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We carefully examine critical metrology and present an improved critical quantum metrology protocol which relies on quenching a system exhibiting a superradiant quantum phase transition beyond its critical point. We show that this approach…
Quantum metrology seeks to leverage the richness of quantum systems for making better measurements than are possible using only classical resources in order to gain a ``quantum advantage''. Quantum metrology schemes must also be resilient…
Relativistic quantum metrology provides an optimal strategy for the estimation of parameters encoded in quantum fields in flat and curved spacetime. These parameters usually correspond to physical quantities of interest such as proper…
Quantum metrology aims to enhance measurement precision beyond the classical limit by leveraging quantum resources. Unlike multi-parameter dynamic quantum metrology, many questions regarding multiparameter quantum metrology at thermal…
The usual notion of separability has to be reconsidered when applied to states describing identical particles. A definition of separability not related to any a priori Hilbert space tensor product structure is needed: this can be given in…
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…
In this work we study the properties of an purification-based entropic metric for measuring the distance between both quantum states and quantum processes. This metric is defined as the square root of the entropy of the average of two…
For a given quantum state used in sensing, the quantum Cram\'er-Rao bound (QCRB) sets a fundamental limit on the precision achievable by an unbiased estimator of an unknown parameter, determined by the inverse of the quantum Fisher…
Landauer's principle gives a fundamental limit to the thermodynamic cost of erasing information. Its saturation requires a reversible isothermal process, and hence infinite time. We develop a finite-time version of Landauer's principle for…
We introduce a quantum measurement process that is capable of characterizing an unknown state of a system almost without disturbing or collapsing it. The underlying idea is to extract information of a system from the thermodynamic…
We examine metrological scenarios where the parameter of interest is encoded onto a quantum state through the action of a noisy quantum gate and investigate the ultimate bound to precision by analyzing the behaviour of the Quantum Fisher…
In quantum metrology, quantum probe states are capable of estimating unknown physical parameters to precisions beyond classical limits. What qualities do such states possess? Here we relate the performance of a probe state at estimating a…
Quantum measurement of a system can change its mean energy, as well as entropy. A selective measurement (classical or quantum) can be used as a "Maxwell's demon" to power a single-temperature heat engine, by decreasing the entropy. Quantum…
Resolving frequencies in a time-dependent field is classically limited by the measurement bandwidth. Using tools from quantum metrology and quantum control may overcome this limit, yet the full advantage afforded by entanglement so far…
The purpose of this paper is to survey some topics on mathematical foundations of quantum information developed mainly by the present author and co-workers for the last three decades. The topics include an axiomatic construction of quantum…
Quantum measurements are basic operations that play a critical role in the study and application of quantum information. We study how the use of quantum, coherent, and classical thermal states of light in a circuit quantum electrodynamics…
Connections between information theory and thermodynamics have proven to be very useful to establish bounding limits for physical processes. Ideas such as Landauer's erasure principle and information assisted work extraction have greatly…
Studies of quantum metrology have shown that the use of many-body entangled states can lead to an enhancement in sensitivity when compared to product states. In this paper, we quantify the metrological advantage of entanglement in a setting…
We address the framework of analysing quantum metrology in the information-theoretic picture. Firstly we show how to extract the maximum amount of information in general via suitable state initialization of the probes at the beginning and a…
Postselected weak measurement has shown significant potential for detecting small physical effects due to its unique weak-value-amplification phenomenon. Previous works suggest that Heisenberg-limit precision can be attained using only the…