We study the impact of finite-size effects on the key rate of continuous-variable (CV) measurement-device-independent (MDI) quantum key distribution (QKD). Inspired by the parameter estimation technique developed in [Rupert \textit{et al.} Phys. Rev. A \textbf{90}, 062310 (2014)]~we adapt it to study CV-MDI-QKD and, assuming realistic experimental conditions, we analyze the impact of finite-size effects on the key rate. We find that, increasing the block-size, the performance of the protocol converges towards the ideal one, and that block-sizes between $10^{6}$ and $10^{9}$ data points can already provide a key rate $\sim10^{-2}$ bit/use over metropolitan distances.
We introduce a framework for graphical security proofs in device-independent quantum cryptography using the methods of categorical quantum mechanics. We are optimistic that this approach will make some of the highly complex proofs in quantum cryptography more accessible, facilitate the discovery of new proofs, and enable automated proof verification. As an example of our framework, we reprove a previous result from device-independent quantum cryptography: any linear randomness expansion protocol can be converted into an unbounded randomness expansion protocol. We give a graphical proof of this…
In the distrustful quantum cryptography model the different parties have conflicting interests and do not trust one another. Nevertheless, they trust the quantum devices in their labs. The aim of the device-independent approach to cryptography is to do away with the necessity of making this assumption, and, consequently, significantly increase security. In this paper we enquire whether the scope of the device-independent approach can be extended to the distrustful cryptography model, thereby rendering it `fully' distrustful. We answer this question in the affirmative by presenting a device-ind…
Device-independent quantum cryptography with input leakage
University of Vigo（维戈大学）；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AtlanTTic研究中心）
Quantum communication has demonstrated its usefulness for quantum cryptography far beyond quantum key distribution. One domain is two-party cryptography, whose goal is to allow two parties who may not trust each other to solve joint tasks. Another interesting application is position-based cryptography whose goal is to use the geographical location of an entity as its only identifying credential. Unfortunately, security of these protocols is not possible against an all powerful adversary. However, if we impose some realistic physical constraints on the adversary, there exist protocols for which…
A new quantum cryptography protocol, based on all unselected states of a qubit as a sort of alphabet with continuous set of letters, is proposed. Its effectiveness is calculated and shown to be essentially higher than those of the other known protocols.
We use the probability of error as a measure of distinguishability between two pure and two mixed symmetric coherent states in the context of continuous variable quantum cryptography. We show that the two mixed symmetric coherent states (in which the various components have the same real part) never give an eavesdropper more information than two pure coherent states.
We present the optimal collective attack on a Quantum Key Distribution (QKD) protocol in the "device-independent" security scenario, where no assumptions are made about the way the QKD devices work or on what quantum system they operate. Our main result is a tight bound on the Holevo information between one of the authorized parties and the eavesdropper, as a function of the amount of violation of a Bell-type inequality.
We analyze the asymptotic security of the family of Gaussian modulated Quantum Key Distribution protocols for Continuous Variables systems. We prove that the Gaussian unitary attack is optimal for all the considered bounds on the key rate when the first and second momenta of the canonical variables involved are known by the honest parties.
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.
We demonstrate an implementation of quantum key distribution with continuous variables based on a go-&-return configuration over distances up to 14km. This configuration leads to self-compensation of polarisation and phase fluctuations. We observe a high degree of stability of our set-up over many hours.
We present the first device-independent quantum cryptography protocol for continuous variables. Our scheme is based on the Gottesman-Kitaev-Preskill encoding scheme whereby a qubit is embedded in the infinite-dimensional space of a quantum harmonic oscillator. The novel application of discrete-variable device-independent quantum key distribution to this encoding enables a continuous-variable analogue. Since the security of this protocol is based on discrete-variables we inherit by default security against collective attacks and, under certain memoryless assumptions, coherent attacks. We find t…
We investigate the security of continuous-variable (CV) quantum key distribution (QKD) using coherent states in the presence of quadrature excess noise. We consider an eavesdropping attack which uses a linear amplifier and beam splitter. This attack makes a link between beam-splitting attack and intercept-resend attack (classical teleportation attack). We also show how postselection loses its efficiency in a realistic channel.
In this letter, first, we investigate the security of a continuous-variable quantum cryptographic scheme with a postselection process against individual beam splitting attack. It is shown that the scheme can be secure in the presence of the transmission loss owing to the postselection. Second, we provide a loss limit for continuous-variable quantum cryptography using coherent states taking into account excess Gaussian noise on quadrature distribution. Since the excess noise is reduced by the loss mechanism, a realistic intercept-resend attack which makes a Gaussian mixture of coherent states g…
The goal of two-party cryptography is to enable two parties, Alice and Bob, to solve common tasks without the need for mutual trust. Examples of such tasks are private access to a database, and secure identification. Quantum communication enables security for all of these problems in the noisy-storage model by sending more signals than the adversary can store in a certain time frame. Here, we initiate the study of device-independent protocols for two-party cryptography in the noisy-storage model. Specifically, we present a relatively easy to implement protocol for a cryptographic building bloc…
In continuous-variable quantum information processing detectors are necessarily coarse grained and of finite range. We discuss how especially the latter feature is a bug and may easily lead to overoptimistic estimates of entanglement and of security, when missed data outside the detector range are ignored. We show that entropic separability or security criteria are much superior to variance-based criteria for mitigating the negative effects of this bug.
Quantum discord is the minimal bipartite resource which is needed for a secure quantum key distribution, being a cryptographic primitive equivalent to non-orthogonality. Its role becomes crucial in device-dependent quantum cryptography, where the presence of preparation and detection noise (inaccessible to all parties) may be so strong to prevent the distribution and distillation of entanglement. The necessity of entanglement is re-affirmed in the stronger scenario of device-independent quantum cryptography, where all sources of noise are ascribed to the eavesdropper.
Quantum cryptography with the predetermined key was experimentally realized using Einstein-Podolsky-Rosen(EPR) correlations of continuously bright optical beams. Only one of two EPR correlated beams is transmitted with the signals modulated on quadrature phases and amplitudes, and the other one is retained by the authorized receiver. The modulated small signals are totally submerged in the large quantum noise of the signal beam, therefore nobody except the authorized receiver can decode the signals. Usability of imperfect quantum correlation, high transmission and detection efficiencies, and s…
Reliable Entropy Estimation from Observed Statistics for Device-Independent Quantum Cryptography
Institute for Quantum Information, RWTH Aachen University（亚琛工业大学量子信息研究所）；Institut für Theoretische Physik, Leibniz Universität Hannover（汉诺威莱布尼茨大学理论物理研究所）
We introduce new quantum key distribution protocols using quantum continuous variables, that are secure against individual attacks for any transmission of the optical line between Alice and Bob. In particular, it is not required that this transmission is larger than 50 %. Though squeezing or entanglement may be helpful, they are not required, and there is no need for quantum memories or entanglement purification. These protocols can thus be implemented using coherent states and homodyne detection, and they may be more efficient than usual protocols using quantum discrete variables.
We demonstrate that secure quantum key distribution systems based on continuous variables implementations can operate beyond the apparent 3 dB loss limit that is implied by the beam splitting attack . The loss limit was established for standard minimum uncertainty states such as coherent states. We show that by an appropriate postselection mechanism we can enter a region where Eve's knowledge falls behind the information shared between Alice and Bob even in the presence of substantial losses.
A general study of arbitrary finite-size coherent attacks against continuous-variable quantum cryptographic schemes is presented. It is shown that, if the size of the blocks that can be coherently attacked by an eavesdropper is fixed and much smaller than the key size, then the optimal attack for a given signal-to-noise ratio in the transmission line is an individual gaussian attack. Consequently, non-gaussian coherent attacks do not need to be considered in the security analysis of such quantum cryptosystems.
Device-independent quantum cryptography allows security even if the devices used to execute the protocol are untrusted - whether this is due to unknown imperfections in the implementation, or because the adversary himself constructed them to subvert the security of the protocol. While device-independence has seen much attention in the domain of quantum key distribution, relatively little is known for general protocols. Here we introduce a new model for device-independence for two-party protocols and position verification in the noisy-storage model. For the first time, we show that such protoco…
In theory, quantum key distribution (QKD) provides information-theoretic security based on the laws of physics. Owing to the imperfections of real-life implementations, however, there is a big gap between the theory and practice of QKD, which has been recently exploited by several quantum hacking activities. To fill this gap, a novel approach, called measurement-device-independent QKD (mdiQKD), has been proposed. It can remove all side-channels from the measurement unit, arguably the most vulnerable part in QKD systems, thus offering a clear avenue towards secure QKD realisations. Here, we rev…
We extend the security proof for continuous variable quantum key distribution protocols using post selection to account for arbitrary eavesdropping attacks by employing the concept of an equivalent protocol where the post-selection is implemented as a series of quantum operations including a virtual distillation. We introduce a particular `Gaussian' post selection and demonstrate that the security can be calculated using only experimentally accessible quantities. Finally we explicitly evaluate the performance for the case of a noisy Gaussian channel in the limit of unbounded key length and fin…
Based on the detection loophole-free photon key distribution (PKD) compatible with classical optical systems, an optical key distribution (OKD) protocol is presented for unconditionally secured cryptography in fiber-optic communications networks using addressable continuous phase basis, where each communication channel is composed of paired transmission lines. The unconditional security in OKD lies in quantum superposition between the paired lines of each channel. The continuous phase basis in OKD can be applied for one-time-pad optical cryptography in networks, whose network address capacity …
Device-independent quantum cryptographic schemes aim to guarantee security to users based only on the output statistics of any components used, and without the need to verify their internal functionality. Since this would protect users against untrustworthy or incompetent manufacturers, sabotage or device degradation, this idea has excited much interest, and many device-independent schemes have been proposed. Here we identify a critical weakness of device-independent protocols that rely on public communication between secure laboratories. Untrusted devices may record their inputs and outputs a…
We propose several methods for quantum key distribution (QKD) based upon the generation and transmission of random distributions of coherent or squeezed states, and we show that they are are secure against individual eavesdropping attacks. These protocols require that the transmission of the optical line between Alice and Bob is larger than 50 %, but they do not rely on "non-classical" features such as squeezing. Their security is a direct consequence of the no-cloning theorem, that limits the signal to noise ratio of possible quantum measurements on the transmission line. Our approach can als…
A recurring problem in quantum mechanics is to estimate either the state of a quantum system or the measurement operator applied to it. If we wish to estimate both, then the difficulty is that the state and the measurement always appear together: to estimate the state, we must use a measurement; to estimate the measurement operator, we must use a state. The data of such quantum estimation experiments come in the form of measurement frequencies. Ideally, the measured average frequencies can be attributed to an average state and an average measurement operator. If this is not the case, we have c…
Multiparty quantum cryptography based on distributed entanglement will find its natural application in the upcoming quantum networks. The security of many multipartite device-independent (DI) protocols, such as DI conference key agreement, relies on bounding the von Neumann entropy of the parties' outcomes conditioned on the eavesdropper's information, given the violation of a multipartite Bell inequality. We consider three parties testing the Mermin-Ardehali-Belinskii-Klyshko (MABK) inequality and certify the privacy of their outcomes by bounding the conditional entropy of a single party's ou…
The phase-coding quantum cryptographic scheme using the homodyne detection and weak coherent state [Hirano et al.,Phys. Rev. A 68, 042331 (2003)] provides the simplest continuous-variable quantum key distribution scheme from the experimental side. However, the inherent loss of the practical system will not only increase the bit error rate (BER) but also affect the security of the final key. In this paper, we propose a single-photon-detection attack, and then the security of the final key will be compromised in some parameter regimes. Our results show that the BER induced by Eve can be lower th…
A quantum cryptography scheme based on entanglement between a single particle state and a vacuum state is proposed. The scheme utilizes linear optics devices to detect the superposition of the vacuum and single particle states. Existence of an eavesdropper can be detected by using a variant of Bell's inequality.
We expand the recently discussed continuous-variable quantum key distribution scheme of Heid and Luetkenhaus (2006) to qudits with a lossy but noiseless quantum channel. Postselection methods are used. Secret key rates are calculated in the presence of loss for the direct and the reverse reconciliation method. In the case of reverse reconciliation the secret key rate increases with higher dimensions, in the case of direct reconciliation the result is reverse. Several ways of optimising the amplitude are discussed. In a next step the used states are generalised to squeezed states. Again secret …
We consider a game in which two separate laboratories collaborate to prepare a quantum system and are then asked to guess the outcome of a measurement performed by a third party in a random basis on that system. Intuitively, by the uncertainty principle and the monogamy of entanglement, the probability that both players simultaneously succeed in guessing the outcome correctly is bounded. We are interested in the question of how the success probability scales when many such games are performed in parallel. We show that any strategy that maximizes the probability to win every game individually i…
In the cryptographic context, an earlier unexplored application of the temporal version of the Bell-type inequality is shown here in the device-independent (DI) scenario. This is done by using the Leggett-Garg inequality (LGI) to demonstrate the security against eavesdropping in a quantum key distribution (QKD) scheme. This typically involves a higher dimensional attack against which the standard BB84 protocol is insecure. For this purpose, we invoke an appropriate form of LGI. While the key generation is done by the usual Bennett-Brassard 1984 (BB84) method, the security check against device …
We present a continuous variable (CV) quantum key distribution (QKD) scheme based on the CV quantum teleportation of coherent states that yields a raw secret key made up of discrete variables for both Alice and Bob. This protocol preserves the efficient detection schemes of current CV technology (no single-photon detection techniques) and, at the same time, has efficient error correction and privacy amplification schemes due to the binary modulation of the key. We show that for a certain type of incoherent attack it is secure for almost any value of the transmittance of the optical line used b…
In a previous paper certain measurable criteria have been derived, that are sufficient to demonstrate the existence of Einstein-Podolsky-Rosen (EPR) correlations for measurements with continuous variable outcomes. Here it is shown how such EPR criteria, which do not demand perfect EPR correlations, can be used to prove the extent of security for continuous variable quantum cryptographic schemes (in analogy to that proposed by Ekert) where Alice and Bob hope to construct a secure sequence of values from measurements performed on continuous-variable EPR-correlated fields sent from a distant sour…
We analyze the security of the two-way continuous-variable quantum key distribution protocol in reverse reconciliation against general two-mode attacks, which represent all accessible attacks at fixed channel parameters. Rather than against one specific attack model, the expression of secret key rates of the two-way protocol are derived against all accessible attack models. It is found that there is an optimal two-mode attack to minimize the performance of the protocol in terms of both secret key rates and maximal transmission distances. We identify the optimal two-mode attack, give the specif…
Experimental quantum cryptography with single photons and imperfect devices
University of Waterloo（滑铁卢大学）；Department for Quantum Technology, University of Münster（明斯特大学量子技术系）；Institute for Physics and Astronomy, Technical University of Berlin（柏林工业大学物理与天文学研究所）；Toshiba Europe Ltd.（东芝欧洲有限公司）；Advanced Quantum Light Sources GmbH（先进量子光源有限公司）；Key Laboratory of Optoelectronic Materials and Devices, Institute of Semiconductors, Chinese Academy of Sciences（中国科学院半导体研究所光电材料与器件重点实验室）
We discuss quantum key distribution protocols using quantum continuous variables. We show that such protocols can be made secure against individual gaussian attacks regardless the transmission of the optical line between Alice and Bob. This is achieved by reversing the reconciliation procedure subsequent to the quantum transmission, that is, using Bob's instead of Alice's data to build the key. Although squeezing or entanglement may be helpful to improve the resistance to noise, they are not required for the protocols to remain secure with high losses. Therefore, these protocols can be impleme…
We analyse the distribution of secure keys using quantum cryptography based on the continuous variable degree of freedom of entangled photon pairs. We derive the information capacity of a scheme based on the spatial entanglement of photons from a realistic source, and show that the standard measures of security known for quadrature-based continuous variable quantum cryptography (CV-QKD) are inadequate. A specific simple eavesdropping attack is analysed to illuminate how secret information may be distilled well beyond the bounds of the usual CV-QKD measures.
We report an experimental quantum key distribution that utilizes balanced homodyne detection, instead of photon counting, to detect weak pulses of coherent light. Although our scheme inherently has a finite error rate, it allows high-efficiency detection and quantum state measurement of the transmitted light using only conventional devices at room temperature. When the average photon number was 0.1, an error rate of 0.08 and "effective" quantum efficiency of 0.76 were obtained.
We consider continuous-variable quantum key distribution with discrete-alphabet encodings. In particular, we study protocols where information is encoded in the phase of displaced coherent (or thermal) states, even though the results can be directly extended to any protocol based on finite constellations of displaced Gaussian states. In this setting, we provide a composable security analysis in the finite-size regime assuming the realistic but restrictive hypothesis of collective Gaussian attacks. Under this assumption, we can efficiently estimate the parameters of the channel via maximum like…
The cloning of quantum variables with continuous spectra is investigated. We define a Gaussian 1-to-2 cloning machine, which copies equally well two conjugate variables such as position and momentum or the two quadrature components of a light mode. The resulting cloning fidelity for coherent states, namely $F=2/3$, is shown to be optimal. An asymmetric version of this Gaussian cloner is then used to assess the security of a continuous-variable quantum key distribution scheme that allows two remote parties to share a Gaussian key. The information versus disturbance tradeoff underlying this cont…
Quantum key distribution (QKD) promises information theoretic secure key as long as the device performs as assumed in the theoretical model. One of the assumptions is an absence of information leakage about individual photon detection outcomes of the receiver unit. Here we investigate the information leakage from a QKD receiver due to photon emission caused by detection events in single-photon detectors (backflash). We test commercial silicon avalanche photodiodes and a photomultiplier tube, and find that the former emit backflashes. We study the spectral, timing and polarization characteristi…
In this thesis we study the finite-size analysis of two continuous-variables quantum key distribution schemes. The first one is the one-way protocol using Gaussian modulation of thermal states and the other is the measurement-device-independent protocol. To do so, we adopt an efficient channel parameter estimation method based on the assumption of the Gaussian variables and the central limit theorem introduced by Ruppert et al. [Phys. Rev. A 90, 062310 (2014)]. Furthermore, we present a composable security analysis of the measurement device independent protocol for coherent attacks with a chan…
Quantum Cryptography, or more accurately, Quantum Key Distribution (QKD) is based on using an unconditionally secure ``quantum channel'' to share a secret key among two users. A manufacturer of QKD devices could, intentionally or not, use a (semi-)classical channel instead of the quantum channel, which would remove the supposedly unconditional security. One example is the BB84 protocol, where the quantum channel can be implemented in polarization of single photons. Here, use of several photons instead of one to encode each bit of the key provides a similar but insecure system. For protocols ba…
Proofs of the security of quantum key distribution are propositions about models written in the mathematical language of quantum mechanics, and the issue is the linking of such models to actual devices in an experiment on security. To explore this issue, we adapt Wittgenstein's method of language games to view quantum language in its application to experimental activity involving transmitting and receiving devices. We sketch concepts with which to think about models in relation to experiments, without assuming the experiments accord with any model included is a concept of one quantum-mechanica…
We consider the security of continuous-variable quantum cryptography as we approach the classical-limit, i.e., when the unknown preparation noise at the sender's station becomes significantly noisy or thermal (even by as much as 10,000 times the variance of the vacuum mode). We show that, provided the channel transmission losses do not exceed 50%, the security of quantum cryptography is not dependent on the channel transmission, and is therefore, incredibly robust against significant amounts of excess preparation noise. We extend these results to consider for the first time quantum cryptograph…
Quantum Cryptography is on the verge of commercial application. One of its greatest limitations is over long distance - secret key rates are low and the longest fibre over which any key has been exchanged is currently 100 km. We investigate the quantum relay, which can increase the maximum distance at which quantum cryptography is possible. The relay splits the channel into sections, and sends a different photon across each section, increasing the signal to noise ratio. The photons are linked as in teleportation, with entangled photon pairs and Bell measurements. We show that such a scheme cou…
Classical and quantum information theory are simply explained. To be more specific it is clarified why Shannon entropy is used as measure of classical information and after a brief review of quantum mechanics it is possible to demonstrate why the density matrix is the main tool of quantum information theory. Then von Neumann entropy is introduced and with its help a great difference between classical and quantum information theory is presented: quantum entanglement. Moreover an information theoretic interpretation of quantum measurement is discussed. Data compression, error correction and nois…
