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 unconditional security when the eavesdropper uses incoherent and coherent eavesdropping strategies. We have also consider realistic noise caused by detector's noise.
We present a formalism for encoding the logical basis of a qubit into subspaces of multiple physical levels. The need for this multilevel encoding arises naturally in situations where the speed of quantum operations exceeds the limits imposed by the addressability of individual energy levels of the qubit physical system. A basic feature of the multilevel encoding formalism is the logical equivalence of different physical states and correspondingly, of different physical transformations. This logical equivalence is a source of a significant flexibility in designing logical operations, while the…
Qubit measurements are central to quantum information processing. In the field of superconducting qubits, standard readout techniques are not only limited by the signal-to-noise ratio, but also by state relaxation during the measurement. In this work, we demonstrate that the limitation due to relaxation can be suppressed by using the many-level Hilbert space of superconducting circuits: in a multilevel encoding, the measurement is only corrupted when multiple errors occur. Employing this technique, we show that we can directly resolve transmon gate errors at the level of one part in $10^3.$ Ex…
We present a detailed security analysis of a d-dimensional quantum key distribution protocol based on two and three mutually unbiased bases (MUBs) both in an asymptotic and finite key length scenario. The finite secret key rates are calculated as a function of the length of the sifted key by (i) generalizing the uncertainly relation-based insight from BB84 to any d-level 2-MUB QKD protocol and (ii) by adopting recent advances in the second-order asymptotics for finite block length quantum coding (for both d-level 2- and 3-MUB QKD protocols). Since the finite and asymptotic secret key rates inc…
We study quantum information properties of a seven-level system realized by a particle in an one-dimensional square-well trap. Features of encodings of seven-level systems in a form of three-qubit or qubit-qutrit systems are discussed. We use the three-qubit encoding of the system in order to investigate subadditivity and strong subadditivity conditions for the thermal state of the particle. The qubit-qutrit encoding is employed to suggest a single qudit algorithm for calculation of parity of a bit string. Obtained results indicate on the potential resource of multilevel systems for realizatio…
Quantum key distribution (QKD) promises provably secure communications. In order to improve the secret key rate, combining a biased basis choice with the decoy-state method is proposed. Concomitantly, there is a basis-independent detection efficiency condition, which usually cannot be satisfied in a practical system, such as the time-phase encoding. Fortunately, this flaw has been recently removed theoretically and experimentally using the fact that the expected yields of single-photon states prepared in two bases stay the same for a given measurement basis. However, the security proofs do not…
We propose efficient-phase-encoding protocols for continuous-variable quantum key distribution using coherent states and postselection. By these phase encodings, the probability of basis mismatch is reduced and total efficiency is increased. We also propose mixed-state protocols by omitting a part of classical communication steps in the efficient-phase-encoding protocols. The omission implies a reduction of information to an eavesdropper and possibly enhances the security of the protocols. We investigate the security of the protocols against individual beam splitting attack.
We present for the first time, a bidirectional Quantum Key Distribution protocol with minimal encoding operations derived from the use of two `nonorthogonal' unitary transformations selected from two mutually unbiased unitary bases; which are indistinguishable in principle for a single use. Along with its decoding procedure, it is a stark contrast to its `orthogonal encoding' predecessors. Defining a more relevant notion of security threshold for such protocols, the current protocol outperforms its predecessor in terms of security as the maximal amount of information an eavesdropper can glean …
Quantum key distribution (QKD) gradually has become a crucial element of practical secure communication. In different scenarios, the security analysis of genuine QKD systems is complicated. A universal secret key rate calculation method, used for realistic factors such as multiple degrees of freedom encoding, asymmetric protocol structures, equipment flaws, environmental noise, and so on, is still lacking. Based on the correlations of statistical data, we propose a security analysis method without restriction on encoding schemes. This method makes a trade-off between applicability and accuracy…
We analyze tolerable quantum bit error rates in secret sharing protocols, and show that using entangled encoding states is advantageous in the case when the eavesdropping attacks are local. We also provide a criterion for security in secret sharing -- a parallel of the Csiszar-Korner criterion in single-receiver cryptography.
Measurement-device-independent quantum key distribution (MDIQKD) is proposed to be secure against any possible detection attacks. The security of the original proposal relies on the assumption that the legitimate users can fully characterize the encoding systems including sources. Here, we propose a MDIQKD protocol where we allow uncharacterized encoding systems as long as qubit sources are used. A security proof of the MDIQKD protocol is presented that does not need the knowledge of the encoding states. Simulation results show that the scheme is practical.
We present an experimental demonstration of a quantum key distribution protocol using coherent polarization states. Post selection is used to ensure a low error rate and security against beam splitting attacks even in the presence of high losses. Signal encoding and readout in polarization bases avoids the difficult task of sending a local oscillator with the quantum channel. This makes our setup robust and easy to implement. A shared key was established for losses up to 64%.
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.
The Goldenberg-Vaidman (GV) protocol for quantum key distribution (QKD) uses orthogonal encoding states of a particle. Its security arises because operations accessible to Eve are insufficient to distinguish the two states encoding the secret bit. We propose a two-particle cryptographic protocol for quantum secure direct communication, wherein orthogonal states encode the secret, and security arises from restricting Eve from accessing any two-particle operations. However, there is a non-trivial difference between the two cases. While the encoding states are perfectly indistinguishable in GV, t…
Side-channel-secure quantum key distribution with correlated sources
University of Science and Technology of China（中国科学技术大学）；Laboratory of Quantum Information, University of Science and Technology of China（中国科学技术大学量子信息实验室）；Anhui Province Key Laboratory of Quantum Network, University of Science and Technology of China（中国科学技术大学安徽省量子网络重点实验室）；CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China（中国科学技术大学中国科学院量子信息与量子物理前沿卓越中心）
We consider two quantum cryptographic schemes relying on encoding the key into qudits, i.e. quantum states in a d-dimensional Hilbert space. The first cryptosystem uses two mutually unbiased bases (thereby extending the BB84 scheme), while the second exploits all the d+1 available such bases (extending the six-state protocol for qubits). We derive the information gained by a potential eavesdropper applying a cloning-based individual attack, along with an upper bound on the error rate that ensures unconditional security against coherent attacks.
Inherent gate errors can arise in quantum computation when the actual system Hamiltonian or Hilbert space deviates from the desired one. Two important examples we address are spin-coupled quantum dots in the presence of spin-orbit perturbations to the Heisenberg exchange interaction, and off-resonant transitions of a qubit embedded in a multilevel Hilbert space. We propose a ``dressed qubit'' transformation for dealing with such inherent errors. Unlike quantum error correction, the dressed qubits method does not require additional operations or encoding redundancy, is insenstitive to error mag…
In this paper, we study the unconditional security of the so-called measurement device independent quantum key distribution (MDIQKD) with the basis-dependent flaw in the context of phase encoding schemes. We propose two schemes for the phase encoding, the first one employs a phase locking technique with the use of non-phase-randomized coherent pulses, and the second one uses conversion of standard BB84 phase encoding pulses into polarization modes. We prove the unconditional security of these schemes and we also simulate the key generation rate based on simple device models that accommodate im…
Weak coherent states as a photon source for quantum cryptography have limit in secure data rate and transmission distance because of the presence of multi-photon events and loss in transmission line. Two-photon events in a coherent state can be taken out by a two-photon interference scheme. We investigate the security issue of utilizing this modified coherent state in quantum cryptography. A 4 dB improvement in secure data rate or a nearly two-fold increase in transmission distance over the coherent state are found. With a recently proposed and improved encoding strategy, further improvement i…
Measurement-device-independent quantum key distribution (MDIQKD) is a revolutionary protocol since it is physically immune to all attacks on the detection side. However, the protocol still keeps the strict assumptions on the source side that the four BB84-states must be perfectly prepared to ensure security. Some protocols release part of the assumptions in the encoding system to keep the practical security, but the performance would be dramatically reduced. In this work, we present a MDIQKD protocol that requires less knowledge of encoding system to combat the troublesome modulation errors an…
Dirac notation is the most common way to describe quantum states and operations on states. It is very convenient and allows for quick visual distinction between vectors, scalars and operators. For quantum processes that involve interactions of multiple systems an even better visualisation has been proposed by Coecke and Kissinger, in the form of a diagrammatic formalism [CK2017]. Their notation expresses formulas in the form of diagrams, somewhat similar to Feynman diagrams, and is more general than the circuit notation for quantum computing. This document consists of two parts. (1) We give a …
In the quantum version of a Trojan-horse attack, photons are injected into the optical modules of a quantum key distribution system in an attempt to read information direct from the encoding devices. To stop the Trojan photons, the use of passive optical components has been suggested. However, to date, there is no quantitative bound that specifies such components in relation to the security of the system. Here, we turn the Trojan-horse attack into an information leakage problem. This allows us quantify the system security and relate it to the specification of the optical elements. The analysis…
The problem of unconditional security of quantum cryptography (i.e. the security which is guaranteed by the fundamental laws of nature rather than by technical limitations) is one of the central points in quantum information theory. We propose a relativistic quantum cryptosystem and prove its unconditional security against any eavesdropping attempts. Relativistic causality arguments allow to demonstrate the security of the system in a simple way. Since the proposed protocol does not employ collective measurements and quantum codes, the cryptosystem can be experimentally realized with the prese…
We report an experimental implementation of free-space quantum secure direct communication based on single photons. The quantum communication scheme uses phase encoding, and the asymmetric Mach-Zehnder interferometer is optimized so as to automatically compensate phase drift of the photons during their transitions over the free-space medium. An information transmission rate of 500 bps over a 10-meter free space with a mean quantum bit error rate of 0.49%$\pm$0.27% is achieved. The security is analyzed under the scenario that Eve performs collective attack and photon number splitting collective…
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…
Quantum key distribution(QKD) is one of the most significant areas in quantum information theory. For nearly four decades, substantial QKD schemes are developed. In early years, the security of QKD protocols is depend on switching different bases, namely based on non-orthogonal state encoding. The most famous example is the BB84 protocol. Later, other techniques were developed for orthogonal state encoding. Examples of such protocols include the GV protocol and order-rearrangement protocols. In this paper, we present two QKD protocols based on orthogonal state encoding. One of them does not ne…
In this work, we study the security of coherent-state quantum key distribution with a strong reference pulse. The consideration is based on a powerful soft filtering attack and uses realistic parameters of the equipment. Our model allows us to relate the secure key generation rate and distance with the energy of signal and reference pulses. We propose a two-pass quantum key distribution phase encoding optical scheme with a strong reference pulse. This simple for realization scheme is experimentally tested showing stable operation. Here we describe the tuning technique and solution for the prob…
The first quantum cryptography protocol, proposed by Bennett and Brassard in 1984 (BB84), has been widely studied in the last years. This protocol uses four states (more precisely, two complementary bases) for the encoding of the classical bit. Recently, it has been noticed that by using the same four states, but a different encoding of information, one can define a new protocol which is more robust in practical implementations, specifically when attenuated laser pulses are used instead of single-photon sources [V. Scarani et al., Phys. Rev. Lett. {\bf 92}, 057901 (2004); referred to as SARG04…
We improve the flexibility in designing access structures of quantum stabilizer-based secret sharing schemes for classical secrets, by introducing message randomization in their encoding procedures. We generalize the Gilbert-Varshamov bound for deterministic encoding to randomized encoding of classical secrets. We also provide an explicit example of a ramp secret sharing scheme with which multiple symbols in its classical secret are revealed to an intermediate set, and justify the necessity of incorporating strong security criterion of conventional secret sharing. Finally, we propose an explic…
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 prove that the teleportation based quantum cryptography protocol presented in [Opt. Commun. 283, 184 (2010)], which is built using only orthogonal states encoding the classical bits that are teleported from Alice to Bob, is asymptotically secure against all types of individual and collective attacks. We then investigate modifications to that protocol leading to greater secret-key rates and to security against coherent attacks. In other words, we show an unconditional secure quantum key distribution protocol that does not need non-orthogonal quantum states to encode the bits of the secret ke…
One of the applications of quantum technology is to use quantum states and measurements to communicate which offers more reliable security promises. Quantum data hiding, which gives the source party the ability of sharing data among multiple receivers and revealing it at a later time depending on his/her will, is one of the promising information sharing schemes which may address practical security issues. In this work, we propose a novel quantum data hiding protocol. By concatenating different subprotocols which apply to rather symmetric hiding scenarios, we cover a variety of more general hid…
The round-robin differential phase shift (RRDPS) quantum key distribution (QKD) protocol is a unique quantum key distribution protocol whose security has not been understood through an information-disturbance trade-off relation, and a sufficient amount of privacy amplification was given independently of signal disturbance. Here, we discuss the security of the RRDPS protocol in the asymptotic regime when a good estimate of the bit error rate is available as a measure of signal disturbance. The uniqueness of the RRDPS protocol shows up as a peculiar form of information-disturbance trade-off curv…
The physical layer describes how communication signals are encoded and transmitted across a channel. Physical security often requires either restricting access to the channel or performing periodic manual inspections. In this tutorial, we describe how the field of quantum communication offers new techniques for securing the physical layer. We describe the use of quantum seals as a unique way to test the integrity and authenticity of a communication channel and to provide security for the physical layer. We present the theoretical and physical underpinnings of quantum seals including the quantu…
Semi-device independent (Semi-DI) quantum random number generators (QRNG) gained attention for security applications, offering an excellent trade-off between security and generation rate. This paper presents a proof-of-principle time-bin encoding semi-DI QRNG experiments based on a prepare-and-measure scheme. The protocol requires two simple assumptions and a measurable condition: an upper-bound on the prepared pulses' energy. We lower-bound the conditional min-entropy from the energy-bound and the input-output correlation, determining the amount of genuine randomness that can be certified. Mo…
We demonstrate the decoy-state quantum key distribution (QKD) with one-way quantum communication in polarization space over 102km. Further, we simplify the experimental setup and use only one detector to implement the one-way decoy-state QKD over 75km, with the advantage to overcome the security loopholes due to the efficiency mismatch of detectors. Our experimental implementation can really offer the unconditionally secure final keys. We use 3 different intensities of 0, 0.2 and 0.6 for the pulses of source in our experiment. In order to eliminate the influences of polarization mode dispersio…
We introduce a ternary quantum key distribution (QKD) protocol and asymptotic security proof based on three coherent states and homodyne detection. Previous work had considered the binary case of two coherent states and here we nontrivially extend this to three. Our motivation is to leverage the practical benefits of both discrete and continuous (Gaussian) encoding schemes creating a best-of-both-worlds approach; namely, the postprocessing of discrete encodings and the hardware benefits of continuous ones. We present a thorough and detailed security proof in the limit of infinite signal states…
Quantum Key Distribution (QKD) allows distant parties to exchange cryptographic keys with unconditional security by encoding information on the degrees of freedom of photons. Polarization encoding has been extensively used in QKD implementations along free-space, optical fiber and satellite-based links. However, the polarization encoders used in such implementations are unstable, expensive, complex and can even exhibit side-channels that undermine the security of the implemented protocol. Here we propose a self-compensating polarization encoder based on a Lithium Niobate phase modulator inside…
Quantum key distribution (QKD) allows two users to communicate with theoretically provable secrecy by encoding information on photonic qubits. Current encoders are complex, however, which reduces their appeal for practical use and introduces potential vulnerabilities to quantum attacks. Distributed-phase-reference (DPR) systems were introduced as a simpler alternative, but have not yet been proven practically secure against all classes of attack. Here we demonstrate the first DPR QKD system with information-theoretic security. Using a novel light source, where the coherence between pulses can …
Quantum Key Recycling (QKR) is a quantum-cryptographic primitive that allows one to re-use keys in an unconditionally secure way. By removing the need to repeatedly generate new keys it improves communication efficiency. Skoric and de Vries recently proposed a QKR scheme based on 8-state encoding (four bases). It does not require quantum computers for encryption/decryption but only single-qubit operations. We provide a missing ingredient in the security analysis of this scheme in the case of noisy channels: accurate bounds on the privacy amplification. We determine optimal attacks against the …
The ability to distribute secret keys between two parties with information-theoretic security, that is, regardless of the capacities of a malevolent eavesdropper, is one of the most celebrated results in the field of quantum information processing and communication. Indeed, quantum key distribution illustrates the power of encoding information on the quantum properties of light and has far reaching implications in high-security applications. Today, quantum key distribution systems operate in real-world conditions and are commercially available. As with most quantum information protocols, quant…
One of the simplest methods for implementing quantum key distribution over fiber-optic communication is the Bennett-Brassard 1984 protocol with phase encoding (PE-BB84 protocol), in which the sender uses phase modulation over double pulses from a laser and the receiver uses a passive delayed interferometer. Using essentially the same setup and by regarding a train of many pulses as a single block, one can carry out the so-called differential quadrature phase shift (DQPS) protocol, which is a variant of differential phase shift (DPS) protocols. Here we prove the security of the DQPS protocol ba…
We study the security of quantum string commitment (QSC) protocols with group covariant encoding scheme. First we consider a class of QSC protocol, which is general enough to incorporate all the QSC protocols given in the preceding literatures. Then among those protocols, we consider group covariant protocols and show that the exact upperbound on the binding condition can be calculated. Next using this result, we prove that for every irreducible representation of a finite group, there always exists a corresponding nontrivial QSC protocol which reaches a level of security impossible to achieve …
