This paper provides a security proof of the Bennett-Brassard (BB84) quantum key distribution protocol in practical implementation. To prove the security, it is not assumed that defects in the devices are absorbed into an adversary's attack. In fact, the only assumption in the proof is that the source is characterized. The proof is performed by lower-bounding adversary's Renyi entropy about the key before privacy amplification. The bound reveals the leading factors reducing the key generation rate.
We prove the security of a high-capacity quantum key distribution protocol over noisy channels. By using entanglement purification protocol, we construct a modified version of the protocol in which we separate it into two consecutive stages. We prove their securities respectively and hence the security of the whole protocol.
It is repeatedly and persistently claimed in the literature that a specific trace criterion $d$ would guarantee universal composition security in quantum cryptography. Currently that is the sole basis of unconditional security claim in quantum key distribution. In this paper, it is shown that just security against known-plaintext attacks when the generated key is used in direct encryption is not provided by $d$. The problem is directly connected with several general problems in the existing unconditional security proofs in quantum key distribution. A number of issues will be clarified concerni…
We describe the popular BB84 protocol and critically examine its security proof as presented by Shor and Preskill. The proof requires the use of quantum error correcting codes called the Calderbank-Shor-Steanne (CSS) quantum codes. These quantum codes are constructed in the quantum domain from two suitable classical linear codes, one used to correct for bit-flip errors and the other for phase-flip errors. Consequently, as a prelude to the security proof, the report reviews the essential properties of linear codes, especially the concept of cosets, before building the quantum codes that are uti…
Unconditional security of the BB84 quantum key distribution protocol has been proved by exploiting the fundamental laws of quantum mechanics, but the practical quantum key distribution system maybe hacked by considering the imperfect state preparation and measurement respectively. Until now, different attacking schemes have been proposed by utilizing imperfect devices, but the general security analysis model against all of the practical attacking schemes has not been proposed. Here, we demonstrate that the general practical attacking schemes can be divided into the Trojan horse attack, strong …
We show the information-theoretic security proof of the differential-phase-shift (DPS) quantum key distribution (QKD) protocol based on the complementarity approach [arXiv:0704.3661 (2007)]. Our security proof provides a slightly better key generation rate compared to the one derived in the previous security proof in [arXiv:1208.1995 (2012)] that is based on the Shor-Preskill approach [Phys. Rev. Lett. ${\bf 85}$, 441 (2000)]. This improvement is obtained because the complementarity approach can employ more detailed information on Alice's sending state in estimating the leaked information to a…
We prove the security of the 1984 protocol of Bennett and Brassard (BB84) for quantum key distribution. We first give a key distribution protocol based on entanglement purification, which can be proven secure using methods from Lo and Chau's proof of security for a similar protocol. We then show that the security of this protocol implies the security of BB84. The entanglement-purification based protocol uses Calderbank-Shor-Steane (CSS) codes, and properties of these codes are used to remove the use of quantum computation from the Lo-Chau protocol.
Two-way Gaussian protocols have the potential to increase quantum key distribution (QKD) protocols' secret-key rates by orders of magnitudes~[Phys.~Rev.~A {\bf 94}, 012322 (2016)]. Security proofs for two-way protocols, however, are underdeveloped at present. In this paper, we establish a security proof framework for the general coherent attack on two-way Gaussian protocols in the asymptotic regime. We first prove that coherent-attack security can be reduced to collective-attack security for all two-way QKD protocols. Next, we identify two different constraints that each provide intrusion para…
Quantum Key Distribution (QKD) in principle offers unconditional security based on the laws of physics. Continuous variable (CV) quantum key distribution has the potential for high-key-rate and low-cost implementations using standard telecom components. Despite tremendous theoretical and experimental progress in continuous-variable quantum key distribution, the security has not been rigorously established for most current continuous-variable quantum key distribution systems that have imperfections. Among the imperfections, intensity fluctuation is a significant principal problem affecting secu…
We prove the security of quantum key distribution against the most general attacks which can be performed on the channel, by an eavesdropper who has unlimited computation abilities, and the full power allowed by the rules of classical and quantum physics. A key created that way can then be used to transmit secure messages in a way that their security is also unaffected in the future.
We present an extension of the first proof for the unconditional security of the BB84 quantum key distribution protocol which was given by Mayers. We remove the constraint that a perfect BB84 quantum source is required and the proof given here covers a range of practical quantum sources. Nothing is assumed about the detector except that the efficiency with which signals are detected is basis independent.
Recently, Pawlowski [Phys. Rev. A 82, 032313 (2010)] claimed to have proven the security of a quantum key distribution by using only the monogamy of Bell's inequality violations. In the proof, however, he tacitly assumed that the eavesdropper's outcome is binary. The assumption cannot be justified because Eve's (eavesdropper's) power can only be limited by natural principle. We provide a counter-example for a step of the proof.
We prove the unconditional security of an entanglement-based quantum-key-distribution protocol using detectors that respond to multiple modes of light and cannot distinguish between one from two or more photons. Even with such practical detectors, any defect in the source is automatically detected as an increase in the error rate or in the rate of double clicks.
It is widely believed that quantum key distribution (QKD) has been proved unconditionally secure for realistic models applicable to various current experimental schemes. Here we summarize briefly why this is not the case, from both the viewpoints of fundamental quantitative security and applicable models of security analysis, with some morals drawn.
We give the first composable security proof for continuous-variable quantum key distribution with coherent states against collective attacks. Crucially, in the limit of large blocks the secret key rate converges to the usual value computed from the Holevo bound. Combining our proof with either the de Finetti theorem or the Postselection technique then shows the security of the protocol against general attacks, thereby confirming the long-standing conjecture that Gaussian attacks are optimal asymptotically in the composable security framework. We expect that our parameter estimation procedure, …
We discuss long code problems in the Bennett-Brassard 1984 (BB84) quantum key distribution protocol and describe how they can be overcome by concatenation of the protocol. Observing that concatenated modified Lo-Chau protocol finally reduces to the concatenated BB84 protocol, we give the unconditional security of the concatenated BB84 protocol.
Numerical security analysis for practical quantum key distribution
Vigo Quantum Communication Center, University of Vigo（维戈量子通信中心，维戈大学）；School of Telecommunication Engineering, Department of Signal Theory and Communications, University of Vigo（维戈大学电信工程学院信号理论与通信系）；atlanTTic Research Center, University of Vigo（维戈大学atlanTTic研究中心）
In a deterministic quantum key distribution (DQKD) protocol with a two-way quantum channel, Bob sends a qubit to Alice who then encodes a key bit onto the qubit and sends it back to Bob. After measuring the returned qubit, Bob can obtain Alice's key bit immediately, without basis reconciliation. Since an eavesdropper may attack the qubits traveling on either the Bob-Alice channel or the Alice-Bob channel, the security analysis of DQKD with a two-way quantum channel is complicated and its unconditional security has been controversial. This paper presents a security proof of a single-photon four…
Rigorous mathematical proofs of the security of continuous-variable quantum key distribution (CV QKD) have been obtained recently. Unfortunately, these security proofs rely on assumptions that are hardly met in experimental practice. Here I investigate these issues in detail, and discuss experimentally-friendly workarounds to assess the security of CV QKD. The aim of this paper is to show that there are hidden and unsolved issues and to indicate possible partial solutions. To provide a complete and rigorous mathematical security proof is out of the scope of this contribution.
Differential phase shift quantum key distribution systems have a high potential for achieving high speed key generation. However, its unconditional security proof is still missing, even though it has been proposed for many years. Here, we prove its security against collective attacks with a weak coherent light source in the noiseless case (i.e. no bit error). The only assumptions are that quantum theory is correct, the devices are perfect and trusted and the key size is infinite. Our proof works on threshold detectors. We compute the lower bound of the secret key generation rate using the info…
We present a continuous-variable quantum key distribution protocol combining a discrete modulation and reverse reconciliation. This protocol is proven unconditionally secure and allows the distribution of secret keys over long distances, thanks to a reverse reconciliation scheme efficient at very low signal-to-noise ratio.
A simple proof of the unconditional security of a relativistic quantum cryptosystem based on orthogonal states is proposed. Restrictions imposed by special relativity allow to substantially simplify the proof compared with the non-relativistic cryptosystems involving non-orthogonal states. Important for the proposed protocol is the spatio-temporal structure of the quantum states which is actually ignored in the non-relativistic protocols employing only the structure of the state space of the information carriers. As a consequence, the simplification arises because of the inefficiency of collec…
We present a complete protocol for BB84 quantum key distribution for a realistic setting (noise, loss, multi-photon signals of the source) that covers many of todays experimental implementations. The security of this protocol is shown against an eavesdropper having unrestricted power to manipulate the signals coherently on their path from sender to receiver. The protocol and the security proof take into account the effects concerning the finite size of the generated key.
We derive a proof of security for the Differential Phase Shift Quantum Key Distribution (DPSQKD) protocol under the assumption that Eve is restricted to individual attacks. The security proof is derived by bounding the average collision probability, which leads directly to a bound on Eve's mutual information on the final key. The security proof applies to realistic sources based on pulsed coherent light. We then compare individual attacks to sequential attacks and show that individual attacks are more powerful.
We present an approach to the unconditional security of quantum key distribution protocols based on the uncertainty principle. The approach applies to every case that has been treated via the argument by Shor and Preskill, and relieve them from the constraints of finding quantum error correcting codes. It can also treat the cases with uncharacterized apparatuses. We derive a secure key rate for the Bennett-Brassard-1984 protocol with an arbitrary source characterized only by a single parameter representing the basis dependence.
In optical implementations of the phase-encoded BB84 protocol, the bit information is usually encoded in the phase of two consecutive photon pulses generated in a Mach-Zehnder interferometer. In the actual experimental realization, the loss in the arms of the Mach-Zehnder interferometer is not balanced, for example because only one arm contains a lossy phase modulator. Therefore, the amplitudes of the pulses is not balanced, and the structure of the signals and measurements no longer corresponds to the (balanced) ideal BB84 protocol. Hence, the BB84 security analysis no longer applies in this …
We provide security bounds against coherent attacks for two families of quantum key distribution protocols that use $d$-dimensional quantum systems. In the asymptotic regime, both the secret key rate for fixed noise and the robustness to noise increase with $d$. The finite-key corrections are found to be almost insensitive to $d\lesssim 20$.
Security proof of practical quantum key distribution (QKD) has attracted a lot of attentions in recent years. Most of real-life QKD implementations are based on phase-coding BB84 protocol, which usually uses Unbalanced Mach-Zehnder Interferometer (UMZI) as the information coder and decoder. However, the long arm and short arm of UMZI will introduce different loss in practical experimental realizations, the state emitted by Alice's side is nolonger standard BB84 states. In this paper, we will give a security analysis in this situation. Counterintuitively, active compensation for this different …
The security of quantum key distribution (QKD) has been proven for different protocols, in particular for the BB84 protocol. It has been shown that this scheme is robust against eventual imperfections in the state preparation, and sending only three different states delivers the same secret key rate achievable with four states. In this work, we prove, in a finite-key scenario, that the security of this protocol can be maintained even with less measurement operators on the receiver. This allows us to implement a time-bin encoding scheme with a minimum amount of resources.
We give a proof that entanglement purification, even with noisy apparatus, is sufficient to disentangle an eavesdropper (Eve) from the communication channel. In the security regime, the purification process factorises the overall initial state into a tensor-product state of Alice and Bob, on one side, and Eve on the other side, thus establishing a completely private, albeit noisy, quantum communication channel between Alice and Bob. The security regime is found to coincide for all practical purposes with the purification regime of a two-way recurrence protocol. This makes two-way entanglement …
Privacy amplification (PA) is an essential post-processing step in quantum key distribution (QKD) for removing any information an eavesdropper may have on the final secret key. In this paper, we consider delaying PA of the final key after its use in one-time pad encryption and prove its security. We prove that the security and the key generation rate are not affected by delaying PA. Delaying PA has two applications: it serves as a tool for significantly simplifying the security proof of QKD with a two-way quantum channel, and also it is useful in QKD networks with trusted relays. To illustrate…
We devise a simple modification that essentially doubles the efficiency of the BB84 quantum key distribution scheme proposed by Bennett and Brassard. We also prove the security of our modified scheme against the most general eavesdropping attack that is allowed by the laws of physics. The first major ingredient of our scheme is the assignment of significantly different probabilities to the different polarization bases during both transmission and reception, thus reducing the fraction of discarded data. A second major ingredient of our scheme is a refined analysis of accepted data: We divide th…
Among many quantum key distribution (QKD) protocols, the round-robin differential phase shift (RRDPS) protocol is unique in that it can upper-bound the amount of the information leakage without monitoring the signal disturbance. To expedite implementation of the protocol, however, the number of pulses forming a single block should be kept small, which significantly decreases the key rates in the original security proof. In the present paper, we refine the security proof of the RRDPS protocol in the finite-sized regime and achieve a tighter estimation for the information leakage without changin…
Quantum key distribution allows two parties, traditionally known as Alice and Bob, to establish a secure random cryptographic key if, firstly, they have access to a quantum communication channel, and secondly, they can exchange classical public messages which can be monitored but not altered by an eavesdropper, Eve. Quantum key distribution provides perfect security because, unlike its classical counterpart, it relies on the laws of physics rather than on ensuring that successful eavesdropping would require excessive computational effort. However, security proofs of quantum key distribution ar…
In this paper, we rigorously prove the intuition that in security proofs for BB84 one may regard an incoming signal to Bob as a qubit state. From this result, it follows that all security proofs for BB84 based on a virtual qubit entanglement distillation protocol, which was originally proposed by Lo and Chau [H.-K. Lo and H. F. Chau, Science 283, 2050 (1999)], and Shor and Preskill [P. W. Shor and J. Preskill, Phys. Rev. Lett. 85, 441 (2000)], are all valid even if Bob's actual apparatus cannot distill a qubit state explicitly. As a consequence, especially, the well-known result that a higher …
Continuous-variable quantum key distribution (CV-QKD) has many practical advantages including compatibility with current optical communication technology. Implementation using heterodyne measurements is particularly attractive since it eliminates the need for active phase locking of the remote pair of local oscillators, but the full security of CV QKD with discrete modulation was only proved for a protocol using homodyne measurements. Here we propose an all-heterodyne CV-QKD protocol with binary modulation and prove its security against general attacks in the finite-key regime. Although replac…
We give a security proof of the `Round Robin Differential Phase Shift' Quantum Key Distribution scheme, and we give a tight bound on the required amount of privacy amplification. Our proof consists of the following steps. We construct an EPR variant of the scheme. We identify Eve's optimal way of coupling an ancilla to an EPR qudit pair under the constraint that the bit error rate between Alice and Bob should not exceed a value beta. As a function of beta we derive, for finite key size, the trace distance between the real state and a state in which no leakage exists. For asymptotic key size we…
The practical homodyne detector model of continuous-variable quantum key distribution models the inherent imperfections of the practical homodyne detector, namely the limited detection efficiency and the electronic noise, into trusted loss. However, the conventional practical homodyne detector model is valid only when both the imperfections of the practical homodyne detector are calibrated. In this paper, we show a modified practical homodyne detector model that can model the imperfections separately. The phase-sensitive amplifier is further applied to compensate the imperfections of the pract…
Many papers proved the security of quantum key distribution (QKD) system, in the asymptotic framework. The degree of the security has not been discussed in the finite coding-length framework, sufficiently. However, to guarantee any implemented QKD system requires, it is needed to evaluate a protocol with a finite coding-length. For this purpose, we derive a tight upper bound of the eavesdropper's information. This bound is better than existing bounds. We also obtain the exponential rate of the eavesdropper's information. Further, we approximate our bound by using the normal distribution.
A consolidated and accessible security proof for finite-size decoy-state quantum key distribution
Fraunhofer Institute for Telecommunications, Heinrich-Hertz-Institut, HHI（弗劳恩霍夫电信研究所，海因里希·赫兹研究所）；Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo（滑铁卢大学量子计算研究所及物理与天文学系）；Vigo Quantum Communication Center, University of Vigo（维戈大学维戈量子通信中心）；Escuela de Ingeniería de Telecomunicación, Department of Signal Theory and Communications, University of Vigo（维戈大学电信工程学院信号理论与通信系）；AtlanTTic Research Center, University of Vigo（维戈大学阿特兰蒂克研究中心）
The majority of research to date has concentrated on the quantum key distribution (QKD) between two parties. In general, the QKD protocols proposed for the multiparty scenario often involve the usage of a maximally entangled state, such as GHZ, which is challenging to implement in practice. This paper examines the prepare and measure version of multiparty communication through quantum key distribution. It is sufficient to have the capability of preparing and measuring a single qubit state. The security of the multiparty prepare and measure QKD is demonstrated by utilizing the well-known techni…
We show that monogamy of Bell's inequality violations, which is strictly weaker condition than no-signaling is enough to prove security of quantum key distribution. We derive our results for a whole class of monogamy constraints and generalize our results to any theory that communicating parties may have access to. Some of these theories do not respect no-signaling principle yet still allow for secure communication. This proves that no-signaling is only a sufficient condition for the possibility of secure communication, but not the necessary one. We also present some new qualitative results co…
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…
Quantum secure direct communication is one of the important mode of quantum communication, which sends secret information through a quantum channel directly without setting up a prior key. Over the past decade, numerous protocols have been proposed, and part of them have been experimentally demonstrated. However, the strict security proof is still in suspense. Two-way protocol is seen as one of the most practical protocol, in this paper, the security of the two-way quantum secure direct communication protocol will be proved against general attacks when the noisy and lossy channel is taken into…
We give a Shor-Preskill type security-proof to the quantum key distribution without public announcement of bases [W.Y. Hwang et al., Phys. Lett. A 244, 489 (1998)]. First, we modify the Lo-Chau protocol once more so that it finally reduces to the quantum key distribution without public announcement of bases. Then we show how we can estimate the error rate in the code bits based on that in the checked bits in the proposed protocol, that is the central point of the proof. We discuss the problem of imperfect sources and that of large deviation in the error rate distributions. We discuss when the …
One of the simplest security proofs of quantum key distribution is based on the so-called complementarity scenario, which involves the complementarity control of an actual protocol and a virtual protocol [M. Koashi, e-print arXiv:0704.3661 (2007)]. The existing virtual protocol has a limitation in classical postprocessing, i.e., the syndrome for the error-correction step has to be encrypted. In this paper, we remove this limitation by constructing a quantum circuit for the virtual protocol. Moreover, our circuit with a shield system gives an intuitive proof of why adding noise to the sifted ke…
We present full generalisations of entropic security and entropic indistinguishability to the quantum world where no assumption but a limit on the knowledge of the adversary is made. This limit is quantified using the quantum conditional min-entropy as introduced by Renato Renner. A proof of the equivalence between the two security definitions is presented. We also provide proofs of security for two different cyphers in this model and a proof for a lower bound on the key length required by any such cypher. These cyphers generalise existing schemes for approximate quantum encryption to the entr…
Due to its ability to tolerate high channel loss, decoy-state quantum key distribution (QKD) has been one of the main focuses within the QKD community. Notably, several experimental groups have demonstrated that it is secure and feasible under real-world conditions. Crucially, however, the security and feasibility claims made by most of these experiments were obtained under the assumption that the eavesdropper is restricted to particular types of attacks or that the finite-key effects are neglected. Unfortunately, such assumptions are not possible to guarantee in practice. In this work, we pro…
In this reply I address the comment by W-Y. Hwang and O. Gittsovich on my paper [Phys. Rev. A {\bf 82}, 032313 (2010)]. The authors of the comment point out that I use implicit assumption that the alphabet of the eavesdropper is binary. They claim that such assumption is unrealistic. Here I show that even without this assumption the main result of my paper still holds.
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…
Twin-field (TF) quantum key distribution (QKD) was conjectured to beat the private capacity of a point-to-point QKD link by using single-photon interference in a central measuring station. This remarkable conjecture has recently triggered an intense research activity to prove its security. Here, we introduce a TF-type QKD protocol which is conceptually simpler than the original proposal. It relies on local phase randomization, instead of global phase randomization, which significantly simplifies its security analysis and is arguably less demanding experimentally. We demonstrate that the secure…
Quantum key distribution (QKD) is the first quantum information task to reach the level of mature technology, already fit for commercialization. It aims at the creation of a secret key between authorized partners connected by a quantum channel and a classical authenticated channel. The security of the key can in principle be guaranteed without putting any restriction on the eavesdropper's power. The first two sections provide a concise up-to-date review of QKD, biased toward the practical side. The rest of the paper presents the essential theoretical tools that have been developed to assess th…
