Upcoming seminars

Abstract: We study the problem of testing identity of a collection of unknown quantum states given sample access to this collection, each state appearing with some known probability. We show that for a collection of d-dimensional quantum states of cardinality N, the sample complexity is O(\sqrt{N}d/\epsilon^2), which is optimal up to a constant. The test is obtained by estimating the mean squared Hilbert-Schmidt distance between the states, thanks to a suitable generalization of the estimator of the Hilbert-Schmidt distance between two unknown states by Bădescu, O'Donnell, and Wright.

Non-locality refers to the existence of correlations between local measurements on a shared resource, that cannot be explained by any local realistic theory. So far, it has been investigated mostly in isolated quantum systems. Here I will show that non-local correlations are present, can be detected and might be robust against noise also in many-body open quantum systems, both in the steady-state or in the transient regime.

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Continuous-variable (CV) representation of quantum mechanics plays a major role in quantum information theory and quantum optics, espe- cially in quantum state and process tomography. As an example, one might consider inferring the non-classicality of an unknown state, based on whether or not it can be written as a statistical mixture of classical (coher- ent) states. However, there is a major challenge here: the weight function (P-function) is a highly singular function for most cases. Here is where the concept of filtering is useful.