Related papers: Extremal generalized quantum measurements
We investigate the theory of finite observables, i.e., resolutions of the finite-dimensional identity by means of positive operators, that have a physical interpretation in terms of measurement schemes. We focus on extremal and rank-one…
We investigate Gaussian quantum states in view of their exceptional role within the space of all continuous variables states. A general method for deriving extremality results is provided and applied to entanglement measures, secret key…
In this work, we consider optimal state discrimination for a quantum system that interacts with an environment, i.e., states evolve under a quantum channel. We show the conditions on a quantum channel and an ensemble of states such that a…
The emergence of quantum devices has raised a significant issue: how to certify the quantum properties of a device without placing trust in it. To characterise quantum states and measurements in a device-independent way, up to some degree…
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.
Motivated by quantum resource theories, we introduce a notion of incompatibility for quantum measurements relative to a reference basis. The notion arises by considering states diagonal in that basis and investigating whether probability…
Quantum state tomography is the standard tool in current experiments for verifying that a state prepared in the lab is close to an ideal target state, but up to now there were no rigorous methods for evaluating the precision of the state…
Generalized quantum measurements (POVMs or POMs) are important for optimally extracting information for quantum communication and computation. The standard realization via the Neumark extension requires extensive resources in the form of…
In this work we investigate how to quantify the coherence of quantum measurements. First, we establish a resource theoretical framework to address the coherence of measurement and show that any statistical distance can be adopted to define…
A complete set of mutually unbiased bases for a Hilbert space of dimension N is analogous in some respects to a certain finite geometric structure, namely, an affine plane. Another kind of quantum measurement, known as a symmetric…
This essay reviews a modern understanding of a quantum measurement. Rather than reducing the picture to the observer's experience with quantum system, we try to put it in the context of a broader physical picture. We also attempt to…
Quantum mechanics has greatly impacted our understanding of the microscopic nature. One of the key concepts of this theory is generalized measurements, which have proven useful in various quantum information processing tasks. However,…
The objective of this work is to develop a recursive, discrete time quantum filtering equation for a system that interacts with a probe, on which measurements are performed according to the Positive Operator Valued Measures (POVMs)…
Quantum state tomography is a fundamental tool in quantum information processing. It allows us to estimate the state of a quantum system by measuring different observables on many identically prepared copies of the system. This is, in…
We obtain a formal characterization of the compatibility or otherwise of a set of positive-operator-valued measures (POVMs) via their Naimark extensions. We show that a set of POVMs is jointly measurable if and only if there exists a single…
The conventional definition of extremality of a finite collection of sets is extended by replacing a fixed point (extremal point) in the intersection of the sets by a collection of sequences of points in the individual sets with the…
Quantization of a probability measure means representing it with a finite set of Dirac masses that approximates the input distribution well enough (in some metric space of probability measures). Various methods exists to do so, but the…
Optimal and finite positive operator valued measurements on a finite number $N$ of identically prepared systems have been presented recently. With physical realization in mind we propose here optimal and minimal generalized quantum…
A quantum probability measure--or quantum measurement--is said to be clean if it cannot be irreversibly connected to any other quantum probability measure via a quantum channel. The notion of a clean quantum measure was introduced by…
An algebraic procedure to find extremal density matrices for any Hamiltonian of a qudit system is established. The extremal density matrices for pure states provide a complete description of the system, that is, the energy spectra of the…