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Precise measurement is crucial to science and technology. However, the rule of nature imposes various restrictions on the precision that can be achieved depending on specific methods of measurement. In particular, quantum mechanics poses…
One of the main quests in quantum metrology, and quantum parameter estimation in general, is to find out the highest achievable precision with given resources and design schemes that attain that precision. In this article we present a…
Protocols for discriminating between a pair of channels or for estimating a channel parameter can often be aided by adaptivity or by entanglement between the probe states. This can make it difficult to bound the best possible performance…
We investigate the parameter estimation problem in a two-qubit system, in which each qubit is independently interacting with its Markovian environment. We study in detail the sensitivity of the estimation on the decoherence rate $\gamma$…
In this thesis, first, we investigate the metrological usefulness of a family of states known as unpolarized Dicke states, which turn to be very sensitive to the magnetic field. Quantum mechanics plays a central role in achieving such a…
This work unifies the equilibrium and non-equilibrium frameworks of quantum metrology within the context of many-body systems. We investigate dynamic sensing schemes to derive an upper bound on the quantum Fisher information for probe…
Simultaneously estimating multiple parameters at the ultimate limit is a central challenge in quantum metrology, often hindered by inherent incompatibilities in optimal estimation strategies. At its most extreme, this incompatibility…
This paper studies quantum limits to dynamical sensors in the presence of decoherence. A modified purification approach is used to obtain tighter quantum detection and estimation error bounds for optical phase sensing and optomechanical…
We address the problem of sensing the curvature of a manifold by performing measurements on a particle constrained to the manifold itself. In particular, we consider situations where the dynamics of the particle is quantum mechanical and…
We address open quantum systems out-of-equilibrium as effective quantum probes for the characterisation of their environment. We discuss estimation schemes for parameters driving a de-phasing evolution of the probe and then focus on qubits,…
The speed of light $c$ sets a strict upper bound on the speed of information transfer in both classical and quantum systems. In nonrelativistic quantum systems, the Lieb-Robinson Theorem imposes an emergent speed limit $v \hspace{-0.2mm}…
Critical quantum metrology aims to harness critical properties near quantum phase transitions to enhance parameter estimation precision. However, critical slowing down inherently limits the achievable precision within a finite evolution…
Quantum effects in metrology can in principle enhance measurement precision from the so-called standard quantum limit to the Heisenberg Limit. Further advancements in quantum metrology largely rely on innovative metrology protocols that can…
Quantum phenomena offer the possibility of measuring physical quantities with precision beyond classical limits. However, current progress is constrained by scalability, environmental noise, and challenges in practical integration. This…
The energy-time uncertainty relation puts a fundamental limit on the precision of radars and lidars for the estimation of range and velocity. The precision in the estimation of the range (through the time of arrival) and the velocity…
Measurements of an object's temperature are important in many disciplines, from astronomy to engineering, as are estimates of an object's spatial configuration. We present the quantum optimal estimator for the temperature of a distant body…
In order to provide a guaranteed precision and a more accurate judgement about the true value of the Cram\'{e}r-Rao bound and its scaling behavior, an upper bound (equivalently a lower bound on the quantum Fisher information) for precision…
Quantum Fisher information matrices (QFIMs) are fundamental to estimation theory: they encode the ultimate limit for the sensitivity with which a set of parameters can be estimated using a given probe. Since the limit invokes the inverse of…
Quantum sensing with undetected photons is a technique where photons of one wavelength probe a sample, but information is extracted by measuring photons of another wavelength that never interacts with the sample. This has seen significant…
Quantum technologies exploit entanglement to revolutionize computing, measurements, and communications. This has stimulated the research in different areas of physics to engineer and manipulate fragile many-particle entangled states.…