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Jérémie Roland

Possible papers associated with this exact author name in Arrow. This page groups case-insensitive exact name matches and is not a full identity disambiguation profile.

5 papers

1 author row

SODA Conference 2021 Conference Paper

Analytic quantum weak coin flipping protocols with arbitrarily small bias

Atul Singh Arora
Jérémie Roland
Chrysoula Vlachou

Weak coin flipping (WCF) is a fundamental cryptographic primitive for two-party secure computation, where two distrustful parties need to remotely establish a shared random bit whilst having opposite preferred outcomes. It is the strongest known primitive with arbitrarily close to perfect security quantumly while classically, its security is completely compromised (unless one makes further assumptions, such as computational hardness). A WCF protocol is said to have bias ∊ if neither party can force their preferred outcome with probability greater than 1/2 + ∊. Classical WCF protocols are shown to have bias 1/2, i. e. , a cheating party can always force their preferred outcome. On the other hand, there exist quantum WCF protocols with arbitrarily small bias, as Mochon showed in his seminal work in 2007 [arXiv: 0711. 4114]. In particular, he proved the existence of a family of WCF protocols approaching bias ∊ ( k ) = 1/(4 k +2) for arbitrarily large k and proposed a protocol with bias 1/6. Last year, Arora, Roland and Weis presented a protocol with bias 1/10 and to go below this bias, they designed an algorithm that numerically constructs unitary matrices corresponding to WCF protocols with arbitrarily small bias [STOC'19, p. 205–216]. In this work, we present new techniques which yield a fully analytical construction of WCF protocols with bias arbitrarily close to zero, thus achieving a solution that has been missing for more than a decade. Furthermore, our new techniques lead to a simplified proof of existence of WCF protocols by circumventing the non-constructive part of Mochon's proof. As an example, we illustrate the construction of a WCF protocol with bias 1/14.

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STOC Conference 2019 Conference Paper

Quantum weak coin flipping

Atul Singh Arora
Jérémie Roland
Stephan Weis

We investigate weak coin flipping, a fundamental cryptographic primitive where two distrustful parties need to remotely establish a shared random bit. A cheating player can try to bias the output bit towards a preferred value. For weak coin flipping the players have known opposite preferred values. A weak coin-flipping protocol has a bias є if neither player can force the outcome towards their preferred value with probability more than 1/2+є. While it is known that all classical protocols have є=1/2, Mochon showed in 2007 that quantumly weak coin flipping can be achieved with arbitrarily small bias (near perfect) but the former best known explicit protocol has bias 1/6 (also due to Mochon, 2005). We propose a framework to construct new explicit protocols achieving biases below 1/6. In particular, we construct explicit unitaries for protocols with bias down to 1/10. To go lower, we introduce what we call the Elliptic Monotone Align (EMA) algorithm which, together with the framework, allows us to construct protocols with arbitrarily small biases.

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FOCS Conference 2012 Conference Paper

Lower Bounds on Information Complexity via Zero-Communication Protocols and Applications

Iordanis Kerenidis
Sophie Laplante
Virginie Lerays
Jérémie Roland
David Xiao

We show that almost all known lower bound methods for communication complexity are also lower bounds for the information complexity. In particular, we define a relaxed version of the partition bound of Jain and Klauck and prove that it lower bounds the information complexity of any function. Our relaxed partition bound subsumes all norm based methods (e. g. the γ2 method) and rectangle-based methods (e. g. the rectangle/corruption bound, the smooth rectangle bound, and the discrepancy bound), except the partition bound. Our result uses a new connection between rectangles and zero-communication protocols where the players can either output a value or abort. We prove the following compression lemma: given a protocol for a function f with information complexity I, one can construct a zero-communication protocol that has non-abort probability at least 2 -O(I) and that computes f correctly with high probability conditioned on not aborting. Then, we show how such a zero-communication protocol relates to the relaxed partition bound. We use our main theorem to resolve three of the open questions raised by Braver man. First, we show that the information complexity of the Vector in Subspace Problem is O(n 1/3 ), which, in turn, implies that there exists an exponential separation between quantum communication complexity and classical information complexity. Moreover, we provide an O(n) lower bound on the information complexity of the Gap Hamming Distance Problem.

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MFCS Conference 2009 Conference Paper

The Communication Complexity of Non-signaling Distributions

Julien Degorre
Marc Kaplan
Sophie Laplante
Jérémie Roland

Abstract We study a model of communication complexity that encompasses many well-studied problems, including classical and quantum communication complexity, the complexity of simulating distributions arising from bipartite measurements of shared quantum states, and XOR games. In this model, Alice gets an input x, Bob gets an input y, and their goal is to each produce an output a, b distributed according to some pre-specified joint distribution p ( a, b | x, y ). Our results apply to any non-signaling distribution, that is, those where Alice’s marginal distribution does not depend on Bob’s input, and vice versa. By introducing a simple new technique based on affine combinations of lower-complexity distributions, we give the first general technique to apply to all these settings, with elementary proofs and very intuitive interpretations. The lower bounds we obtain can be expressed as linear programs (or SDPs for quantum communication). We show that the dual formulations have a striking interpretation, since they coincide with maximum violations of Bell and Tsirelson inequalities. The dual expressions are closely related to the winning probability of XOR games. Despite their apparent simplicity, these lower bounds subsume many known communication complexity lower bound methods, most notably the recent lower bounds of Linial and Shraibman for the special case of Boolean functions. We show that as in the case of Boolean functions, the gap between the quantum and classical lower bounds is at most linear in the size of the support of the distribution, and does not depend on the size of the inputs. This translates into a bound on the gap between maximal Bell and Tsirelson inequality violations, which was previously known only for the case of distributions with Boolean outcomes and uniform marginals. It also allows us to show that for some distributions, information theoretic methods are necessary to prove strong lower bounds. Finally, we give an exponential upper bound on quantum and classical communication complexity in the simultaneous messages model, for any non-signaling distribution.

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STOC Conference 2007 Conference Paper

Search via quantum walk

Frédéric Magniez
Ashwin Nayak 0001
Jérémie Roland
Miklos Santha

We propose a new method for designing quantum search algorithms forfinding a "marked" element in the state space of a classical Markovchain. The algorithm is based on a quantum walk à la Szegedy [25] that is defined in terms of the Markov chain. The main new idea is to apply quantum phase estimation to the quantumwalk in order to implement an approximate reflection operator. Thisoperatoris then used in an amplitude amplification scheme. As a result weconsiderably expand the scope of the previous approaches ofAmbainis [6] and Szegedy [25]. Our algorithm combines the benefits of these approaches in terms of beingable to find marked elements, incurring the smaller cost of the two,and being applicable to a larger class of Markov chain. In addition,it is conceptually simple, avoids several technical difficulties in the previous analyses, and leads to improvements in various aspects of several algorithms based on quantum walk.

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