M. Genovese, C. Novero
We propose a quantum transmission based on bi-photons which are doubly-entangled both in polarisation and phase. This scheme finds a natural application in quantum cryptography, where we show that an eventual eavesdropper is bound to introduce a larger error on the quantum communication than for a single entangled bi-photon communication, when steeling the same information.
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Quantum cryptography is reviewed, first using entanglement both for the intuition and for the experimental realizations. Next, the implementation is simplified in several steps until it becomes practical. At this point entanglement has disappeared. This method can be seen as a lesson of Applied Physics. Finally, security issues, e.g. photon number splitting attacks, and counter-measures are discussed.
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.
Security proof for quantum cryptography against entanglement-measurement attack
本文提出利用两种窃听检查方法证明量子密码对抗纠缠测量攻击的安全性，通过最大纠缠态协议演示证明过程。
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.
Multi-photon states from parametric down-conversion can be entangled both in polarization and photon number. Maximal high-dimensional entanglement can be concentrated from these states via photon counting. This makes them natural candidates for quantum key distribution, where the presence of more than one photon per detection interval has up to now been considered as undesirable. We propose a simple multi-photon protocol for the case of low losses and point out the robustness of the entanglement under photon loss.
We give a proof that entanglement purification, even with noisy apparatus, is sufficient to disentangle an eavesdropper (Eve) from the communication channel. In the security regime, the purification process factorises the overall initial state into a tensor-product state of Alice and Bob, on one side, and Eve on the other side, thus establishing a completely private, albeit noisy, quantum communication channel between Alice and Bob. The security regime is found to coincide for all practical purposes with the purification regime of a two-way recurrence protocol. This makes two-way entanglement …
Recently, position-based quantum cryptography has been claimed to be unconditionally secure. In contrary, here we show that the existing proposals for position-based quantum cryptography are, in fact, insecure if entanglement is shared among two adversaries. Specifically, we demonstrate how the adversaries can incorporate ideas of quantum teleportation and quantum secret sharing to compromise the security with certainty. The common flaw to all current protocols is that the Pauli operators always map a codeword to a codeword (up to an irrelevant overall phase). We propose a modified scheme lack…
We present a quantum key distribution (QKD) system based on polarisation entanglement for use in telecom fibers. A QKD exchange up to 50km was demonstrated in the laboratory with a secure key rate of 550 bit/s. The system is compact, portable with a fully automated start-up and stabilisation modules for polarisation, synchronisation and photon coupling allow a hands-off operation. Stable and reliable key exchange in a deployed optical fiber of 16km length was demonstrated. In this fiber network we achieved over two weeks an automatic key generation with an average key rate of 2000 bit/s withou…
Granting information privacy is of crucial importance in our society, notably in fiber communication networks. Quantum cryptography provides a unique means to establish, at remote locations, identical strings of genuine random bits, with a level of secrecy unattainable using classical resources. However, several constraints, such as non-optimized photon number statistics and resources, detectors' noise, and optical losses, currently limit the performances in terms of both achievable secret key rates and distances. Here, these issues are addressed using an approach that combines both fundamenta…
In state-of-the-art quantum key distribution (QKD) systems, the main limiting factor in increasing the key generation rate is the timing resolution in detecting photons. Here, we present and experimentally demonstrate a strategy to overcome this limitation, also for high-loss and long-distance implementations. We exploit the intrinsic wavelength correlations of entangled photons using wavelength multiplexing to generate a quantum secure key from polarization entanglement. The presented approach can be integrated into both fiber- and satellite-based quantum-communication schemes, without any ch…
Secret Entanglement, Public Geometry. Quantum Cryptography from a Geometric Perspective
从几何视角提出量子密码学的新方法，利用纠缠分层和几何度量实现信息编码与安全传输。
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.
Instantaneous measurements of non-local observables between space-like separated regions can be performed without violating causality. This feat relies on the use of entanglement. Here we propose novel protocols for this task and the related problem of multipartite quantum computation with local operations and a single round of classical communication. Compared to previously known techniques, our protocols reduce the entanglement consumption by an exponential amount. We also prove a linear lower bound on the amount of entanglement required for the implementation of a certain non-local measurem…
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…
Advantage of multi-partite entanglement for quantum cryptography over long and short ranged networks
本文证明了基于GHZ态变体的秘密共享协议在面对一般攻击时的安全性，并发现量子中继器能解锁多体纠缠在长距离量子密码学中相对点对点方法的性能优势。
An efficient quantum cryptography network protocol is proposed with d-dimension polarized photons, without resorting to entanglement and quantum memory. A server on the network, say Alice, provides the service for preparing and measuring single photons whose initial state are |0>. The users code the information on the single photons with some unitary operations. For preventing the untrustworthy server Alice from eavesdropping the quantum lines, a nonorthogonal-coding technique (decoy-photon technique) is used in the process that the quantum signal is transmitted between the users. This protoco…
This thesis presents a study of the structure of bipartite quantum states. In the first part, the representation theory of the unitary and symmetric groups is used to analyse the spectra of quantum states. In particular, it is shown how to derive a one-to-one relation between the spectra of a bipartite quantum state and its reduced states, and the Kronecker coefficients of the symmetric group. In the second part, the focus lies on the entanglement of bipartite quantum states. Drawing on an analogy between entanglement distillation and secret-key agreement in classical cryptography, a new entan…
Entanglement between three or more parties exhibits a realm of properties unknown to two-party states. Bipartite states are easily classified using the Schmidt decomposition. The Schmidt coefficients of a bipartite pure state encompass all the non-local properties of the state and can be "seen" by looking at one party's density matrix only. Pure states of three and more parties however lack such a simple form. They have more invariants under local unitary transformations than any one party can "see" on their sub-system. These "hidden non-localities" will allow us to exhibit a class of multipar…
We investigate theoretically the use of non-ideal ferromagnetic contacts as a mean to detect quantum entanglement of electron spins in transport experiments. We use a designated entanglement witness and find a minimal spin polarization of $η> 1/\sqrt{3} \approx 58 %$ required to demonstrate spin entanglement. This is significantly less stringent than the ubiquitous tests of Bell's inequality with $η> 1/\sqrt[4]{2}\approx 84%$. In addition, we discuss the impact of decoherence and noise on entanglement detection and apply the presented framework to a simple quantum cryptography protocol. Our re…
This paper presents a hybrid cryptographic protocol, using quantum and classical resources, for authentication and authorization in a network. One or more trusted servers distribute streams of entangled photons to individual resources that seek to communicate. It is assumed that each resource shares a previously distributed secret key with the trusted server, and that resources can communicate with the server using both classical and quantum channels. Resources do not share secret keys with each other, so that the key distribution problem for the network is reduced from O(n^2) to O(n). Some ad…
Exponential Advantage of Multipartite Entanglement over Quantum Communication with Applications to Bounded-Storage Cryptography
该研究确立了多体纠缠相较无预共享纠缠的量子通信的指数优势，构造了双源随机数提取器，在受限存储密码学中实现了纠缠与无纠缠量子侧信息的指数分离。
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 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…
Quantum computing had a profound impact on cryptography. Shor's discovery of an efficient quantum algorithm for factoring large integers implies that many existing classical systems based on computational assumptions can be broken, once a quantum computer is built. It is therefore imperative to find other means of implementing secure protocols. This thesis aims to contribute to the understanding of both the physical limitations, as well as the possibilities of cryptography in the quantum setting. In particular, we investigate several questions that are crucial to the security of quantum protoc…
We propose a novel double-entanglement-based quantum cryptography protocol that is both efficient and deterministic. The proposal uses photon pairs with entanglement both in polarization and in time degrees of freedom; each measurement in which both of the two communicating parties register a photon can establish one and only one perfect correlation and thus deterministically create a key bit. Eavesdropping can be detected by violation of local realism. A variation of the protocol shows a higher security, similarly to the six-state protocol, under individual attacks. Our scheme allows a robust…
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…
Controlled entanglement source for quantum cryptography
本研究提出一种通过光学泵浦相位随机化为纠缠源增加访问控制的简单协议，有效管理用户对量子密码学纠缠资源的使用，并可作为设备无关量子密钥分发记忆攻击的低成本对策，实验验证了其可行性。
We investigate a new strategy for incoherent eavesdropping in Ekert's entanglement based quantum key distribution protocol. We show that under certain assumptions of symmetry the effectiveness of this strategy reduces to that of the original single qubit protocol of Bennett and Brassard.
Pseudo-Entanglement is Necessary for EFI Pairs
该研究证明EFI对的存在意味着伪纠缠的存在，确立伪纠缠为多数计算密码学的新最小假设，强化了密码学与物理世界的联系。
Recently the explicit applicability of bound entanglement in quantum cryptography has been shown. In this paper some of recent results respecting this topic are reviewed. In particular relevant notions and definitions are reminded. The new construction of bound entangled states containing secure correlations is presented. It provides low dimensional 6\otimes6 bound entangled states with nonzero distillable key.
Computational Cryptography from Pseudoentanglement
该研究通过EFI对建立伪纠缠与计算密码学最小假设之间的联系，证明特定操作性定义下伪纠缠的存在等价于EFI对的存在，为密码学提供新视角并搭建两领域桥梁。
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 present a setup for quantum cryptography based on photon pairs in energy-time Bell states and show its feasability in a laboratory experiment. Our scheme combines the advantages of using photon pairs instead of faint laser pulses and the possibility to preserve energy-time entanglement over long distances. Moreover, using 4-dimensional energy-time states, no fast random change of bases is required in our setup : Nature itself decides whether to measure in the energy or in the time base.
Implementation of space-division multiplexed entanglement-based quantum cryptography over multicore fiber
本文在19芯多芯光纤中实验实现空分复用的纠缠量子密钥分发，利用SPDC光子对动量相关性将偏振纠缠光子对送入不同纤芯，并在411米传输后评估6芯与12芯配置的密钥率提升。
This paper addresses the application of quantum entanglement and cryptography for automation and control of dynamic systems. A dynamic system is a system where the rates of changes of its state variables are not negligible. Quantum entanglement is realized by the Spontaneous Parametric Down-conversion process. Two entangled autonomous systems exhibit correlated behavior without any classical communication in between them due to the quantum entanglement phenomenon. Specifically, the behavior of a system, Bob, at a distance, is correlated with a corresponding system, Alice. In an automation scen…
Multipartite cryptography is useful for some particular missions. In this paper, we present a quantum key distribution scheme in which three separated observers can securely share a set of keys by using a sequence of $3$-particle GHZ states. We prove that the violation of Svetlichny's inequality can be utilized to test for eavesdropping, and even when the eavesdropper can completely control the outcomes of two participants' measurements, our scheme still ensures the security of the keys distribution. This scheme can be easily extended to the case of $N$-party keys distribution, and the violati…
A highly attenuated laser pulse which gives a weak coherent state is widely used in quantum key distribution (QKD) experiments. A weak coherent state has multi-photon components, which opens up a security loophole to the sophisticated eavesdropper. With a small adjustment of the hardware, we prove that the decoy state method can close this loophole and substantially improve the QKD performance. We also propose a few practical decoy state protocols, study statistical fluctuations and perform experimental demonstrations. Moreover, we apply the methods from entanglement distillation protocols bas…
Computational Entanglement Theory
本文建立计算纠缠理论，定义计算一次性纠缠成本与可提取纠缠，证明其与信息论度量的差距，并基于后量子假设构造伪纠缠态。
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.
All our former experience with application of quantum theory seems to say: {\it what is predicted by quantum formalism must occur in laboratory}. But the essence of quantum formalism - entanglement, recognized by Einstein, Podolsky, Rosen and Schrödinger - waited over 70 years to enter to laboratories as a new resource as real as energy. This holistic property of compound quantum systems, which involves nonclassical correlations between subsystems, is a potential for many quantum processes, including ``canonical'' ones: quantum cryptography, quantum teleportation and dense coding. However, it …
We analyze the security of quantum cryptography schemes for $d$-level systems using 2 or $d+1$ maximally conjugated bases, under individual eavesdropping attacks based on cloning machines and measurement after the basis reconciliation. We consider classical advantage distillation protocols, that allow to extract a key even in situations where the mutual information between the honest parties is smaller than the eavesdropper's information. In this scenario, advantage distillation protocols are shown to be as powerful as quantum distillation: key distillation is possible using classical techniqu…
We show that non-maximally entangled states can be used to build a quantum key distribution (QKD) scheme whose security and key rate transmission is nearly equivalent to those of standard QKD protocols. These aspects can be controlled by using the new free parameter in the present scheme, namely, the degree of partial entanglement. Furthermore, we discuss how to build a controlled QKD scheme, also based on partially entangled states, where a third party can decide whether or not Alice and Bob are allowed to share a key.
Quantum computing and quantum communications are exciting new frontiers in computing and communications. Indeed, the massive investments made by the governments of the US, China, and EU in these new technologies are not a secret and are based on the expected potential of these technologies to revolutionize communications, computing, and security. In addition to several field trials and hero experiments, a number of companies such as Google and IBM are actively working in these areas and some have already reported impressive demonstrations in the past few years. While there is some skepticism a…
Quantum secret sharing (QSS) is a protocol to split a message into several parts so that no subset of parts is sufficient to read the message, but the entire set is. In the scheme, three parties Alice, Bob and Charlie first share a three-photon entangled state, Charlie can then force Alice and Bob to cooperate to be able to establish the secret key with him by performing proper polarization measurements on his photon and announcing which polarization basis he has chosen. In a similar manner, in third-man quantum cryptography (TQC) the third-man, Charlie, can control whether Alice and Bob can c…
The security of a cryptographic key that is generated by communication through a noisy quantum channel relies on the ability to distill a shorter secure key sequence from a longer insecure one. For an important class of protocols, which exploit tomographically complete measurements on entangled pairs of any dimension, we show that the noise threshold for classical advantage distillation is identical with the threshold for quantum entanglement distillation. As a consequence, the two distillation procedures are equivalent: neither offers a security advantage over the other.
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…
We give a security proof of quantum cryptography based entirely on entanglement purification. Our proof applies to all possible attacks (individual and coherent). It implies the security of cryptographic keys distributed with the help of entanglement-based quantum repeaters. We prove the security of the obtained quantum channel which may not only be used for quantum key distribution, but also for secure, albeit noisy, transmission of quantum information.
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.
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…
We derive complementarity relations for arbitrary quantum states of multiparty systems, of arbitrary number of parties and dimensions, between the purity of a part of the system and several correlation quantities, including entanglement and other quantum correlations as well as classical and total correlations, of that part with the remainder of the system. We subsequently use such a complementarity relation, between purity and quantum mutual information in the tripartite scenario, to provide a bound on the secret key rate for individual attacks on a quantum key distribution protocol.
When the 4-state or the 6-state protocol of quantum cryptography is carried out on a noisy (i.e. realistic) quantum channel, then the raw key has to be processed to reduce the information of an adversary Eve down to an arbitrarily low value, providing Alice and Bob with a secret key. In principle, quantum algorithms as well as classical algorithms can be used for this processing. A natural question is: up to which error rate on the raw key is a secret-key agreement at all possible? Under the assumption of incoherent eavesdropping, we find that the quantum and classical limits are precisely the…
Entanglement swapping under quantum information masking
该研究探讨量子信息掩蔽下的纠缠交换，其成果为量子信息掩蔽方案在基于纠缠交换的量子密码学中的应用奠定了基础。
Shared entanglement between spatially separated systems is an essential resource for quantum information processing including long-distance quantum cryptography and teleportation. While purification protocols for mixed distributed entangled quantum states exist, it is not clear how to optimally distribute entanglement to remote locations. Here, we describe a deterministic protocol for generating a maximally entangled state between remote locations that only uses local operations on qubits, and requires no classical communication between the separated parties. The procedure may provide protecti…
We present a generalized tomographic quantum key distribution protocol in which the two parties share a Bell diagonal mixed state of two qubits. We show that if an eavesdropper performs a coherent measurement on many quantum ancilla states simultaneously, classical methods of secure key distillation are less effective than quantum entanglement distillation protocols. We also show that certain Bell diagonal states are resistant to any attempt of incoherent eavesdropping.
Two-photon interference effects, such as the Hong-Ou-Mandel (HOM) effect, can be used to characterize to what extent two photons are identical. Identical photons are necessary for both linear optics quantum computing and single-photon quantum cryptography. We study here how storage and delay of photons in coupled cavity arrays, which inevitably will lead to changes in the photons' spectral and temporal profiles, affects their HOM interference. In addition we consider various types of entanglement that occur naturally in such a context.
In the cited paper [White, T., Mutus, J., Dressel, J. et al., "Preserving entanglement during weak measurement demonstrated with a violation of the Bell-Leggett-Garg inequality", npj Quantum Information 2, 15022 (2016), arXiv:1504.02707], experimental results were presented that clearly prove that the quantum entanglement between two qubits is preserved after weak enough measurements are performed on them. The theoretical interpretation of the reported results, however, requires further consideration. The remarks made in this paper may have serious implications both for quantum foundations and…
Cryptography without Long-Term Quantum Memory and Global Entanglement: Classical Setups for One-Time Programs, Copy Protection, and Stateful Obfuscation
本文利用仅支持经典查询的预言机与半量子令牌，在无长期量子存储器和全局纠缠条件下构造半量子 OTP、RAM 混淆，并进一步实现长命一次性程序与复制保护。
There has been spectacular progress in the field of quantum information in recent decades. The development of this field highlights the importance of the role of entanglement in quantum computing, quantum teleportation and quantum cryptography. These notes serve to provide a gentle introduction to the entanglement of bipartite states. In these notes, we introduce Bell's theorem in the form derived by Clauser, Horne, Shimony and Holt. We discuss the Schmidt decomposition and the Peres-Horodecki criterion in the entanglement of pure and mixed bipartite states. Finally, we describe a teleportatio…
Recently, a "counterfactual" quantum key distribution scheme was proposed by Tae-Gon Noh [1]. In this scheme, two legitimate distant peers may share secret keys even when the information carriers are not traveled in the quantum channel. We find that this protocol is equivalent to an entanglement distillation protocol (EDP). According to this equivalence, a strict security proof and the asymptotic key bit rate are both obtained when perfect single photon source is applied and Trojan-horse attack can be detected. We also find that the security of this scheme is deeply related with not only the b…
We provide a complete proof of the security of quantum cryptography against any eavesdropping attack including coherent measurements even in the presence of noise. Polarization-based cryptographic schemes are shown to be equivalent to EPR-based schemes. We also show that the performance of a noisy channel approaches that of a noiseless one as the error rate tends to zero. (i.e., the secrecy capacity $C_s (ε) \to C_s (0)$ as $ε\to 0$.) One implication of our results is that one can {\it double} the efficiency of a most well-known quantum cryptographic scheme proposed by Bennett and Brassard sim…
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