Thomas Vidick

Fully Device-Independent Quantum Key Distribution

Quantum cryptography promises levels of security that are impossible to replicate in a classical world. Can this security be guaranteed even when the quantum devices on which the protocol relies are untrusted? This central question dates back to the early 1990s when the challenge of achieving device-independent quantum key distribution was first formulated. We answer this challenge by rigorously proving the device-independent security of a slight variant of Ekerts original entanglement-based protocol against the most general (coherent) attacks. The resulting protocol is robust: While assuming only that the devices can be modeled by the laws of quantum mechanics and are spatially isolated from each other and from any adversarys laboratory, it achieves a linear key rate and tolerates a constant noise rate in the devices. In particular, the devices may have quantum memory and share arbitrary quantum correlations with the eavesdropper. The proof of security is based on a new quantitative understanding of the monogamous nature of quantum correlations in the context of a multiparty protocol.

Trevisan's extractor in the presence of quantum side information

Randomness extraction involves the processing of purely classical information and is therefore usually studied with in the framework of classical probability theory. However, such a classical treatment is generally too restrictive for applications where side information about the values taken by classical random variables may be represented by the state of a quantum system. This is particularly relevant in the context of cryptography, where an adversary may make use of quantum devices. Here, we show that the well-known construction paradigm for extractors proposed by Trevisan is sound in the presence of quantum side information. We exploit the modularity of this paradigm to give several concrete extractor constructions, which, e.g., extract all the conditional (smooth) min-entropy of the source using a seed of length polylogarithmic in the input, or only require the seed to be weakly random.

A Multi-prover Interactive Proof for NEXP Sound against Entangled Provers

We prove a strong limitation on the ability of entangled provers to collude in a multiplayer game. Our main result is the first nontrivial lower bound on the class MIP* of languages having multi-prover interactive proofs with entangled provers, namely MIP* contains NEXP, the class of languages decidable in non-deterministic exponential time. While Babai, Fort now, and Lund (Computational Complexity 1991) proved the celebrated equality MIP = NEXP in the absence of entanglement, ever since the introduction of the class MIP* it was open whether shared entanglement between the provers could weaken or strengthen the computational power of multi-prover interactive proofs. Our result shows that it does not weaken their computational power: MIP* contains MIP. At the heart of our result is a proof that Babai, Fort now, and Lunds multilinearity test is sound even in the presence of entanglement between the provers, and our analysis of this test could be of independent interest. As a byproduct we show that the correlations produced by any entangled strategy which succeeds in the multilinearity test with high probability can always be closely approximated using shared randomness alone.

Parallel repetition of entangled games

We consider one-round games between a classical referee and two players. One of the main questions in this area is the parallel repetition question: Is there a way to decrease the maximum winning probability of a game without increasing the number of rounds or the number of players? Classically, efforts to resolve this question, open for many years, have culminated in Razs celebrated parallel repetition theorem on one hand, and in efficient product testers for PCPs on the other. In the case where players share entanglement, the only previously known results are for special cases of games, and are based on techniques that seem inherently limited. Here we show for the first time that the maximum success probability of entangled games can be reduced through parallel repetition, provided it was not initially 1. Our proof is inspired by a seminal result of Feige and Kilian in the context of classical two-prover one-round interactive proofs. One of the main components in our proof is an orthogonalization lemma for operators, which might be of independent interest.

A parallel repetition theorem for entangled projection games

We study the behavior of the entangled value of two-player one-round projection games under parallel repetition. We show that for any projection game G of entangled value

Efficient rounding for the noncommutative grothendieck inequality

{1- \epsilon < 1}

A Multiprover Interactive Proof System for the Local Hamiltonian Problem

1-ϵ<1, the value of the k-fold repetition of G goes to zero as