QUROPE Quantum Information Processing and Communication in Europe

Contemporary understanding of correlations in quantum many-body systems and in quantum phase transitions is based to a large extent on the recent intensive studies of entanglement in many-body systems.

Macroscopic realism, the classical world view that macroscopic objects exist independently of and are not influenced by measurements, is usually tested using Leggett-Garg inequalities. Recently, another necessary condition called no-signaling in time (NSIT) has been proposed as a witness for non-classical behavior.

We investigate structural properties of the completely positive semidefinite cone CS^n_+, consisting of all the n×n symmetric matrices that admit a Gram representation by positive semidefinite matrices of any size. This cone has been introduced to model quantum graph parameters as conic optimization problems. Recently it has also been used to characterize the set Q of bipartite quantum correlations, as projection of an affine section of it. We have two main results concerning the structure of the completely positive semidefinite cone, namely about its interior and about its closure.

We show how to use the radiation pressure optomechanical coupling between a mechanical oscillator and an optical cavity field to generate in a heralded way a single quantum of mechanical motion (a Fock state). Starting with the oscillator close to its ground state, a laser pumping the upper motional sideband produces correlated photon-phonon pairs via optomechanical parametric down-conversion.

Entangled quantum systems have properties that have fundamentally overthrown the classical worldview. Increasing the complexity of entangled states by expanding their dimensionality allows the implementation of novel fundamental tests of nature, and moreover also enables genuinely new protocols for quantum information processing.

Quantum steering is a form of bipartite quantum correlations that is intermediate between entanglement and Bell nonlocality. It allows for entanglement certification when the measurements performed by one of the parties are not characterised (or untrusted) and has applications in quantum key distribution. Despite its foundational and applied importance, quantum steering lacks a quantitative assessment.

Bell inequalities define experimentally observable quantities to detect non-locality. In general, they involve correlation functions of all the parties. Unfortunately, these measurements are hard to implement for systems consisting of many constituents, where only few-body correlation functions are accessible.

Physical principles constrain the way nonlocal correlations can be distributed among parties in a Bell experiment. Here, we show that in any no-signalling theory the amount of violation of a certain class of Bell inequalities tightly bounds the knowledge that an external observer can gain about outcomes of any single measurement performed by the parties.

The Clauser-Horne-Shimony-Holt inequality was originally proposed as a Bell inequality to detect nonlocality in bipartite systems. However, it can also be used to certify the nonlocality of multipartite quantum states. We apply this to study the nonlocality of multipartite Greenberger-Horne-Zeilinger, W and graph states under local decoherence processes.