Jonathan Silman

Violating Bell's inequalities in vacuum

We employ an approach wherein the ground state entanglement of a relativistic free scalar field is directly probed in a controlled manner. The approach consists of having a pair of initially nonentangled detectors locally interact with the vacuum for a finite duration T, such that the two detectors remain causally disconnected, and then analyzing the resulting detector mixed state. We show that the correlations between arbitrarily far-apart regions of the vacuum cannot be reproduced by a local hidden-variable model, and that as a function of the distance L between the regions, the entanglement decreases at a slower rate than {approx}exp[-(L/cT){sup 3}].

Using complete measurement statistics for optimal device-independent randomness evaluation

The majority of recent works investigating the link between non-locality and randomness, e.g. in the context of device-independent cryptography, do so with respect to some specific Bell inequality, usually the CHSH inequality. However, the joint probabilities characterizing the measurement outcomes of a Bell test are richer than just the degree of violation of a single Bell inequality. In this work we show how to take this extra information into account in a systematic manner in order to optimally evaluate the randomness that can be certified from non-local correlations. We further show that taking into account the complete set of outcome probabilities is equivalent to optimizing over all possible Bell inequalities, thereby allowing us to determine the optimal Bell inequality for certifying the maximal amount of randomness from a given set of non-local correlations.

Fully Distrustful Quantum Bit Commitment and Coin Flipping

J. Silman, A. Chailloux, N. Aharon, I. Kerenidis, 5 S. Pironio, and S. Massar Laboratoire d’Information Quantique, Université Libre de Bruxelles, 1050 Bruxelles, Belgium LIAFA, Univ. Paris 7, F-75205 Paris, France; and Univ. Paris-Sud, 91405 Orsay, France School of Physics and Astronomy, Tel-Aviv University, Tel-Aviv 69978, Israel LIAFA, Univ. Paris 7 CNRS; F-75205 Paris, France Centre for Quantum Technologies, National University of Singapore, Singapore 117543

Quantum dice rolling: a multi-outcome generalization of quantum coin flipping

The problem of quantum dice rolling (DR)—a generalization of the problem of quantum coin flipping (CF) to more than two outcomes and parties—is studied in both its weak and strong variants. We prove by construction that quantum mechanics allows for (i) weak N-sided DR admitting arbitrarily small bias for any N and (ii) two-party strong N-sided DR saturating Kitaevs bound for any N. To derive (ii) we also prove by construction that quantum mechanics allows for (iii) strong imbalanced CF saturating Kitaevs bound for any degree of imbalance. Furthermore, as a corollary of (ii) we introduce a family of optimal 2m-party strong nm-sided DR protocols for any pair m and n.

Device-independent randomness generation in the presence of weak cross-talk.

Device-independent protocols use nonlocality to certify that they are performing properly. This is achieved via Bell experiments on entangled quantum systems, which are kept isolated from one another during the measurements. However, with present-day technology, perfect isolation comes at the price of experimental complexity and extremely low data rates. Here we argue that for device-independent randomness generation--and other device-independent protocols where the devices are in the same lab--we can slightly relax the requirement of perfect isolation and still retain most of the advantages of the device-independent approach, by allowing a little cross-talk between the devices. This opens up the possibility of using existent experimental systems with high data rates, such as Josephson phase qubits on the same chip, thereby bringing device-independent randomness generation much closer to practical application.

Device-Independent Bit Commitment based on the CHSH Inequality

Bit commitment and coin flipping occupy a unique place in the device-independent landscape, as the only device-independent protocols thus far suggested for these tasks are reliant on tripartite GHZ correlations. Indeed, we know of no other bipartite tasks, which admit a device-independent formulation, but which are not known to be implementable using only bipartite nonlocality. Another interesting feature of these protocols is that the pseudo-telepathic nature of GHZ correlations -- in contrast to the generally statistical character of nonlocal correlations, such as those arising in the violation of the CHSH inequality -- is essential to their formulation and analysis. In this work, we present a device-independent bit commitment protocol based on CHSH testing, which achieves the same security as the optimal GHZ-based protocol. The protocol is analyzed in the most general settings, where the devices are used repeatedly and may have long-term quantum memory. We also recast the protocol in a post-quantum setting where both honest and dishonest parties are restricted only by the impossibility of signaling, and find that overall the supra-quantum structure allows for greater security.

On the relation between Bell's inequalities and nonlocal games

We investigate the relation between Bells inequalities and nonlocal games by presenting a systematic method for their bilateral conversion. In particular, we show that while to any nonlocal game there naturally corresponds a unique Bells inequality, the converse is not true. As an illustration of the method we present a number of nonlocal games that admits better odds when played using quantum resources.

Long-range entanglement in the Dirac vacuum

Recently, there have been a number of works investigating the entanglement properties of distinct noncomplementary parts of discrete and continuous bosonic systems in ground and thermal states. The relativistic fermionic case, however, has yet to be expressly addressed. In this paper we investigate the entanglement between a pair of far-apart regions of the (3+1)-dimensional massless Dirac vacuum via a previously introduced distillation protocol [Reznik et al., Phys. Rev. A 71, 042104 (2005)]. We show that entanglement persists over arbitrary distances, and that as a function of L/R, where L is the distance between the regions and R is their typical scale, it decays no faster than {approx}exp[-(L/R){sup 2}]. We discuss the similarities with and differences from analogous results obtained for the massless Klein-Gordon vacuum.

Secure and Robust Transmission and Verification of Unknown Quantum States in Minkowski Space

An important class of cryptographic applications of relativistic quantum information work as follows. B generates a random qudit and supplies it to A at point P. A is supposed to transmit it at near light speed c to to one of a number of possible pairwise spacelike separated points Q1, …, Qn. As transmission is supposed to be secure, in the sense that B cannot tell in advance which Qj will be chosen. This poses significant practical challenges, since secure reliable long-range transmission of quantum data at speeds near to c is presently not easy. Here we propose different techniques to overcome these diffculties. We introduce protocols that allow secure long-range implementations even when both parties control only widely separated laboratories of small size. In particular we introduce a protocol in which A needs send the qudit only over a short distance, and securely transmits classical information (for instance using a one time pad) over the remaining distance. We further show that by using parallel implementations of the protocols security can be maintained in the presence of moderate amounts of losses and errors.

Device-independent randomness generation from several Bell estimators

Device-independent randomness generation and quantum key distribution protocols rely on a fundamental relation between the non-locality of quantum theory and its random character. This relation is usually expressed in terms of a trade-off between the probability of guessing correctly the outcomes of measurements performed on quantum systems and the amount of violation of a given Bell inequality. However, a more accurate assessment of the randomness produced in Bell experiments can be obtained if the value of several Bell expressions is simultaneously taken into account, or if the full set of probabilities characterizing the behavior of the device is considered. We introduce protocols for device-independent randomness generation, secure against classical side information, that rely on the estimation of an arbitrary number of Bell expressions or even directly on the experimental frequencies of measurement outcomes. Asymptotically, this results in an optimal generation of randomness from experimental data (as measured by the min-entropy), without having to assume beforehand that the devices violate a specific Bell inequality.