BEGIN:VCALENDAR VERSION:2.0 PRODID:Icfo X-PUBLISHED-TTL:P1W BEGIN:VEVENT UID:6a3df52ff3ea8 DTSTART:20260629T083000Z SEQUENCE:0 TRANSP:OPAQUE LOCATION:Elements Room SUMMARY:ICFO | ANUBHAV KUMAR SRIVASTAVA CLASS:PUBLIC DESCRIPTION:Quantum mechanics both constrains and empowers precision measur ement: the uncertainty principle imposes fundamental limits on parameter e stimation\, which quantum resources such as entanglement and superposition can saturate. Quantum metrology develops protocols that exploit non-class ical probe states and optimal data processing to surpass the standard quan tum limit. In practice\, however\, realizing this advantage requires solvi ng three problems: designing experimentally feasible many-body probes with near-optimal sensitivity\, certifying metrological resources from incompl ete measurement data\, and implementing optimal readout schemes that remai n tractable at scale. This thesis develops a unified framework for all thr ee challenges\, combining quantum simulation\, convex optimization\, and c lassical-shadow techniques to bring quantum-enhanced metrology closer to e xperimental reality.\nThe first part addresses quantum thermometry at nano - and sub-nanokelvin scales. Using the quantum Fisher information (QFI) as the sensitivity measure\, we show that an experimentally accessible syste m of spinless fermions in a one-dimensional optical lattice\, described by the Rice&ndash\;Mele (RM) model\, realizes a near-optimal local quantum t hermometer approaching the fundamental Cramé\;r&ndash\;Rao bound. We characterize how the topological and trivial regimes\, the lattice fillin g\, and a tunable staggered potential control its sensitivity\, and show t hat the probe equilibrates with a coupled bath without perturbing it. We f urther analyse a global thermometry scheme based on classical-shadow tomog raphy of thermal states\, comparing its sample complexity with standard pr otocols.\nThe second part develops two complementary tools for quantum-enh anced sensing and its certification. We introduce a sensor based on a frus trated Kitaev trimer whose nonlinear spectral response implements a thresh olded rectifying detector: for a zero-mean omnidirectional signal\, the ac cumulated phase vanishes below a tunable threshold and\, above it\, is pro portional to the signal's second moment. Entangled multi-trimer configurat ions attain Heisenberg-limited sensitivity. We then formulate a semidefini te programme (SDP) that computes the minimal QFI compatible with incomplet e expectation-value data\, yielding rigorous lower bounds without full sta te tomography. Applied to multi-headed cat states generated by one-axis-tw isting dynamics\, the SDP certifies metrological usefulness from low-order moments more tightly than conventional squeezing inequalities.\nThe third part addresses the gap between optimal measurement schemes and the measur ements achievable on current quantum platforms. The optimal observable sat urating the quantum Cramé\;r&ndash\;Rao bound is generically a highl y nonlocal operator whose Pauli weight grows with system size. We introduc e Clifford lensing\, a framework in which classically simulable Clifford c ircuits map the optimal observable onto an operator of reduced Pauli weigh t\, refocusing distributed phase information onto fewer qubits. We establi sh a correspondence between quantum error-correcting codes and interferome tric constructions enforcing deterministic phase kickback\, and develop me trologically sufficient partial-shadow tomography protocols that preserve the full QFI. The resulting schemes require exponentially fewer samples th an naï\;ve shadow estimation and are validated on liquid-state nuclear magnetic resonance (NMR) systems of up to 15 qubits.Together\, these resu lts demonstrate that near-optimal quantum metrology is achievable with acc essible probes\, data-efficient certification\, and scalable readout\, pro viding a unified route from fundamental metrological bounds to practical q uantum-enhanced sensing.\nThesis Director: Prof. Dr. Maciej Lewenstein and Dr. Marcin Plodzien DTSTAMP:20260626T034240Z END:VEVENT END:VCALENDAR