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Quantum measurement is a basic tool to manifest intrinsic quantum effects from fundamental tests to quantum information applications. While a measurement is typically performed to gain information on a quantum state, its role in quantum…
We take a tour of a set of equiangular lines in eight-dimensional Hilbert space. This structure defines an informationally complete measurement, that is, a way to represent all quantum states of three-qubit systems as probability…
Quantum sensing exploits quantum phenomena to enhance the detection and estimation of classical parameters of physical systems and biological entities, particularly so as to overcome the inefficiencies of its classical counterparts. A…
A solution to the second measurement problem, determining what prior microscopic properties can be inferred from measurement outcomes ("pointer positions"), is worked out for projective and generalized (POVM) measurements, using consistent…
It is proposed a possible new approach of quantum measurements (QMS), disconnected of the traditional interpretation of uncertainty relations and independent of any appeal to the strange idea of collapse (reduction) of wave functions. The…
Multimode Gaussian states are a versatile resource for quantum information technologies and have been realized across a wide range of physical platforms. Recent progress in the large-scale generation of such states provides a key ingredient…
Here we propose an implementation of all possible Positive Operator Value Measures (POVMs) of two-photon polarization states. POVMs are the most general class of quantum measurements. Our setup requires linear optics, Bell State…
We address the possibility of using even/odd states of orbital angular momentum (OAM) of photons for the quantum information tasks. Single photon qubit states and two photon entangled states in even/odd basis of OAM are considered. We…
Characterizing multipartite entanglement is a fundamental problem in quantum information theory. The concept of $k$-stretchability [Szalay, Quantum 3, 204 (2019)] provides a framework for describing multipartite entanglement structures. We…
It is crucial for various quantum information processing tasks that the state of a quantum system can be determined reliably and efficiently from general quantum measurements. One important class of measurements for this purpose is…
The general formalism of quantum mechanics for the description of statistical experiments is briefly reviewed, introducing in particular position and momentum observables as POVM characterized by their covariance properties with respect to…
This paper presents an overview of close parallels that exist between the theory of positive operator-valued measures (POVMs) associated with a separable Hilbert space and the theory of frames on that space, including its most important…
We present the results of generalized measurements of optical polarization designed to provide one of three or four distinct outcomes. This has allowed us to discriminate between nonorthogonal polarization states with an error probability…
We present the first complete optimization of quantum tomography, for states, POVMs, and various classes of transformations, for arbitrary prior ensemble and arbitrary representation, giving corresponding feasible experimental schemes.
Quantum metrology promises high-precision measurements beyond the capability of any classical techniques, and has the potential to be integral to investigative techniques. However, all sensors must tolerate imperfections if they are to be…
We present a correspondence between positive operator valued measures (POVMs) and sets of generalized coherent states. Positive operator valued measures describe quantum observables and, similarly to quantum states, also quantum observables…
This essay constitutes a review of the information geometric approach to renormalization developed in the recent works of B\'eny and Osborne as well as a detailed work-through of some of their contents. A noncommutative generalization of…
Quantum imaging, one of the pillars of quantum technologies, is well-suited to study sensitive samples which require low-light conditions, like biological tissues. In this context, interaction-free measurements (IFM) allow us infer the…
Postselection can compress the metrological information and improve sensitivity in the presence of certain types of technical noise. Postselected quantum metrology with pure states has been significantly advanced recently. However,…
Symmetric informationally complete (SIC) POVMs are a class of quantum measurements which, in addition to being informationally complete, satisfy three conditions: 1) every POVM element is rank one, 2) the Hilbert-Schmidt inner product…