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 appeared that this new resource is very complex and difficult to detect. Being usually fragile to environment, it is robust against conceptual and mathematical tools, the task of which is to decipher its rich structure.
This article reviews basic aspects of entanglement including its characterization, detection, distillation and quantifying. In particular, the authors discuss various manifestations of entanglement via Bell inequalities, entropic inequalities, entanglement witnesses, quantum cryptography and point out some interrelations. They also discuss a basic role of entanglement in quantum communication within distant labs paradigm and stress some peculiarities such as irreversibility of entanglement manipulations including its extremal form - bound entanglement phenomenon. A basic role of entanglement witnesses in detection of entanglement is emphasized.
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.
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.
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…
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…
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…
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…
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.
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
Okinawa Institute of Science and Technology Graduate University（冲绳科学技术大学院大学）；INESC-ID, Instituto Superior Técnico, Universidade de Lisboa（葡萄牙里斯本大学高等技术学院INESC-ID）
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.
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…
We discuss the unambiguous measurement of quantum nonorthogonal states in connection with the quantum cryptography. We show that checking a ratio of null one to signal is essential in detecting a certain kind of eavesdropping in the case of two nonorthogonal states quantum cryptography. We prove that it is not needed in the case of the four states quantum cryptography.
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.
Quantum cryptography is a new method for secret communications offering the ultimate security assurance of the inviolability of a Law of Nature. In this paper we shall describe the theory of quantum cryptography, its potential relevance and the development of a prototype system at Los Alamos, which utilises the phenomenon of single-photon interference to perform quantum cryptography over an optical fiber communications link.
We present a new approach to simulate quantum cryptography protocols using event-based processes. The method is validated by simulating the BB84 protocol and the Ekert protocol, both without and with the presence of an eavesdropper.
We report experimental studies on the effect of the depolarizing quantum channel on weak-pulse BB84 and SARG04 quantum cryptography. The experimental results show that, in real world conditions in which channel depolarization cannot be ignored, BB84 should perform better than SARG04.
Noise causes severe difficulties in implementing quantum computing and quantum cryptography. Several schemes have been suggested to reduce this problem, mainly focusing on quantum computation. Motivated by quantum cryptography, we suggest a coding which uses $N$ quantum bits ($N=n^2$) to encode one quantum bit, and reduces the error exponentially with $n$. Our result suggests the possibility of distributing a secure key over very long distances, and maintaining quantum states for very long times. It also provides a new quantum privacy amplification against a strong adversary.
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 cryptography could well be the first application of quantum mechanics at the individual quanta level. The very fast progress in both theory and experiments over the recent years are reviewed, with emphasis on open questions and technological issues.
We propose an alternative quantum cryptography protocol using the quantum interference effect. The efficiency of creating sifted key can reach 100\% in principle, which is higher than previous protocols. Especially, compared with the typical quantum key distribution, the present scheme does not require the authorized parties to check their bases. Because the potential eavesdropper can only access part of the quantum system, the proposed scheme has natural practical security advantages. The scheme can be implemented with current technologies and opens promising possibilities for quantum cryptog…
It has been shown that the predictions of some new phenomena (e.g., teleportation and cryptography) are based on some assumptions added to the quantum-mechanical model or modifying some of its basic axioms. The hitherto experiments presented as a support of the mentioned phenomena may be hardly regarded as sufficient, as they may be interpreted alternatively on the basis of simple interference processes.
We study optimal eavesdropping in quantum cryptography with three-dimensional systems, and show that this scheme is more secure than protocols using two-dimensional states. We generalize the according eavesdropping transformation to arbitrary dimensions, and discuss the connection with optimal quantum cloning.
A large number of quantum location verification protocols have been proposed. All existing protocols in this field are based on symmetric cryptography where verifiers and the prover use the same secret key. The prover obtains secret key from different verifiers, in pieces through public channels, which may result in security compromise. In this paper, we give a formulism to prove information-theoretic position-based quantum cryptography is possible in asymmetric quantum setting. We propose a quantum location verification protocol based on asymmetric quantum cryptographic where two different ke…
We propose and discuss a specific scheme allowing to realize a Quantum Cryptography qutrit protocol. This protocol exploits the polarization properties of single frequency and single spatial mode biphotons.
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…
