Miguel Navascués

Attempts to understand multipartite quantum nonlocality are thwarted by the difficulty of devising quantum Bell inequalities (QBI) for systems composed of more than a few separate parties. In this work, we introduce the notion of ``tight connectors", a class of tensors which, if contracted according to some simple rules, result in tight QBIs. The new inequalities are saturated by tensor network states, whose structure mimics the corresponding network of connectors. Some tight connectors are furthermore ``fully self-testing'', which implies that the QBI they generate through contractions can only be maximized with such a tensor network state and specific measurement operators (modulo local isometries). We provide large analytic families of tight, fully self-testing connectors that allow the generation, via contraction, of N-partite QBIs with a ratio between the maximum quantum and classical values that grows exponentially with N. In turn, our method provides a modular recipe for the generation of extremal quantum behaviours and associated tight bounds in arbitrarily large systems.

We consider a non-relativistic quantum particle in an infinite line. We estimate the maximum probability of finding the particle at some distant position given that it is initially bound in some region. We prove that quantum mechanics allows for greater probabilities than classical mechanics - thus obtaining a new kind of quantum advantage. We show that this effect is mathematically related to quantum backflow, and use this to improve the upper bounds on the Bracken-Mellow constant. Several generalizations are studied.

Abstract A preparation game is a task whereby a player sequentially sends a number of quantum states to a referee, who probes each of them and announces the measurement result. The measurement setting in each round, as well as the final score of the game, are decided by the referee based on the past history of settings and measurement outcomes. Many experimental tasks in quantum information, such as entanglement quantification or magic state detection, can be cast as preparation games. In this paper, we introduce general methods to design n-round preparation games, with tight bounds on the average game scores achievable by players subject to constraints on their preparation devices. We illustrate our results by devising new adaptive measurement protocols for entanglement detection and quantification. Surprisingly, we find that the standard procedure in entanglement detection, namely, estimating n times the average value of a given entanglement witness, is in general sub-optimal for detecting the entanglement of a specific quantum state. On the contrary, there exist n-round experimental scenarios where detecting the entanglement of a known state optimally requires adaptive measurement schemes.