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We consider group-covariant positive operator valued measures (POVMs) on a finite dimensional quantum system. Following Neumark's theorem a POVM can be implemented by an orthogonal measurement on a larger system. Accordingly, our goal is to…
The most general type of measurement in quantum physics is modeled by a positive operator-valued measure (POVM). Mathematically, a POVM is a generalization of a measure, whose values are not real numbers, but positive operators on a Hilbert…
Similarly to quantum states, also quantum measurements can be "mixed", corresponding to a random choice within an ensemble of measuring apparatuses. Such mixing is equivalent to a sort of hidden variable, which produces a noise of purely…
Positive Operator Value Measures (POVMs) are the most general class of quantum measurements. We propose a setup in which all possible POVMs of a single photon polarization state (corresponding to all possible sets of two-dimensional Kraus…
A quantum measurement can be described by a set of matrices, one for each possible outcome, which represents the positive operator-valued measure (POVM) of the sensor. Efficient protocols of POVM extraction for arbitrary sensors are…
It is well-known in quantum information theory that a positive operator valued measure (POVM) is the most general kind of quantum measurement. Mathematically, a quantum probability is a normalised POVM, namely a function on certain subsets…
A quantum measurement, often referred to as positive operator-valued measurement (POVM), is a set of positive operators $P_j=P_j^\dag\geq 0$ summing to identity, $\sum_jP_j=\mathbb{1}$. This can be seen as a generalization of a probability…
Quantum coherence is a fundamental feature of quantum physics and plays a significant role in quantum information processing. By generalizing the resource theory of coherence from von Neumann measurements to positive operator-valued…
We review the relationship between positive operator-valued measures (POVMs) in quantum measurement theory and asymptotic morphisms in the C*-algebra E-theory of Connes and Higson. The theory of asymptotic spectral measures, as introduced…
The spin-coherent-state positive-operator-valued-measure (POVM) is a fundamental measurement in quantum science, with applications including tomography, metrology, teleportation, benchmarking, and measurement of Husimi phase space…
It is important problem to clarify the class of implementable quantum measurements from both fundamental and applicable viewpoints. Positive-Operator-Valued Measure (POVM) measurements are implementable by the indirect measurement methods,…
We introduce several notions of random positive operator valued measures (POVMs), and we prove that some of them are equivalent. We then study statistical properties of the effect operators for the canonical examples, obtaining limiting…
We give an overview of joint unsharp measurements of non-commuting observables using positive operator valued measures (POVMs). We exemplify the role played by joint measurability of POVMs in entropic uncertainty relation for Alice's pair…
In many a traditional physics textbook, a quantum measurement is defined as a projective measurement represented by a Hermitian operator. In quantum information theory, however, the concept of a measurement is dealt with in complete…
In quantum theory general measurements are described by so-called Positive Operator-Valued Measures (POVMs). We show that in $d$-dimensional quantum systems an application of depolarizing noise with constant (independent of $d$) visibility…
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)…
In this paper we shall introduce the mathematical framework for the description of measurements of quantum processes. Using this framework the process estimation problems can be treated in the similar way as the state estimation problems,…
We tackle the dynamical description of the quantum measurement process, by explicitly addressing the interaction between the system under investigation with the measurement apparatus, the latter ultimately considered as macroscopic quantum…
Generalized quantum measurements (also known as POVMs) are of great importance in quantum information and quantum foundations, but often difficult to perform. We present an experimental approach which can in principle be used to perform…
We describe a technique for self consistently characterizing both the quantum state of a single qubit system, and the positive-operator-valued measure (POVM) that describes measurements on the system. The method works with only ten…