We provide a simple method to obtain an upper bound on the secret key rate that is particularly suited to analyze practical realizations of quantum key distribution protocols with imperfect devices. We consider the so-called trusted device scenario where Eve cannot modify the actual detection devices employed by Alice and Bob. The upper bound obtained is based on the available measurements results, but it includes the effect of the noise and losses present in the detectors of the legitimate users.
We consider controllability of two conjugate observables Z and X by two parties with classical communication. The ability is specified by two alternative tasks, (i) agreement on Z and (ii) preparation of an eigenstate of X with use of an extra communication channel. We prove that their feasibility is equivalent to that of key distillation if the extra channel is quantum, and to that of entanglement distillation if it is classical. This clarifies the distinction between two entanglement measures, distillable key and distillable entanglement.
In this work, we investigate what kinds of quantum states are feasible to perform perfectly secure secret sharing, and present its necessary and sufficient conditions. We also show that the states are bipartite distillable for all bipartite splits, and hence the states could be distillable into the Greenberger-Horne-Zeilinger state. We finally exhibit a class of secret-sharing states, which have an arbitrarily small amount of bipartite distillable entanglement for a certain split.
Quantum secret sharing allows each player to have classical information for secret sharing in quantum mechanical ways. In this work, we construct a class of quantum states on which players can quantumly perform secret sharing secure against dishonest players as well as eavesdropper. We here call them the genuine secret-sharing states. In addition, we show that if $N$ players share an $N$-party genuine secret-sharing state, then arbitrary $M$ players out of the total players can share an $M$-party genuine secret-sharing state by means of local operations and classical communication on the state…
We look into multipartite quantum states on which quantum cryptographic protocols including quantum key distribution and quantum secret sharing can be perfectly performed, and define the quantum cryptographic resource distillable rate as the asymptotic rate at which such multipartite state can be distilled from a given multipartite state. Investigating several relations between entanglement and the rate, we show that there exists a multipartite bound entangled state whose quantum cryptographic resource distillable rate is strictly positive, that is, there exists a multipartite entangled state …
Four-qubit Smolin bound entangled state has a distinct feature: the state is not distillable when every qubit is seperated from each other; but it makes two separated qubit entangled if the other qubits group together. Here the feature is applied to quantum secret sharing, a QSS protocol similar to Ekert 91 protocol of QKD is proposed. The security problem, disadvantage and advantageof this protocol are disscused.
It is shown that (i) all entangled states can be mapped by single-copy measurements into probability distributions containing secret correlations, and (ii) if a probability distribution obtained from a quantum state contains secret correlations, then this state has to be entangled. These results prove the existence of a two-way connection between secret and quantum correlations in the process of preparation. They also imply that either it is possible to map any bound entangled state into a distillable probability distribution or bipartite bound information exists.
Recently it has been shown that quantum cryptography beyond pure entanglement distillation is possible and a paradigm for the associated protocols has been established. Here we systematically generalize the whole paradigm to the multipartite scenario. We provide constructions of new classes of multipartite bound entangled states, i.e., those with underlying twisted GHZ structure and nonzero distillable cryptographic key. We quantitatively estimate the key from below with help of the privacy squeezing technique.
The security of a deterministic quantum scheme for communication, namely the LM05 [1], is studied in presence of a lossy channel under the assumption of imperfect generation and detection of single photons. It is shown that the scheme allows for a rate of distillable secure bits higher than that pertaining to BB84 [2]. We report on a first implementation of LM05 with weak pulses.
Non-additivity is one of the distinctive traits of Quantum Information Theory: the combined use of quantum objects may be more advantageous than the sum of their individual uses. Non-additivity effects have been proven, for example, for quantum channel capacities, entanglement distillation or state estimation. In this work, we consider whether non-additivity effects can be found in Classical Information Theory. We work in the secret-key agreement scenario in which two honest parties, having access to correlated classical data that are also correlated to an eavesdropper, aim at distilling a sec…
We relate the problem of irreversibility of entanglement with the recently defined measures of quantum correlation - quantum discord and one-way quantum deficit. We show that the entanglement of formation is always strictly larger than the coherent information and the entanglement cost is also larger in most cases. We prove irreversibility of entanglement under LOCC for a family of entangled states. This family is a generalization of the maximally correlated states for which we also give an analytic expression for the distillable entanglement, the relative entropy of entanglement, the distilla…
The squashed entanglement is a fundamental entanglement measure in quantum information theory, finding application as an upper bound on the distillable secret key or distillable entanglement of a quantum state or a quantum channel. This paper simplifies proofs that the squashed entanglement is an upper bound on distillable key for finite-dimensional quantum systems and solidifies such proofs for infinite-dimensional quantum systems. More specifically, this paper establishes that the logarithm of the dimension of the key system (call it $\log_{2}K$) in an $\varepsilon$-approximate private state…
We demonstrate a new construction for perfect quantum secret sharing (QSS) schemes based on imperfect "ramp" secret sharing combined with classical encryption, in which the individual parties' shares are split into quantum and classical components, allowing the former to be of lower dimension than the secret itself. We show that such schemes can be performed with smaller quantum components and lower overall quantum communication than required for existing methods. We further demonstrate that one may combine both imperfect quantum and imperfect classical secret sharing to produce an overall per…
We consider the problem of secret key extraction when $n$ honest parties and an eavesdropper share correlated information. We present a family of probability distributions and give the full characterization of its distillation properties. This formalism allows us to design a rich variety of cryptographic scenarios. In particular, we provide examples of multipartite probability distributions containing non-distillable secret correlations, also known as bound information.
We study and solve the problem of distilling secret key from quantum states representing correlation between two parties (Alice and Bob) and an eavesdropper (Eve) via one-way public discussion: we prove a coding theorem to achieve the "wire-tapper" bound, the difference of the mutual information Alice-Bob and that of Alice-Eve, for so-called cqq-correlations, via one-way public communication. This result yields information--theoretic formulas for the distillable secret key, giving ``ultimate'' key rate bounds if Eve is assumed to possess a purification of Alice and Bob's joint state. Specialis…
We investigate one-way communication scenarios where Bob manipulating on his parts can transfer some sub-system to the environment. We define reduced versions of quantum communication rates and further, prove new upper bounds on one-way quantum secret key, distillable entanglement and quantum channel capacity by means of their reduced versions. It is shown that in some cases they drastically improve their estimation.
We study the problem of secret key distillation from bipartite states in the scenario where Alice and Bob can only perform measurements at the single-copy level and classically process the obtained outcomes. Even with these limitations, secret bits can be asymptotically distilled by the honest parties from any two-qubit entangled state, under any individual attack. Our results point out a complete equivalence between two-qubit entanglement and secure key distribution: a key can be established through a one-qubit channel if and only if it allows to distribute entanglement. These results can be …
We derive a formal connection between quantum data hiding and quantum privacy, confirming the intuition behind the construction of bound entangled states from which secret bits can be extracted. We present three main results. First, we show how to simplify the class of private states and related states via reversible local operation and one-way communication. Second, we obtain a bound on the one-way distillable entanglement of private states in terms of restricted relative entropy measures, which is tight in many cases and shows that protocols for one-way distillation of key out of states with…
Within entanglement theory there are criteria which certify that some quantum states cannot be distilled into pure entanglement. An example is the positive partial transposition criterion. Here we present, for the first time, the analogous thing for secret correlations. We introduce a computable criterion which certifies that a probability distribution between two honest parties and an eavesdropper cannot be (asymptotically) distilled into a secret key. The existence of non-distillable correlations with positive secrecy cost, also known as bound information, is an open question. This criterion…
Quantum key distribution over probabilistic quantum repeaters is addressed. We compare, under practical assumptions, two such schemes in terms of their secure key generation rates per quantum memory. The two schemes under investigation are the one proposed by Duan et al. in [Nat. 414, 413 (2001)] and that of Sangouard et al. in [Phys. Rev. A 76, 050301 (2007)]. We consider various sources of imperfection in both protocols, such as nonzero double-photon probabilities at the sources, dark counts in detectors, and inefficiencies in the channel, photodetectors and memories. We also consider memory…
For single-photon quantum key generation between two users, it is shown that the use of a shared secret key extended via a pseudo-random number generator may simultaneously enhance the security and efficiency of the cryptosystem. This effect arises from the intrinsic performance difference between quantum detectors with versus without knowledge of the key, a purely quantum effect and a new principle for key generation. No intrusion level estimation is needed and the method is directly applicable to realistic systems with imperfections. Quantum direct encryption is also made possible by such us…
Sequential Quantum Secret Sharing schemes (QSS) do not use entangled states for secret sharing, rather they rely on sequential operations of the players on a single state which is circulated between the players. In order to check the viability of these schemes under imperfect operations and noise in the channels, we consider one such scheme in detail and show that under moderate conditions it is still possible to extract viable secure shared keys in this scheme. Although we specifically consider only one type of sequential scheme and three different noise models, our method is fairly general t…
Distribution and distillation of entanglement over quantum networks is a basic task for Quantum Internet applications. A fundamental question is then to determine the ultimate performance of entanglement distribution over a given network. Although this question has been extensively explored for bipartite entanglement-distribution scenarios, less is known about multipartite entanglement distribution. Here we establish the fundamental limit of distributing multipartite entanglement, in the form of GHZ states, over a quantum network. In particular, we determine the multipartite entanglement distr…
A secret key shared through quantum key distribution between two cooperative players is secure against any eavesdropping attack allowed by the laws of physics. Yet, such a key can be established only when the quantum channel error rate due to eavesdropping or imperfect apparatus is low. Here, I report a practical quantum key distribution scheme making use of an adaptive privacy amplification procedure with two-way classical communication. Then, I prove that the scheme generates a secret key whenever the bit error rate of the quantum channel is less than $0.5-0.1\sqrt{5} \approx 27.6%$, thereby…
In practical quantum key distribution (QKD) system, the state preparation and measurement are imperfect comparing with the ideal BB84 protocol, which are always state-dependent in practical realizations. If the state-dependent imperfections can not be regarded as an unitary transformation, it should not be considered as part of quantum channel noise introduced by the eavesdropper, the commonly used secret key rate formula GLLP can not be applied correspondingly. In this paper, the unconditional security of quantum key distribution with state-dependent imperfection has been analyzed by estimati…
The proof of the No-Go Theorem of unconditionally secure quantum bit commitment depends on the assumption that Alice knows every detail of the protocol, including the probability distributions associated with all the random variables generated by Bob. We argue that this condition may not be universally satisfied. In fact it can be shown that when Bob is allowed to use a secret probability distribution, the joint quantum state is inevitably mixed. It is then natural to ask if Alice can still cheat. A positive answer has been given by us [13] for the perfect concealing case. In this paper, we pr…
In single-qubit quantum secret sharing, a secret is shared between N parties via manipulation and measurement of one qubit at a time. Each qubit is sent to all N parties in sequence; the secret is encoded in the first participant's preparation of the qubit state and the subsequent participants' choices of state rotation or measurement basis. We present a protocol for single-qubit quantum secret sharing using polarization entanglement of photon pairs produced in type-I spontaneous parametric downconversion. We investigate the protocol's security against eavesdropping attack under common experim…
Quantum key distribution performs the trick of growing a secret key in two distant places connected by a quantum channel. The main reason is that the legitimate users can bound the information gathered by the eavesdropper. In practical systems, whether because of finite resources or external conditions, the quantum channel is subject to fluctuations. A rate adaptive information reconciliation protocol, that adapts to the changes in the communication channel, is then required to minimize the leakage of information in the classical postprocessing. We consider here the leakage of a rate-adaptive …
We analyze various prominent quantum repeater protocols in the context of long-distance quantum key distribution. These protocols are the original quantum repeater proposal by Briegel, Dür, Cirac and Zoller, the so-called hybrid quantum repeater using optical coherent states dispersively interacting with atomic spin qubits, and the Duan-Lukin-Cirac-Zoller-type repeater using atomic ensembles together with linear optics and, in its most recent extension, heralded qubit amplifiers. For our analysis, we investigate the most important experimental parameters of every repeater component and find th…
We investigate Gaussian quantum states in view of their exceptional role within the space of all continuous variables states. A general method for deriving extremality results is provided and applied to entanglement measures, secret key distillation and the classical capacity of Bosonic quantum channels. We prove that for every given covariance matrix the distillable secret key rate and the entanglement, if measured appropriately, are minimized by Gaussian states. This result leads to a clearer picture of the validity of frequently made Gaussian approximations. Moreover, it implies that Gaussi…
We consider distillation of secret bits from partially secret noisy correlations P_ABE, shared between two honest parties and an eavesdropper. The most studied distillation scenario consists of joint operations on a large number of copies of the distribution (P_ABE)^N, assisted with public communication. Here we consider distillation with only one copy of the distribution, and instead of rates, the 'quality' of the distilled secret bits is optimized, where the 'quality' is quantified by the secret-bit fraction of the result. The secret-bit fraction of a binary distribution is the proportion wh…
The influence of imperfections on achievable secret-key generation rates of quantum key distribution protocols is investigated. As examples of relevant imperfections, we consider tagging of Alice's qubits and dark counts at Bob's detectors, while we focus on a powerful eavesdropping strategy which takes full advantage of tagged signals. It is demonstrated that error correction and privacy amplification based on a combination of a two-way classical communication protocol and asymmetric Calderbank-Shor-Steane codes may significantly postpone the disastrous influence of dark counts. As a result, …
As quantum key distribution becomes a mature technology, it appears clearly that some assumptions made in the security proofs cannot be justified in practical implementations. This might open the door to possible side-channel attacks. We examine several discrepancies between theoretical models and experimental setups in the case of continuous-variable quantum key distribution. We study in particular the impact of an imperfect modulation on the security of Gaussian protocols and show that approximating the theoretical Gaussian modulation with a discrete one is sufficient in practice. We also ad…
We develop a connection between tripartite information $I_3$, secret sharing protocols and multi-unitaries. This leads to explicit ((2,3)) threshold schemes in arbitrary dimension minimizing tripartite information $I_3$. As an application we show that Page scrambling unitaries simultaneously work for all secrets shared by Alice. Using the $I_3$-Ansatz for imperfect sharing schemes we discover examples of VIP sharing schemes.
We study how the imperfection of intensity modulator effects on the security of a practical quantum key distribution system. The extinction ratio of the realistic intensity modulator is considered in our security analysis. We show that the secret key rate increases, under the practical assumption that the indeterminable noise introduced by the imperfect intensity modulator can not be controlled by the eavesdropper.
Upper bounds on the secret-key-agreement capacity of a quantum channel serve as a way to assess the performance of practical quantum-key-distribution protocols conducted over that channel. In particular, if a protocol employs a quantum repeater, achieving secret-key rates exceeding these upper bounds is a witness to having a working quantum repeater. In this paper, we extend a recent advance [Liuzzo-Scorpo et al., arXiv:1705.03017] in the theory of the teleportation simulation of single-mode phase-insensitive Gaussian channels such that it now applies to the relative entropy of entanglement me…
The feasibility of trust-free long-haul quantum key distribution (QKD) networks is addressed. We combine measurement-device-independent QKD (MDI-QKD), as an access technology, with a quantum repeater setup, at the core of future quantum communication networks. This will provide a quantum link none of whose intermediary nodes need to be trusted, or, in our terminology, a trust-free QKD link. As the main figure of merit, we calculate the secret key generation rate when a particular probabilistic quantum repeater protocol is in use. We assume the users are equipped with imperfect single photon so…
The faraday mirror (FM) plays a very important role in maintaining the stability of two way plug-and-play quantum key distribution (QKD) system. However, the practical FM is imperfect, which will not only introduce additional quantum bit error rate (QBER) but also leave a loophole for Eve to spy the secret key. In this paper, we propose a passive faraday mirror attack in two way QKD system based on the imperfection of FM. Our analysis shows that, if the FM is imperfect, the dimension of Hilbert space spanned by the four states sent by Alice is three instead of two. Thus Eve can distinguish the…
Multiparty quantum communication is an important branch of quantum networks. It enables private information transmission with information-theoretic security among legitimate parties. We propose a sender-controlled measurement-device-independent multiparty quantum communication protocol. The sender Alice divides a private message into several parts and delivers them to different receivers for secret sharing with imperfect measurement devices and untrusted ancillary nodes. Furthermore, Alice acts as an active controller and checks the security of quantum channels and the reliability of each rece…
Quantum secure direct communication (QSDC) and deterministic secure quantum communication (DSQC) are two important branches of quantum cryptography, where one can transmit a secret message securely without encrypting it by a prior key. In the practical scenario, an adversary can apply detector-side-channel attacks to get some non-negligible amount of information about the secret message. Measurement-device-independent (MDI) quantum protocols can remove this kind of detector-side-channel attack, by introducing an untrusted third party (UTP), who performs all the measurements during the protocol…
Quantum key distribution (QKD) has been proved to be information-theoretically secure in theory. Unfortunately, the imperfect devices in practice compromise its security. Thus, to improve the security property of practical QKD systems, a commonly used method is to patch the loopholes in the existing QKD systems. However, in this work, we show an adversary's capability of exploiting the imperfection of the patch itself to bypass the patch. Specifically, we experimentally demonstrate that, in the detector under test, the patch of photocurrent monitor against the detector blinding attack can be d…
While it is usually known that the mean value of a single observable is enough to detect entanglement or its distillability, the counterpart of such an approach in the case of quatum privacy has been missing. Here we develop the concept of a privacy witness, i.e. a single observable that may detect presence of the secure key even in the case of bound entanglement. Then we develop the notion of secret key estimation based on few observables and discuss the witness decomposition into local measurements. The surprising property of the witness is that with the help of a low number of product mesur…
Quantum key distribution (QKD) provides ultimate cryptographic security based on the laws of quantum mechanics. For point-to-point QKD protocols, the security of the generated key is compromised by detector side channel attacks. This problem can be solved with measurement device independent QKD (mdi-QKD). However, mdi-QKD has shown limited performances in terms of the secret key generation rate, due to post-selection in the Bell measurements. We show that high dimensional (Hi-D) encoding (qudits) improves the performance of current mdi-QKD implementations. The scheme is proven to be unconditio…
Robust quantum key distribution with imperfections in state preparation and characterization
Henan Key Laboratory of Quantum Information and Cryptography, IEU（IEU量子信息与密码学河南省重点实验室）；State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Key Lab of Navigation and Location Services, Department of Electronic Engineering, Shanghai Jiao Tong University（上海交通大学电子工程系先进光通信系统与网络国家重点实验室上海导航与定位服务重点实验室）
