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We introduce a method to determine whether a given generalised quantum measurement is isolated or it belongs to a family of measurements having the same prescribed symmetry. The technique proposed reduces to solving a linear system of…
We report an experimental implementation of a single-qubit generalised measurement scenario(POVM) based on a quantum walk model. The qubit is encoded in a single-photon polarisation. The photon performs a quantum walk on an array of optical…
Generalized measurement schemes on one part of bipartite states, which would leave the set of all separable states insensitive are explored here to understand quantumness of correlations in a more general perspecitve. This is done by…
Standard quantum measurements are projective. However, the full scope of quantum measurements is represented by positive operator-valued measures (POVMs) and many of these break the limitations of projective measurements as resources in…
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…
Mutually unbiased bases (MUBs) and symmetric informationally complete (SIC) positive operator-valued measurements (POVMs) are two related topics in quantum information theory. They are generalized to mutually unbiased measurements (MUMs)…
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…
In this survey, we relate frame theory and quantum information theory, focusing on quantum 2-designs. These are arrangements of weighted subspaces which are in a specific sense optimal for quantum state tomography. After a brief…
We consider the existence in arbitrary finite dimensions d of a POVM comprised of d^2 rank-one operators all of whose operator inner products are equal. Such a set is called a ``symmetric, informationally complete'' POVM (SIC-POVM) and is…
We analyze the possible results of the most general measurement on two copies of a quantum state. We show that $\mu$ can label a set of outcomes of such measurement if and only if there is a family of completely co--positive (ccP) maps…
We introduce and implement a technique to extend the quantum computational power of cluster states by replacing some projective measurements with generalized quantum measurements (POVMs). As an experimental demonstration we fully realize an…
We study the geometric measure of entanglement (GM) of pure symmetric states related to rank-one positive-operator-valued measures (POVMs) and establish a general connection with quantum state estimation theory, especially the maximum…
Loss induced generalized measurements have been introduced years ago as a mean to implement generalized quantum measurements (POVM). Here the original idea is extended to a complete equivalence of lossy evolution and a certain widely used…
We introduce random matrix theory to study the tomographic efficiency of a wide class of measurements constructed out of weighted 2-designs, including symmetric informationally complete (SIC) probability operator measurements (POMs). In…
A concept of the generalized quantum measurement is introduced as the transformation, which establishes a correspondence between the initial states of the object system and final states of the object--measuring device (meter) system with…
C. A. Fuchs and M. Sasaki defined the quantumness of a set of quantum states in \cite{Quantumness}, which is closely related to the fidelity loss in transmission of the quantum states through a classical channel. In \cite{Fuchs}, Fuchs…
A general noncommutative-geometric theory of principal bundles is presented. Quantum groups play the role of structure groups. General quantum spaces play the role of base manifolds. A differential calculus on quantum principal bundles is…
A linear map of qudit tomogram onto qubit tomogram (qubit portrait) is proposed as a characteristics of the qudit state. Using the qubit portrait method the Bell inequalities for two qubits and two qutrits are discussed in framework of…
Comparing probability distributions is a core challenge across the natural, social, and computational sciences. Existing methods, such as Maximum Mean Discrepancy (MMD), struggle in high-dimensional and non-compact domains. Here we…
The article undertakes the problem of pure state estimation from projective measurements based on photon counting. Two generic frames for qubit tomography are considered -- one composed of the elements of the SIC-POVM and the other defined…