BEGIN:VCALENDAR VERSION:2.0 PRODID:Icfo X-PUBLISHED-TTL:P1W BEGIN:VEVENT UID:69d4b63abe031 DTSTART:20250327T080000Z SEQUENCE:0 TRANSP:OPAQUE LOCATION:Elements Room SUMMARY:ICFO | GUILLEM-JACOB MÜLLER RIGAT CLASS:PUBLIC DESCRIPTION:Almost a hundred years ago\, the modern quantum theory was born and\, from the outset\, challenged classical physics with revolutionary c oncepts. Arguably\, quantum entanglement\, which describes correlations th at cannot be explained classically (e.g. via statistical mechanics) is the most notable of them. On the other hand\, quantum entanglement is an esse ntial resource to certain information processing tasks and fuels emergent technologies such as quantum computing\, simulation or sensing. Hence\, th e evaluation of a state&rsquo\;s resource content\, as prepared in a devic e\, is a prerequisite to assess the advantage it may provide in these quan tum-enhanced applications. Over the last decades\, the second quantum revo lution brought new experimental capabilities to generate and control massi vely correlated states in many-body systems. Such advances have also posed remarkable theoretical challenges. Most of the entanglement measures and detection approaches do not scale well and are extremely hard to implement as the system&rsquo\;s size grows towards the macroscopic scale. This the sis primarily aims at developing reliable theoretical tools to certify the preparation of entangled states and other quantum correlations in many[1] body systems from accessible observables. In doing so\, we reconcile vario us information-theoretic measures to the laboratory by constructing witnes ses that can be readily tested in current experiments. In the course of th is work\, we address the certification of a number of resources related to quantum entanglement ranging from coherence to Bell nonlocality. A common aspect among these resources is their convexity\, namely\, the fact that the resource content cannot be produced nor amplified by mere statistical mixing of dif[1]ferent states. This observation is also a key technical pr operty for almost all of our contributions. Here\, we focus on those many- body systems that are most easily probed by permutation-invariant or colle ctive observables\, such as spin ensembles or spinor Bose Einstein condens ates. In this respect\, the symmetries of the observables can be leveraged to construct entanglement criteria with a more favorable scaling. The res ource content of a physical system is certified \;from the statistics it produces. Within the quantum formalism\, such statistics are encoded in the density matrix\, which is reconstructed based on finite information f rom experimentally available probes. We start the thesis by outlining a pr actical machine-learning assisted protocol to improve and denoise the infe rence of such statistics in realistic scenarios. Subsequently\, we discuss the certification of metrologically useful entanglement by introducing a simple algorithm to evaluate the minimal quantum Fisher information compat ible with a set of iv arbitrary mean values. Our approach enables to syste matically tighten well \;known spin squeezing parameters and reveal th e sensing power of many-body states with minimal experimental effort. Next \, we address the detection of entanglement from averages and uncertaintie s of collective observables by formulating a single condition testing a nu mber of witnesses\, including those proposed in the past such as the gener alized spin squeezing inequalities. We apply our approach to unveil new en tanglement witnesses tailored to Bose-Einstein condensates based on Zeeman sublevels populations. We also discuss\, to some extent\, the witnessing of the Schmidt number\, the central bipartite entanglement measure\, using similar observables. Then\, we tackle the converse problem of detecting s eparable states from mathematical techniques based on invertible positive maps. The last part of the thesis is devoted to Bell nonlocality\, one of the strongest forms of nonclassicality beyond quantum entanglement. We fir st scale Bell dimension witness\, i.e. criteria whose violation signals th e impos[1]sibility of explaining the inferred statistics with a Hilbert sp ace of a given local dimension\, to the many-body regime. In particular\, we propose that the violation depth of a specific three-outcome Bell inequ ality can be used to robustly certify the number of qutrits in an ensemble . We close the thesis by presenting a data-driven approach to detect Bell nonlocality from one- and two-body spin correlations averaged over all per mutation of parties. This methodology allows us to discover tighter Bell i nequalities tailored to spin squeezed states and many-body spin singlets o f arbitrary spin.\nThursday March 27\, 09:00 h. Elements Room\nThesis Dire ctor: Prof. Dr. Maciej Lewenstein and Dr. Iré\;né\;e Fré \;rot DTSTAMP:20260407T074602Z END:VEVENT END:VCALENDAR