crucial work by Eberhard demonstrated that weakly entangled two-qubit states have a far greater resistance to the detection loophole than maximally entangled states, allowing one to close the loophole with detection efficiency greater than 2/3. Here we demonstrate that this same limit holds for photon-counting CHSH Bell tests which can demonstrate non-locality for higher dimensiona…
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 practi…
Finite-key security analysis of decoy-state QKD with source and detector imperfections
University of Vigo（维戈大学）；Vigo Quantum Communication Center, University of Vigo（维戈量子通信中心，维戈大学）；Escuela de Ingeniería de Telecomunicación, Department of Signal Theory and Communications, University of Vigo（电信工程学院，信号理论与通信系，维戈大学）；atlanTTic Research Center, University of Vigo（atlanTTic研究中心，维戈大学）
We propose efficient-phase-encoding protocols for continuous-variable quantum key distribution using coherent states and postselection. By these phase encodings, the probability of basis mismatch is reduced and total efficiency is increased. We also propose mixed-state protocols by omitting a part of classical communication steps in the efficient-phase-encoding protocols. The omission implies a reduction of information to an eavesdropper and possibly enhances the security of the protocols. We investigate the security of the protocols against individual beam splitting attack.
Analytic properties of cross-click operators in passive multi-basis photodetection: monotonicity, exact convergence rates, and dimension reduction for quantum key distribution
Quantum cryptography harnesses quantum light, in particular single photons, to provide security guarantees that cannot be reached by classical means. For each cryptographic task, the security feature of interest is directly related to the photons' non-classical properties. Quantum dot-based single-photon sources are remarkable candidates, as they can in principle emit deterministically, with high brightness and low multiphoton contribution. Here, we show that these sources provide additional security benefits, thanks to the tunability of coherence in the emitted photon-number states. We identi…
Device-independent quantum key distribution (DI-QKD) offers the strongest form of security against eavesdroppers bounded by the laws of quantum mechanics. However, a practical implementation is still pending due to the requirement of combinations of visibility and detection efficiency that are beyond those possible with current technology. This mismatch motivates the search for DI-QKD protocols that can close the gap between theoretical and practical security. In this work, we present two DI-QKD protocols whose security relies on Bell inequalities with more than two inputs and two outputs. We …
It is known that measurement-device-independent quantum key distribution (MDI-QKD) provides ultimate security from all types of side-channel attack against detectors at the expense of low key generation rate. Here, we propose MDI-QKD using 3-dimensional quantum states and show that the protocol improves the secret key rate under the analysis of mismatched-basis statistics. Specifically, we analyze security of the 3d-MDI-QKD protocol with uncharacterized sources, meaning that the original sources contain unwanted states instead of expected one. We simulate secret key rate of the protocol and id…
A highly attenuated laser pulse which gives a weak coherent state is widely used in quantum key distribution (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 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 apply the methods from entanglement distillation protocols bas…
Quantum Cryptography and Autoformalization in Lean
MIT Center for Theoretical Physics – a Leinweber Institute（麻省理工学院理论物理中心——莱因韦伯研究所）；Research Laboratory of Electronics, Massachusetts Institute of Technology（麻省理工学院电子研究实验室）；Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology（麻省理工学院电气工程和计算机科学系）
Quantum no-cloning, the impossibility of perfectly cloning an arbitrary unknown quantum state, is one of the most fundamental limitations due to the laws of quantum mechanics, which underpin the physical security of quantum key distribution. Quantum physics does allow, however, approximate cloning with either imperfect state fidelity and/or probabilistic success. Whereas approximate quantum cloning of single-particle states has been tested previously, experimental cloning of quantum entanglement -- a highly non-classical correlation -- remained unexplored. Based on a multiphoton linear optics …
Side-channel attacks on practical quantum key distribution systems compromise its security. Although some of these attacks can be taken into account, the general recipe of how to eliminate all side-channel flaws is still missing. In this work, we propose a method for estimation of the total passive side-channel information leakage from the Alice's light source. The method relies on Hong-Ou-Mandel interference between different signals emitted by Alice, which reveals their overall mode mismatch without the necessity to measure all individual degrees of freedom independently. We include experime…
In this paper we present a new proof technique for semi-quantum key distribution protocols which makes use of a quantum entropic uncertainty relation to bound an adversary's information. Our new technique provides a more optimistic key-rate bound than previous work relying only on noise statistics (as opposed to using additional mismatched measurements which increase the noise tolerance of this protocol, but at the cost of requiring four times the amount of measurement data). Our new technique may hold application in the proof of security of other semi-quantum protocols or protocols relying on…
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 d…
Measurement-device-independent quantum key distribution (MDI QKD) offers great security in practice because it removes all detector side channels. However, conducting MDI QKD over free-space channels is challenging. One of the largest culprits is the mismatched transmittance of the two independent turbulent channels causing a reduced Hong-Ou-Mandel visibility and thus a lower secret key rate. Here we introduce a dynamic attenuation scheme, where the transmittance of each of the two channels is monitored in real time by transmitting bright light pulses from each users to the measurement device.…
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 improve…
We demonstrate the decoy-state quantum key distribution (QKD) with one-way quantum communication in polarization space over 102km. Further, we simplify the experimental setup and use only one detector to implement the one-way decoy-state QKD over 75km, with the advantage to overcome the security loopholes due to the efficiency mismatch of detectors. Our experimental implementation can really offer the unconditionally secure final keys. We use 3 different intensities of 0, 0.2 and 0.6 for the pulses of source in our experiment. In order to eliminate the influences of polarization mode dispersio…
Reference-frame-independent measurement-device-independent quantum key distribution (RFI-MDI-QKD) is a novel protocol which eliminates all possible attacks on detector side and necessity of reference-frame alignment in source sides. However, its performance may degrade notably due to statistical fluctuations, since more parameters, e.g. yields and error rates for mismatched-basis events, must be accumulated to monitor the security. In this work, we find that the original decoy-states method estimates these yields over pessimistically since it ignores the potential relations between different b…
The information theoretic security promised by quantum key distribution (QKD) holds as long as the assumptions in the theoretical model match the parameters in the physical implementation. The superlinear behaviour of sensitive single-photon detectors represents one such mismatch and can pave the way to powerful attacks hindering the security of QKD systems, a prominent example being the after-gate attack. A longstanding tenet is that trapped carriers causing delayed detection can help mitigate this attack, but despite intensive scrutiny, it remains largely unproven. Here we approach this prob…
