Self-testing refers to the phenomenon that certain extremal quantum correlations (almost) uniquely identify the quantum system under consideration. For instance observing the maximal violation of the CHSH inequality certifies that the two parties share a singlet. While self-testing results are known for several classes of states, in many cases they are only applicable if the observed statistics are almost perfect, which makes them unsuitable for practical applications. Practically relevant self-testing bounds are much less common and moreover they all result from a single numerical method (with one exception which we discuss in detail). In this work we present a new technique for proving analytic self-testing bounds of practically relevant robustness. We obtain improved bounds for the case of self-testing the singlet using the CHSH inequality (in particular we show that non-trivial fidelity with the singlet can be achieved as long as the violation exceeds β * = (16 + 14 √ 2)/17 ≈ 2.11). In case of self-testing the tripartite GHZ state using the Mermin inequality we derive a bound which not only improves on previously known results but turns out to be tight. We discuss other scenarios to which our technique can be immediately applied.Introduction.-In 1964 John Bell showed that correlations resulting from any classical theory are restricted by certain constraints (now known as Bell inequalities) [Bel64] and moreover that these might be violated by quantum systems. Nowadays Bell nonlocality is an active field with numerous applications [BCP + 14]. One of the most striking consequences of Bell's theorem is the fact that the non-classical nature of two (or more) devices can be verified by a classical user. If we moreover assume quantum mechanics to be the underlying theory, we find that certain extremal quantum correlations (almost) uniquely identify the state and measurements under consideration, a phenomenon known as self-testing. For instance the maximal violation of the Clauser-Horne-Shimony-Holt (CHSH) [CHSH69] inequality necessarily implies that the two parties share a singlet (up to local unitaries). While this was already pointed out by Popescu and Rohrlich in 1992 [PR92], it was not widely known until the works of Mayers and Yao [MY98, MY04]. Since then self-testing has received substantial attention and led to the concept of device independence, important in quantum cryptography [BHK05, AGM06, Col06, ABG + 07, CK11] and beyond [Sca12].The central question in self-testing is: given a conditional probability distribution arising from measuring a (multipartite) quantum state, what can be deduced about the state and/or the measurements?Most previous research has focused on the problem of certifying the quantum state shared between the devices. . The common feature of these results is that the robustness is extremely weak, i.e. we can only make a non-trivial statement if the observed statistics are ε-close to the ideal case (for ε ≈ 10 −4 ). Self-testing statements of practically relevant robustness turn out to ...

We consider a game in which two separate laboratories collaborate to prepare a quantum system and are then asked to guess the outcome of a measurement performed by a third party in a random basis on that system. Intuitively, by the uncertainty principle and the monogamy of entanglement, the probability that both players simultaneously succeed in guessing the outcome correctly is bounded. We are interested in the question of how the success probability scales when many such games are performed in parallel. We show that any strategy that maximizes the probability to win every game individually is also optimal for the parallel repetition of the game. Our result implies that the optimal guessing probability can be achieved without the use of entanglement. We explore several applications of this result. Firstly, we show that it implies security for standard BB84 quantum key distribution when the receiving party uses fully untrusted measurement devices, i.e. we show that BB84 is one-sided device independent. Secondly, we show how our result can be used to prove 3

Bit commitment is a fundamental cryptographic primitive in which Bob wishes to commit a secret bit to Alice. Perfectly secure bit commitment between two mistrustful parties is impossible through asynchronous exchange of quantum information. Perfect security is however possible when Alice and Bob split into several agents exchanging classical and quantum information at times and locations suitably chosen to satisfy specific relativistic constraints. Here we report on an implementation of a bit commitment protocol using quantum communication and special relativity. Our protocol is based on [A. Kent, Phys. Rev. Lett. 109, 130501 (2012)] and has the advantage that it is practically feasible with arbitrary large separations between the agents in order to maximize the commitment time. By positioning agents in Geneva and Singapore, we obtain a commitment time of 15 ms. A security analysis considering experimental imperfections and finite statistics is presented.