Jean-Daniel Bancal

Practical private database queries based on a quantum-key-distribution protocol

Private queries allow a user, Alice, to learn an element of a database held by a provider, Bob, without revealing which element she is interested in, while limiting her information about the other elements. We propose to implement private queries based on a quantum-key-distribution protocol, with changes only in the classical postprocessing of the key. This approach makes our scheme both easy to implement and loss tolerant. While unconditionally secure private queries are known to be impossible, we argue that an interesting degree of security can be achieved by relying on fundamental physical principles instead of unverifiable security assumptions in order to protect both the user and the database. We think that the scope exists for such practical private queries to become another remarkable application of quantum information in the footsteps of quantum key distribution.

Quantum non-locality based on finite-speed causal influences leads to superluminal signalling

Non-local quantum correlations between distant particles cannot be explained by signals propagating slower than the speed of light. It is now shown that they cannot be explained by hidden influences propagating faster than the speed of light either, because that would permit faster-than-light communication.

Guess your neighbor's input: A multipartite nonlocal game with no quantum advantage

We present a multipartite nonlocal game in which each player must guess the input received by his neighbor. We show that quantum correlations do not perform better than classical ones at this game, for any prior distribution of the inputs. There exist, however, input distributions for which general no-signaling correlations can outperform classical and quantum correlations. Some of the Bell inequalities associated with our construction correspond to facets of the local polytope. Thus our multipartite game identifies parts of the boundary between quantum and postquantum correlations of maximal dimension. These results suggest that quantum correlations might obey a generalization of the usual no-signaling conditions in a multipartite setting.

Device-independent witnesses of genuine multipartite entanglement

We consider the problem of determining whether genuine multipartite entanglement was produced in an experiment, without relying on a characterization of the systems observed or of the measurements performed. We present an n-partite inequality that is satisfied by all correlations produced by measurements on biseparable quantum states, but which can be violated by n-partite entangled states, such as Greenberger-Horne-Zeilinger states. In contrast to traditional entanglement witnesses, the violation of this inequality implies that the state is not biseparable independently of the Hilbert space dimension and of the measured operators. Violation of this inequality does not imply, however, genuine multipartite nonlocality. We show more generically how the problem of identifying genuine tripartite entanglement in a device-independent way can be addressed through semidefinite programming.

Extremal correlations of the tripartite no-signaling polytope

The no-signaling polytope associated with a Bell scenario with three parties, two inputs, and two outputs, is found to have 53 856 extremal points, belonging to 46 inequivalent classes. We provide a classification of these points according to various definitions of multipartite nonlocality and briefly discuss other issues such as the interconversion between extremal points seen as a resource and the relation of the extremal points to Bell-type inequalities.

More randomness from the same data

Correlations that cannot be reproduced with local variables certify the generation of private randomness. Usually, the violation of a Bell inequality is used to quantify the amount of randomness produced. Here, we show how private randomness generated during a Bell test can be directly quantified from the observed correlations, without the need to process these data into an inequality. The frequency with which the different measurement settings are used during the Bell test can also be taken into account. This improved analysis turns out to be very relevant for Bell tests performed with a finite collection efficiency. In particular, applying our technique to the data of a recent experiment (Christensen et al 2013 Phys. Rev. Lett. 111 130406), we show that about twice as much randomness as previously reported can be potentially extracted from this setup.

Detecting genuine multipartite quantum nonlocality: A simple approach and generalization to arbitrary dimensions

The structure of Bell-type inequalities detecting genuine multipartite nonlocality, and hence detecting genuine multipartite entanglement, is investigated. We first present a simple and intuitive approach to Svetlichnys original inequality, which provides a clear understanding of its structure and of its violation in quantum mechanics. Based on this approach, we then derive a family of Bell-type inequalities for detecting genuine multipartite nonlocality in scenarios involving an arbitrary number of parties and systems of arbitrary dimension. Finally, we discuss the tightness and quantum mechanical violations of these inequalities.

Bell correlations in a Bose-Einstein condensate.

Correlating an atomic condensate Parts of a quantum system can be more “correlated” than what is allowed in the everyday classical world: A measurement on one part of the system can immediately affect a spatially distant component. The strongest of such correlations, Bell correlations, have been detected in small systems containing two to a handful of particles. Schmied et al. used collective measurements to detect Bell correlations among the spins of 480 Rb atoms cooled to a condensed state. This many-body correlated state may be useful as a resource in quantum information processing. Science, this issue p. 441 Strong quantum correlations are detected among the spins of 480 rubidium atoms in a condensed state. Characterizing many-body systems through the quantum correlations between their constituent particles is a major goal of quantum physics. Although entanglement is routinely observed in many systems, we report here the detection of stronger correlations—Bell correlations—between the spins of about 480 atoms in a Bose-Einstein condensate. We derive a Bell correlation witness from a many-particle Bell inequality involving only one- and two-body correlation functions. Our measurement on a spin-squeezed state exceeds the threshold for Bell correlations by 3.8 standard deviations. Our work shows that the strongest possible nonclassical correlations are experimentally accessible in many-body systems and that they can be revealed by collective measurements.

Quantum randomness extraction for various levels of characterization of the devices

The amount of intrinsic randomness that can be extracted from measurement on quantum systems depends on several factors: notably, the power given to the adversary and the level of characterization of the devices of the authorized partners. After presenting a systematic introduction to these notions, in this paper we work in the class of least adversarial power, which is relevant for assessing setups operated by trusted experimentalists, and compare three levels of characterization of the devices. Many recent studies have focused on the so-called ?device-independent? level, in which a lower bound on the amount of intrinsic randomness can be certified without any characterization. The other extreme is the case when all the devices are fully characterized: this ?tomographic? level has been known for a long time. We present for this case a systematic and efficient approach to quantifying the amount of intrinsic randomness, and show that setups involving ancillas (positive-operator valued measures, pointer measurements) may not be interesting here, insofar as one may extract randomness from the ancilla rather than from the system under study. Finally, we study how much randomness can be obtained in presence of an intermediate level of characterization related to the task of ?steering?, in which Bob?s device is fully characterized while Alice?s is a black box. We obtain our results here by adapting the NPA hierarchy of semidefinite programs to the steering scenario.This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ?50 years of Bell?s theorem?.

Device-independent entanglement quantification and related applications.

We present a general method to quantify both bipartite and multipartite entanglement in a device-independent manner, meaning that we put a lower bound on the amount of entanglement present in a system based on the observed data only but independent of any quantum description of the employed devices. Some of the bounds we obtain, such as for the Clauser-Horne-Shimony-Holt Bell inequality or the Svetlichny inequality, are shown to be tight. Besides, device-independent entanglement quantification can serve as a basis for numerous tasks. We show in particular that our method provides a rigorous way to construct dimension witnesses, gives new insights into the question whether bound entangled states can violate a Bell inequality, and can be used to construct device-independent entanglement witnesses involving an arbitrary number of parties.