We consider the cloning of sequences of qubits prepared in the states used in the BB84 or 6-state quantum cryptography protocol, and show that the single-qubit fidelity is unaffected even if entire sequences of qubits are prepared in the same basis. This result is of great importance for practical quantum cryptosystems because it reduces the need for high-speed random number generation without impairing on the security against finite-size attacks.
We suggest that the randomness of the choices of measurement basis by Alice and Bob provides an additional important resource for quantum cryptography. As a specific application, we present a novel protocol for quantum key distribution (QKD) which enhances the BB84 scheme by encrypting the information sent over the classical channel during key sifting. We show that, in the limit of long keys, this process prevents an eavesdropper from reproducing the sifting process carried out by the legitimate users. The inability of the eavesdropper to sift the information gathered by tapping the quantum ch…
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）
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…
Quantum cryptographic protocols based on complementarity are nonsecure against attacks in which complementarity is imitated with classical resources. The Kochen-Specker (KS) theorem provides protection against these attacks, without requiring entanglement or spatially separated composite systems. We analyze the maximum tolerated noise to guarantee the security of a KS-protected cryptographic scheme against these attacks, and describe a photonic realization of this scheme using hybrid ququarts defined by the polarization and orbital angular momentum of single photons.
Random number generators (RNG) are an important resource in many areas: cryptography (both quantum and classical), probabilistic computation (Monte Carlo methods), numerical simulations, industrial testing and labeling, hazard games, scientific research, etc. Because today's computers are deterministic, they can not create random numbers unless complemented with a RNG. Randomness of a RNG can be precisely, scientifically characterized and measured. Especially valuable is the information-theoretic provable RNG (True RNG - TRNG) which, at state of the art, seem to be possible only by use of phys…
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）
The concept of randomness plays an important role in many disciplines. On one hand, the question of whether random processes exist is fundamental for our understanding of nature. On the other hand, randomness is a resource for cryptography, algorithms and simulations. Standard methods for generating randomness rely on assumptions on the devices that are difficult to meet in practice. However, quantum technologies allow for new methods for generating certified randomness. These methods are known as device-independent because do not rely on any modeling of the devices. Here we review the efforts…
By realizing a quantum cryptography system based on polarization entangled photon pairs we establish highly secure keys, because a single photon source is approximated and the inherent randomness of quantum measurements is exploited. We implement a novel key distribution scheme using Wigner's inequality to test the security of the quantum channel, and, alternatively, realize a variant of the BB84 protocol. Our system has two completely independent users separated by 360 m, and generates raw keys at rates of 400 - 800 bits/second with bit error rates arround 3 percent.
Over decades quantum cryptography has been intensively studied for unconditionally secured data transmission in a quantum regime. Due to the quantum loopholes caused by imperfect single photon detectors and/or lossy quantum channels, however, the quantum cryptography is practically inefficient and even vulnerable to eavesdropping. Here, a method of unconditionally secured key distribution potentially compatible with current fiber-optic communications networks is proposed in a classical regime for high-speed optical backbone networks. The unconditional security is due to the quantum superpositi…
In counterfactual quantum key distribution (QKD), two remote parties can securely share random polarization-encoded bits through the blocking rather than the transmission of particles. We propose a semi-counterfactual QKD, i.e., one where the secret bit is shared, and also encoded, based on the blocking or non-blocking of a particle. The scheme is thus semi-counterfactual and not based on polarization encoding. As with other counterfactual schemes and the Goldenberg-Vaidman protocol, but unlike BB84, the encoding states are orthogonal and security arises ultimately from single-particle non-loc…
Random number plays a key role in information science, especially in cryptography. Based on the probabilistic nature of quantum mechanics, quantum random number generators can produce genuine randomness. In particular, random numbers can be produced from laser phase fluctuations with a very high speed, typically in the Gbps regime. In this work, by developing a physical model, we investigate the origin of the randomness in quantum random number generators based on laser phase fluctuations. We show how the randomness essentially stems from spontaneous emissions. The laser phase fluctuation can …
We develop and present a quantum cryptography concept in which phase determinations are made from the time that a photon is detected, as opposed to where the photon is detected, and hence is a non-interferometric process. The phase-encoded quantum information is contained in temporal and polarization superpositions of single photon states, forming a complex qudit of Hilbert dimension D equal to or greater than 4. Based on this, we have developed a new quantum key distribution protocol that allows the generation of secret key in the presence of higher noise than is possible with other protocols…
If two quantum players at a nonlocal game G achieve a superclassical score, then their measurement outcomes must be at least partially random from the perspective of any third player. This is the basis for device-independent quantum cryptography. In this paper we address a related question: does a superclassical score at G guarantee that one player has created randomness from the perspective of the other player? We show that for complete-support games, the answer is yes: even if the second player is given the first player's input at the conclusion of the game, he cannot perfectly recover her o…
What obstructs the realization of useful quantum cryptography is single photon scheme, or entanglement which is not applicable to the current infrastructure of optical communication network. We are concerned with the following question: Can we realize the information theoretically secure symmetric key cipher under "the finite secret key" based on quantum-optical communications? A role of quantum information theory is to give an answer for such a question. As an answer for the question, a new quantum cryptography was proposed by H.P.Yuen, which can realize a secure symmetric key cipher with hig…
We propose a variational quantum attack algorithm (VQAA) for classical AES-like symmetric cryptography, as exemplified the simplified-data encryption standard (S-DES). In the VQAA, the known ciphertext is encoded as the ground state of a Hamiltonian that is constructed through a regular graph, and the ground state can be found using a variational approach. We designed the ansatz and cost function for the S-DES's variational quantum attack. It is surprising that sometimes the VQAA is even faster than Grove's algorithm as demonstrated by our simulation results. The relationships of the entanglem…
Randomness is an invaluable resource in today's life with a broad use reaching from numerical simulations through randomized algorithms to cryptography. However, on the classical level no true randomness is available and even the use of simple quantum devices in a prepare-measure setting suffers from lack of stability and controllability. This gave rise to a group of quantum protocols that provide randomness certified by classical statistical tests -- Device Independent Quantum Random Number Generators. In this paper we review the most relevant results in this field, which allow the production…
For globally connected devices like smart phones, personal computers and Internet-of-things devices, the ability to generate random numbers is essential for execution of cryptographic protocols responsible for information security. Generally, a random number generator should be small, robust, utilize as few hardware and energy resources as possible, yet provide excellent randomness at a high enough speed (bitrate) for a given purpose. In this work we present a quantum random number generator (QRNG) which makes use of a photoelectric effect in single-photon avalanche diodes (SPADs) as a source …
We use a rectangular pulse to freeze the possibility of estimating the coherent parameters ($θ,ϕ$) of a single qubit and the encoded information. It is shown that, as the possibility of estimating the parameters increases, the amount of encoded information decreases. The pulse strength and the detuning between the qubit and the pulse have a different effect on the estimation degree and the encoded information. We show that if the weight parameter, $θ$ is estimated, the encoded information depends on the initial state settings. Meanwhile, the encoded information doesn't depend on the estimated …
Randomness is a valuable resource in science, cryptography, engineering, and information technology. Quantum-mechanical sources of randomness are attractive because of the indeterminism of individual quantum processes. Here we consider the production of random bits from polarization measurements on photons. We first present a pedagogical discussion of how the quantum randomness inherent in such measurements is connected to quantum coherence, and how it can be quantified in terms of the quantum state and an associated entropy value known as min-entropy. We then explore these concepts by perform…
We present a quantum version of a cipher used in cryptography where the message to be communicated is encoded into the relative phase of a quantum state using the shared key. The encoded quantum information carrying the message is actually sent to the recipient over a quantum channel, assuming the proper secrecy of shared key between peers.
We produce two identical keys using, for the first time, entangled trinary quantum systems (qutrits) for quantum key distribution. The advantage of qutrits over the normally used binary quantum systems is an increased coding density and a higher security margin. The qutrits are encoded into the orbital angular momentum of photons, namely Laguerre-Gaussian modes with azimuthal index l +1, 0 and -1, respectively. The orbital angular momentum is controlled with phase holograms. In an Ekert-type protocol the violation of a three-dimensional Bell inequality verifies the security of the generated ke…
In quantum cryptography, device-independent (DI) protocols can be certified secure without requiring assumptions about the inner workings of the devices used to perform the protocol. In order to display nonlocality, which is an essential feature in DI protocols, the device must consist of at least two separate components sharing entanglement. This raises a fundamental question: how much entanglement is needed to run such DI protocols? We present a two-device protocol for DI random number generation (DIRNG) which produces approximately $n$ bits of randomness starting from $n$ pairs of arbitrari…
Quantum physics can be exploited to generate true random numbers, which play important roles in many applications, especially in cryptography. Genuine randomness from the measurement of a quantum system reveals the inherent nature of quantumness --- coherence, an important feature that differentiates quantum mechanics from classical physics. The generation of genuine randomness is generally considered impossible with only classical means. Based on the degree of trustworthiness on devices, quantum random number generators (QRNGs) can be grouped into three categories. The first category, practic…
An $n$-bit string is encoded as a sequence of non-orthogonal quantum states. The parity bit of that $n$-bit string is described by one of two density matrices, $ρ_0^{(n)}$ and $ρ_1^{(n)}$, both in a Hilbert space of dimension $2^n$. In order to derive the parity bit the receiver must distinguish between the two density matrices, e.g., in terms of optimal mutual information. In this paper we find the measurement which provides the optimal mutual information about the parity bit and calculate that information. We prove that this information decreases exponentially with the length of the string i…
In recent years, several hacking attacks have broken the security of quantum cryptography implementations by exploiting the presence of losses and the ability of the eavesdropper to tune detection efficiencies. We present a simple attack of this form that applies to any protocol in which the key is constructed from the results of untrusted measurements performed on particles coming from an insecure source or channel. Because of its generality, the attack applies to a large class of protocols, from standard prepare-and-measure to device-independent schemes. Our attack gives bounds on the critic…
Encoding information in quantum systems can offer surprising advantages but at the same time there are limitations that arise from the fact that measuring an observable may disturb the state of the quantum system. In our work, we provide an in-depth analysis of a simple question: What happens when we perform two measurements sequentially on the same quantum system? This question touches upon some fundamental properties of quantum mechanics, namely the uncertainty principle and the complementarity of quantum measurements. Our results have interesting consequences, for example they can provide a…
Even if the output of a Random Number Generator (RNG) is perfectly uniformly distributed, it may be correlated to pre-existing information and therefore be predictable. Statistical tests are thus not sufficient to guarantee that an RNG is usable for applications, e.g., in cryptography or gambling, where unpredictability is important. To enable such applications a stronger notion of randomness, termed "true randomness", is required, which includes independence from prior information. Quantum systems are particularly suitable for true randomness generation, as their unpredictability can be prove…
Randomness is a central feature of quantum mechanics and an invaluable resource for both classical and quantum technologies. Commonly, in Device-Independent and Semi-Device-Independent scenarios, randomness is certified using projective measurements and the amount of certified randomness is bounded by the dimension of the measured quantum system. In this work, we propose a new Source-Device-Independent protocol, based on Positive Operator Valued Measurement (POVM), which can arbitrarily increase the number of certified bits for any fixed dimension. A tight lower-bound on the quantum conditiona…
Private information retrieval (PIR) is a database query protocol that provides user privacy, in that the user can learn a particular entry of the database of his interest but his query would be hidden from the data centre. Symmetric private information retrieval (SPIR) takes PIR further by additionally offering database privacy, where the user cannot learn any additional entries of the database. Unconditionally secure SPIR solutions with multiple databases are known classically, but are unrealistic because they require long shared secret keys between the parties for secure communication and sh…
We demonstrate non-degenerate down-conversion at 810 and 1550 nm for long-distance fiber based quantum communication using polarization entangled photon pairs. Measurements of the two-photon visibility, without dark count subtraction, have shown that the quantum correlations (raw visibility 89%) allow secure quantum cryptography after 100 km of non-zero dispersion shifted fiber using commercially available single photon detectors. In addition, quantum state tomography has revealed little degradation of state negativity, decreasing from 0.99 at the source to 0.93 after 100 km, indicating minima…
Certifying optimal device-independent quantum randomness in quantum networks
Hangzhou Dianzi University（杭州电子科技大学）；Zhejiang Provincial Key Laboratory of Sensitive Data Security and Confidentiality Governance（浙江省敏感数据安全与保密治理重点实验室）；The University of Hong Kong（香港大学）
Institute of Quantum Technologies and Advanced Computing, KACST（KACST量子技术与先进计算研究所）；Department of Physics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU)（伊玛目穆罕默德·本·沙特伊斯兰大学理学院物理系）；Department of Physics, College of Science, King Khalid University（国王哈立德大学理学院物理系）；Institute for Quantum Science and Technology and Department of Physics, Shanghai University（上海大学量子科学与技术研究院及物理系）；Shanghai Key Laboratory of High Temperature Superconductors, Shanghai University（上海大学高温超导学重点实验室）；NCQOQI, KACST（KACST国家量子光学与量子信息研究中心）
Benchmarking weak randomness in Quantum and Natural Sources
University of Gdańsk（格但斯克大学）；University of Malta（马耳他大学）；Jagiellonian University（雅盖隆大学）；EMGG TerraData Limitada（EMGG TerraData有限公司）；Universidad de Concepción（康塞普西翁大学）；Universidad Católica de la Santísima Concepción（康塞普西翁天主教大学）；SeQure Quantum SpA（SeQure量子股份公司）
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 security of messages encoded via the widely used RSA public key encryption system rests on the enormous computational effort required to find the prime factors of a large number N using classical (i.e., conventional) computers. In 1994, however, Peter Shor showed that for sufficiently large N a quantum computer would be expected to perform the factoring with much less computational effort. This paper endeavors to explain, in a fashion comprehensible to the non-expert readers of this journal: (i) the RSA encryption protocol; (ii) the various quantum computer manipulations constituting the S…
Randomness is a vital resource for modern day information processing, especially for cryptography. A wide range of applications critically rely on abundant, high quality random numbers generated securely. Here we show how to expand a random seed at an exponential rate without trusting the underlying quantum devices. Our approach is secure against the most general adversaries, and has the following new features: cryptographic level of security, tolerating a constant level of imprecision in the devices, requiring only a unit size quantum memory per device component for the honest implementation,…
Randomness is a very important resource for cryptography, algorithms, and scientific simulations. Since all classical processes are considered to be intrinsically deterministic, we must build quantum random number generators which utilize quantum processes to generate true randomness. Quantum random number generators have been realized in different quantum systems, including quantum optical systems, and trapped ions. Here we present a proof-of-concept random number generator based on a nuclear spin system for the first time. The state preparation and measurements are performed with high-fideli…
Pseudo-random number generators are widely used in many branches of science, mainly in applications related to Monte Carlo methods, although they are deterministic in design and, therefore, unsuitable for tackling fundamental problems in security and cryptography. The natural laws of the microscopic realm provide a fairly simple method to generate non-deterministic sequences of random numbers, based on measurements of quantum states. In practice, however, the experimental devices on which quantum random number generators are based are often unable to pass some tests of randomness. In this revi…
We propose a link between logical independence and quantum physics. We demonstrate that quantum systems in the eigenstates of Pauli group operators are capable of encoding mathematical axioms and show that Pauli group quantum measurements are capable of revealing whether or not a given proposition is logically dependent on the axiomatic system. Whenever a mathematical proposition is logically independent of the axioms encoded in the measured state, the measurement associated with the proposition gives random outcomes. This allows for an experimental test of logical independence. Conversely, it…
