Kiyoshi Tamaki, Norbert Lütkenhaus
We show that the security proof of the Bennett 1992 protocol over loss-free channel in (K. Tamaki, M. Koashi, and N. Imoto, Phys. Rev. Lett. 90, 167904 (2003)) can be adapted to accommodate loss. We assumed that Bob's detectors discriminate between single photon states on one hand and vacuum state or multi-photon states on the other hand.
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We prove the unconditional security of the original Bennett 1992 protocol with strong reference pulse. We show that we may place a projection onto suitably defined qubit spaces before the receiver, which makes the analysis as simple as qubit-based protocols. Unlike the single-photon-based qubits, the qubits identified in this scheme are almost surely detected by the receiver even after a lossy channel. This leads to the key generation rate that is proportional to the channel transmission rate for proper choices of experimental parameters.
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 propose a new kind of individual attack, based on randomly selected dissipation, on Bennett-Brassard 1984 protocol of practical quantum key distribution (QKD) system with lossy and noisy quantum channel. Since an adversary with super quantum channel can disguise loss and errors induced by his attack as that of the system, he can obtain innegligible amount of information for a practical QKD system, without being detected by legal participants.
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.
The quantum key distribution protocol without public announcement of bases is equipped with a two-way classical communication symmetric entanglement purification protocol. This modified key distribution protocol is unconditionally secure and has a higher tolerable error rate of 20%, which is higher than previous scheme without public announcement of bases.
Unconditional security proofs of the Bennett-Brassard protocol of quantum key distribution have been obtained recently. These proofs cover also practical implementations that utilize weak coherent pulses in the four signal polarizations. Proven secure rates leave open the possibility that new proofs or new public discussion protocols obtain larger rates over increased distance. In this paper we investigate limits to error rate and signal losses that can be tolerated by future protocols and proofs.
We prove the unconditional security of the Bennett 1992 protocol, by using a reduction to an entanglement distillation protocol initiated by a local filtering process. The bit errors and the phase errors are correlated after the filtering, and we can bound the amount of phase errors from the observed bit errors by an estimation method involving nonorthogonal measurements. The angle between the two states shows a trade-off between accuracy of the estimation and robustness to noises.
We propose an unconditionally secure quantum key distribution (QKD) protocol, which uses a relatively strong signal pulse. While our protocol shares similar security bases as the Bennett 1992 protocol with a strong reference pulse (B92), our scheme uses a smaller number of detectors and it is robust against Rayleigh scattering in an optical fibre. We derive a lower bound of secret key generation rate of our protocol and show that our protocol can cover relatively long distances, assuming precise phase modulations and stable interferometers.
Here, a physical formalism is proposed for an unconditional microwave quantum teleportation of Gaussian states via two-mode squeezed states in lossy environments. The proposed formalism is controllable to be used in both the fridge and free space in case of entanglement between two parties survives. Some possible experimental parameters are estimated for the teleportation of microwave signals with a frequency of 5GHz based on the proposed physical framework. This would be helpful for superconducting inter- and intra-fridge quantum communication as well as open-air quantum microwave communicati…
We introduce a novel form of decoy-state technique to make the single-photon Bennett 1992 protocol robust against losses and noise of a communication channel. Two uninformative states are prepared by the transmitter in order to prevent the unambiguous state discrimination attack and improve the phase-error rate estimation. The presented method does not require strong reference pulses, additional electronics or extra detectors for its implementation.
We present a tight security analysis of the Bennett-Brassard 1984 protocol taking into account the finite size effect of key distillation, and achieving unconditional security. We begin by presenting a concise analysis utilizing the normal approximation of the hypergeometric function. Then next we show that a similarly tight bound can also be obtained by a rigorous argument without relying on any approximation. In particular, for the convenience of experimentalists who wish to evaluate the security of their QKD systems, we also give explicit procedures of our key distillation, and also show ho…
We derive a bound for the security of QKD with finite resources under one-way post-processing, based on a definition of security that is composable and has an operational meaning. While our proof relies on the assumption of collective attacks, unconditional security follows immediately for standard protocols like Bennett-Brassard 1984 and six-states. For single-qubit implementations of such protocols, we find that the secret key rate becomes positive when at least N\sim 10^5 signals are exchanged and processed. For any other discrete-variable protocol, unconditional security can be obtained us…
Basic techniques to prove the unconditional security of quantum cryptography are described. They are applied to a quantum key distribution protocol proposed by Bennett and Brassard in 1984. The proof considers a practical variation on the protocol in which the channel is noisy and photons may be lost during the transmission. The initial coding into the channel must be perfect (i.e., exactly as described in the protocol). No restriction is imposed on the detector used at the receiving side of the channel, except that whether or not the received system is detected must be independent of the basi…
Quantum Key Distribution (QKD) with classical Bob has recently been suggested and proven robust. Following this work, QKD with classical Alice was also suggested and proven robust. The above protocols are ideal in the sense that they make use of qubits. However, in the past, well-known QKD protocols that were proven robust and even proven unconditionally secure, when qubits are used, were found to be totally insecure when photons are used. This is due to sensitivity to photon losses (e.g., Bennett's two-state protocol) or sensitivity to losses combined with multi-photon states (e.g., the photo…
We present here an information theoretic study of Gaussian collective attacks on the continuous variable key distribution protocols based on Gaussian modulation of coherent states. These attacks, overlooked in previous security studies, give a finite advantage to the eavesdropper in the experimentally relevant lossy channel, but are not powerful enough to reduce the range of the reverse reconciliation protocols. Secret key rates are given for the ideal case where Bob performs optimal collective measurements, as well as for the realistic cases where he performs homodyne or heterodyne measuremen…
The lists of bits processed in quantum key distribution are necessarily of finite length. The need for finite-key unconditional security bounds has been recognized long ago, but the theoretical tools have become available only very recently. We provide finite-key unconditional security bounds for two practical implementations of the Bennett-Brassard 1984 coding: prepare-and-measure implementations without decoy states, and entanglement-based implementations. A finite-key bound for prepare-and-measure implementations with decoy states is also derived under a simplified treatment of the statisti…
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.
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.
Quantum Key Distribution (QKD) allows to share random keys between two users with unconditional security: the key is usually generated by exchanging a stream of photons. The long-term vision of QKD is represented by a quantum network, implemented by fiber and free-space links involving ground and/or satellites stations. The presence of the atmospheric turbulence represents an obstacle for free-space quantum communications, due to the increase of optical losses. Here we introduce a method to exploit the atmospheric turbulence as a resource for QKD. An Adaptive Real Time Selection (ARTS) techniq…
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…
Quantum key distribution can be performed with practical signal sources such as weak coherent pulses. One example of such a scheme is the Bennett-Brassard protocol that can be implemented via polarization of the signals, or equivalent signals. It turns out that the most powerful tool at the disposition of an eavesdropper is the photon-number splitting attack. We show that this attack can be extended in the relevant parameter regime such as to preserve the Poissonian photon number distribution of the combination of the signal source and the lossy channel.
Quantum key distribution (QKD) has the potential for widespread real-world applications. To date no secure long-distance experiment has demonstrated the truly practical operation needed to move QKD from the laboratory to the real world due largely to limitations in synchronization and poor detector performance. Here we report results obtained using a fully automated, robust QKD system based on the Bennett Brassard 1984 protocol (BB84) with low-noise superconducting nanowire single-photon detectors (SNSPDs) and decoy levels. Secret key is produced with unconditional security over a record 144.3…
We prove the unconditional security of quantum key distribution protocols using attenuated laser pulses with M different linear polarizations. When M=4, the proof covers the so-called SARG04 protocol [V.~Scarani et al., Phys. Rev.\ Lett. {\bf 92}, 057901 (2004)], which uses exactly the same quantum communication as the Bennett-Brassard 1984 protocol. For a channel with transmission $η$, we show that the key rate in SARG04 scales as $O(η^{3/2})$. When we increase the number of states to M=2k-1 or 2k, the key rate scaling improves as $O(η^{(k+1)/k})$.
Quantum teleportation enables the deterministic exchange of qubits via lossy channels. While it is commonly believed that unconditional teleportation requires a preshared entangled qubit pair, here we demonstrate a protocol that is in principle unconditional and requires only a single photon as an ex-ante prepared resource. The photon successively interacts, first, with the receiver and then with the sender qubit memory. Its detection, followed by classical communication, heralds a successful teleportation. We teleport six mutually unbiased qubit states with average fidelity $\overline{\text{F…
Quantum key distribution (QKD) protocols make it possible for two parties to generate a secret shared key. One of the most important QKD protocols, BB84, was suggested by Bennett and Brassard in 1984. Various proofs of unconditional security for BB84 have been suggested, but the first security proofs were not composable. Here we improve a security proof of BB84 given by [Biham, Boyer, Boykin, Mor, and Roychowdhury, J. Cryptology, 19(4):381-439, 2006] to be composable and match the state-of-the-art results for BB84, and we extend it to prove unconditional security of several variants of the BB8…
We present security proofs for a protocol for Quantum Key Distribution (QKD) based on encoding in finite high-dimensional Hilbert spaces. This protocol is an extension of Bennett's and Brassard's basic protocol from two bases, two state encoding to a multi bases, multi state encoding. We analyze the mutual information between the legitimate parties and the eavesdropper, and the error rate, as function of the dimension of the Hilbert space, while considering optimal incoherent and coherent eavesdropping attacks. We obtain the upper limit for the legitimate party error rate to ensure uncondition…
Quantum physics allows for unconditionally secure communication through insecure communication channels. The achievable rates of quantum-secured communication are fundamentally limited by the laws of quantum physics and in particular by the properties of entanglement. For a lossy communication line, this implies that the secret-key generation rate vanishes at least exponentially with the communication distance. We show that this fundamental limitation can be violated in a realistic scenario where the eavesdropper can store quantum information for only a finite, yet arbitrarily long, time. We c…
Motivated by the Quantum Key Distribution (QKD) protocol, introduced in 1984 in the seminal paper of Bennett and Brassard, we investigate in this paper the achievability of unconditionally secure password-authenticated quantum key exchange (quantum PAKE), where the authentication is implemented by the means of human-memorable passwords. We first show a series of impossibility results forbidding the achievement of very strong security, leaving open the feasibility of achieving a weaker security notion. We then answer this open question positively by presenting a construction for quantum PAKE th…
It is demonstrated that for the entanglement-based version of the Bennett-Brassard (BB84) quantum key distribution protocol, Alice and Bob share provable entanglement if and only if the estimated qubit error rate is below 25% or above 75%. In view of the intimate relation between entanglement and security, this result sheds also new light on the unconditional security of the BB84 protocol in its original prepare-and-measure form. In particular, it indicates that for small qubit error rates 25% is the ultimate upper security bound for any prepare-and-measure BB84-type QKD protocol. On the contr…
Shortcuts to adiabaticity (STA) are powerful quantum control methods, allowing quick evolution into target states of otherwise slow adiabatic dynamics. Such methods have widespread applications in quantum technologies, and various STA protocols have been demonstrated in closed systems. However, realizing STA for open quantum systems has presented a greater challenge, due to complex controls required in existing proposals. Here we present the first experimental demonstration of STA for open quantum systems, using a superconducting circuit QED system consisting of two coupled bosonic oscillators…
This paper begins with a simple proof of the existence of squash operators compatible with the Bennett-Brassard 1984 (BB84) protocol which suits single-mode as well as multi-mode threshold detectors. The proof shows that, when a given detector is symmetric under cyclic group C_4, and a certain observable associated with it has rank two as a matrix, then there always exists a corresponding squash operator. Next, we go on to investigate whether the above restriction of "rank two" can be eliminated; i.e., is cyclic symmetry alone sufficient to guarantee the existence of a squash operator? The mot…
It has been pointed out by Yuen that the security theory of quantum key distribution(QKD) guided by Shor-Preskill theory has serious defects, in particular their key rate theory is not correct. Theory groups of QKD tried to improve several defects. Especially, Renner employed trace distance and quantum leftover Hash Lemma. However, the present theory encountered a problem of a quantitative evaluation of security. To cope with it, he uses a wrong interpretation on the trace distance and its level epsilon_{sec}, and justifies the unconditional security of own system when epsilon_{sec} is 10^{-6 …
Quantum communication holds promise for unconditionally secure transmission of secret messages and faithful transfer of unknown quantum states. Photons appear to be the medium of choice for quantum communication. Owing to photon losses, robust quantum communication over long lossy channels requires quantum repeaters. It is widely believed that a necessary and highly demanding requirement for quantum repeaters is the existence of matter quantum memories at the repeater nodes. Here we show that such a requirement is, in fact, unnecessary by introducing the concept of all photonic quantum repeate…
Device-independent quantum key distribution (DIQKD) guarantees unconditional security of secret key without making assumptions about the internal workings of the devices used. It does so using the loophole-free violation of a Bell's inequality. The primary challenge in realizing DIQKD in practice is the detection loophole problem that is inherent to photonic tests of Bell's inequalities over lossy channels. We revisit the proposal of Curty and Moroder [Phys. Rev. A 84, 010304(R) (2011)] to use a linear optics-based entanglement-swapping relay (ESR) to counter this problem. We consider realisti…
The theory of quantum cryptography aims to guarantee unconditional information-theoretic security against an omnipotent eavesdropper. In many practical scenarios, however, the assumption of an all-powerful adversary is excessive and can be relaxed considerably. In this paper we study secret key distillation across a lossy and noisy quantum wiretap channel between Alice and Bob, with a separately parameterized realistically lossy quantum channel to the eavesdropper Eve. We show that under such restricted eavesdropping, the key rates achievable can exceed the secret key distillation capacity aga…
Deterministic quantum teleportation between distant superconducting chips
该研究通过64米长超低损耗电缆总线连接远距离超导芯片，利用飞行微波光子实现确定性量子态和纠缠门隐形传态，为分布式超导量子计算网络奠定基础。
Quantum channel correction outperforming direct transmission
本文通过预告式放大蒸馏改善有噪声的纠缠信道，并结合纠缠交换实现超越盈亏平衡的量子信道校正，首次无条件提升任意量子信息传输性能，构成真正的量子中继。
Quantum key distribution (QKD) can be used to generate secret keys between two distant parties. Even though QKD has been proven unconditionally secure against eavesdroppers with unlimited computation power, practical implementations of QKD may contain loopholes that may lead to the generated secret keys being compromised. In this paper, we propose a phase-remapping attack targeting two practical bidirectional QKD systems (the "plug & play" system and the Sagnac system). We showed that if the users of the systems are unaware of our attack, the final key shared between them can be compromised in…
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