arXiv subjects
Publications and source records attributed to Valerio Scarani.
The problem of closing the detection loophole with asymmetric systems, such as entangled atom-photon pairs, is addressed. We show that, for the Bell inequality I_3322, a minimal detection efficiency of 43% can be tolerated for one of the particles, if the other one is always detected. We also study the influence of noise and discuss the prospects of experimental implementation.
This is a study of the security of the Coherent One-Way (COW) protocol for quantum cryptography, proposed recently as a simple and fast experimental scheme. In the zero-error regime, the eavesdropper Eve can only take advantage of the losses in the transmission. We consider new attacks, based on unambiguous state discrimination, which perform better than the basic beam-splitting attack, but which can be detected by a careful analysis of the detection statistics. These results stress the importance of testing several statistical parameters in order to achieve higher rates of secret bits.
Bell's theorem states that, to simulate the correlations created by measurement on pure entangled quantum states, shared randomness is not enough: some "non-local" resources are required. It has been demonstrated recently that all projective measurements on the maximally entangled state of two qubits can be simulated with a single use of a "non-local machine". We prove that a strictly larger amount of this non-local resource is required for the simulation of pure non-maximally entangled states of two qubits $\ket{ψ(α)}= \cosα\ket{00}+\sinα\ket{11}$ with $0<α\lesssim\fracπ{7.8}$.
Quantum cryptography shows that one can guarantee the secrecy of correlation on the sole basis of the laws of physics, that is without limiting the computational power of the eavesdropper. The usual security proofs suppose that the authorized partners, Alice and Bob, have a perfect knowledge and control of their quantum systems and devices; for instance, they must be sure that the logical bits have been encoded in true qubits, and not in higher-dimensional systems. In this paper, we present an approach that circumvents this strong assumption. We define protocols, both for the case of bits and for generic $d$-dimensional outcomes, in which the security is guaranteed by the very structure of the Alice-Bob correlations, under the no-signalling condition. The idea is that, if the correlations cannot be produced by shared randomness, then Eve has poor knowledge of Alice's and Bob's symbols. The present study assumes, on the one hand that the eavesdropper Eve performs only individual attacks (this is a limitation to be removed in further work), on the other hand that Eve can distribute any correlation compatible with the no-signalling condition (in this sense her power is greater than what quantum physics allows). Under these assumptions, we prove that the protocols defined here allow extracting secrecy from noisy correlations, when these correlations violate a Bell-type inequality by a sufficiently large amount. The region, in which secrecy extraction is possible, extends within the region of correlations achievable by measurements on entangled quantum states.
One of the most intriguing features of quantum physics is the non-locality of correlations that can be obtained by measuring entangled particles. Recently, it has been noticed that non-locality can be studied without reference to the Hilbert space formalism. I review here the properties of the basic mathematical tool used for such studies, the so called Popescu-Rohrlich-box, in short PR-box. Among its feats, are the simulation of the correlations of the singlet and of other non-local probability distributions. Among its features, the "anomaly of non-locality" and a great power for information-theoretical tasks. Among its failures, the impossibility of reproducing all multi-partite distributions and the triviality of the allowed dynamics.
We present bipartite Bell-type inequalities which allow the two partners to use some non-local resource. Such inequality can only be violated if the parties use a resource which is more non-local than the one permitted by the inequality. We introduce a family of N-inputs non-local machines, which are generalizations of the well-known PR-box. Then we construct Bell-type inequalities that cannot be violated by strategies that use one these new machines. Finally we discuss implications for the simulation of quantum states.
We show that oblivious transfer can be seen as the classical analogue to a quantum channel in the same sense as non-local boxes are for maximally entangled qubits.
The impossibility of perfectly copying (or cloning) an arbitrary quantum state is one of the basic rules governing the physics of quantum systems. The processes that perform the optimal approximate cloning have been found in many cases. These "quantum cloning machines" are important tools for studying a wide variety of tasks, e.g. state estimation and eavesdropping on quantum cryptography. This paper provides a comprehensive review of quantum cloning machines (both for discrete-dimensional and for continuous-variable quantum systems); in addition, it presents the role of cloning in quantum cryptography, the link between optimal cloning and light amplification via stimulated emission, and the experimental demonstrations of optimal quantum cloning.
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 present a detailed study of SARG04 in two different regimes. In the first part, we consider an implementation with a single-photon source: we derive bounds on the error rate $Q$ for security against all possible attacks by the eavesdropper. The lower and the upper bound obtained for SARG04 ($Q\lesssim 10.95%$ and $Q\gtrsim 14.9%$ respectively) are close to those obtained for BB84 ($Q\lesssim 12.4%$ and $Q\gtrsim 14.6%$ respectively). In the second part, we consider the realistic source consisting of an attenuated laser and improve on previous analysis by allowing Alice to optimize the mean number of photons as a function of the distance. SARG04 is found to perform better than BB84, both in secret key rate and in maximal achievable distance, for a wide class of Eve's attacks.
We present and demonstrate a new protocol for practical quantum cryptography, tailored for an implementation with weak coherent pulses to obtain a high key generation rate. The key is obtained by a simple time-of-arrival measurement on the data line; the presence of an eavesdropper is checked by an interferometer on an additional monitoring line. The setup is experimentally simple; moreover, it is tolerant to reduced interference visibility and to photon number splitting attacks, thus featuring a high efficiency in terms of distilled secret bit per qubit.
We investigate cluster states of qubits with respect to their non-local properties. We demonstrate that a Greenberger-Horne-Zeilinger (GHZ) argument holds for any cluster state: more precisely, it holds for any partial, thence mixed, state of a small number of connected qubits (five, in the case of one-dimensional lattices). In addition, we derive a new Bell inequality that is maximally violated by the 4-qubit cluster state and is not violated by the 4-qubit GHZ state.
In practical quantum cryptography, the source sometimes produces multi-photon pulses, thus enabling the eavesdropper Eve to perform the powerful photon-number-splitting (PNS) attack. Recently, it was shown by Curty and Lutkenhaus [Phys. Rev. A 69, 042321 (2004)] that the PNS attack is not always the optimal attack when two photons are present: if errors are present in the correlations Alice-Bob and if Eve cannot modify Bob's detection efficiency, Eve gains a larger amount of information using another attack based on a 2->3 cloning machine. In this work, we extend this analysis to all distances Alice-Bob. We identify a new incoherent 2->3 cloning attack which performs better than those described before. Using it, we confirm that, in the presence of errors, Eve's better strategy uses 2->3 cloning attacks instead of the PNS. However, this improvement is very small for the implementations of the Bennett-Brassard 1984 (BB84) protocol. Thus, the existence of these new attacks is conceptually interesting but basically does not change the value of the security parameters of BB84. The main results are valid both for Poissonian and sub-Poissonian sources.
Correlated photons produced by spontaneous parametric down-conversion are an essential tool for quantum communication, especially suited for long-distance connections. To have a reasonable count rate after all the losses in the propagation and the filters needed to improve the coherence, it is convenient to increase the intensity of the laser that pumps the non-linear crystal. By doing so, however, the importance of the four-photon component of the down-converted field increases, thus degrading the quality of two-photon interferences. In this paper, we present an easy derivation of this nuisance valid for any form of entanglement generated by down-conversion, followed by a full study of the problem for time-bin entanglement. We find that the visibility of two-photon interferences decreases as V=1-2ρ, where ρis, in usual situations, the probability per pulse of creating a detectable photon pair. In particular, the decrease of V is independent of the coherence of the four-photon term. Thanks to the fact that ρcan be measured independently of V, the experimental verification of our prediction is provided for two different configuration of filters.
We present an easy way of observing superluminal group velocities using a birefringent optical fiber and other standard devices. In the theoretical analysis, we show that the optical properties of the setup can be described using the notion of "weak value". The experiment shows that the group velocity can indeed exceed c in the fiber; and we report the first direct observation of the so-called "signal velocity", the speed at which information propagates and that cannot exceed c.
We present a new protocol for practical quantum cryptography, tailored for an implementation with weak coherent pulses. The key is obtained by a very simple time-of-arrival measurement on the data line; an interferometer is built on an additional monitoring line, allowing to monitor the presence of a spy (who would break coherence by her intervention). Against zero-error attacks (the analog of photon-number-splitting attacks), this protocol performs as well as standard protocols with strong reference pulses: the key rate decreases only as the transmission $t$ of the quantum channel. We present also two attacks that introduce errors on the monitoring line: the intercept-resend, and a coherent attack on two subsequent pulses. Finally, we sketch several possible variations of this protocol.
Since Bell's theorem, it is known that quantum correlations cannot be described by local variables (LV) alone: if one does not want to abandon classical mechanisms for correlations, a superluminal form of communication among the particles must be postulated. A natural question is whether such a postulate would imply the possibility of superluminal signaling. Here we show that the assumption of finite-speed superluminal communication indeed leads to signaling when no LV are present, and more generally when only LV derivable from quantum statistics are allowed. When the most general LV are allowed, we prove in a specific case that the model can be made again consistent with relativity, but the question remains open in general.
We present an experiment where two photonic systems of arbitrary dimensions can be entangled. The method is based on spontaneous parametric down conversion with trains of d pump pulses with a fixed phase relation, generated by a mode-locked laser. This leads to a photon pair created in a coherent superposition of $d$ discrete emission times, given by the successive laser pulses. Entanglement is shown by performing a two-photon interference experiment and by observing the visibility of the interference fringes increasing as a function of the dimension d. Factors limiting the visibility, such as the presence of multiple pairs in one train, are discussed.
We introduce a new class of quantum quantum key distribution protocols, tailored to be robust against photon number splitting (PNS) attacks. We study one of these protocols, which differs from the BB84 only in the classical sifting procedure. This protocol is provably better than BB84 against PNS attacks at zero error.