Related papers: Informationally Overcomplete POVMs for Quantum Sta…
We consider the problem of quantum-state tomography under the assumption that the state is pure, and more generally that its rank is bounded by a given value. In this scenario, new notions of informationally complete POVMs emerge, which…
Informationally complete measurements on a quantum system allow to estimate the expectation value of any arbitrary operator by just averaging functions of the experimental outcomes. We show that such kind of measurements can be achieved…
Informationally overcomplete measurements find important applications in quantum tomography and quantum state estimation. The most popular are maximal sets of mutually unbiased bases, for which trace relations between measurement operators…
In recent years, informationally complete measurements have attracted considerable attention, especially in the context of classical shadows. In the particular case of informationally over-complete measurements, for which the number of…
The article establishes a framework for dynamic generation of informationally complete POVMs in quantum state tomography. Assuming that the evolution of a quantum system is given by a dynamical map in the Kraus representation, one can…
Recently introduced shadow tomography protocols use classical shadows of quantum states to predict many target functions of an unknown quantum state. Unlike full quantum state tomography, shadow tomography does not insist on accurate…
We develop an information theoretic interpretation of the number-phase complementarity in atomic systems, where phase is treated as a continuous positive operator valued measure (POVM). The relevant uncertainty principle is obtained as an…
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…
Randomized measurement protocols such as classical shadows represent powerful resources for quantum technologies, with applications ranging from quantum state characterization and process tomography to machine learning and error mitigation.…
We consider the statistical properties of photon detection with imperfect detectors that exhibit dark counts and less than unit efficiency, in the context of tomographic reconstruction. In this context, the detectors are used to implement…
Symmetric informationally complete positive operator valued measures (SIC-POVMs) are studied within the framework of the probability representation of quantum mechanics. A SIC-POVM is shown to be a special case of the probability…
In the signal-processing literature, a frame is a mechanism for performing analysis and reconstruction in a Hilbert space. By contrast, in quantum theory, a positive operator-valued measure (POVM) decomposes a Hilbert-space vector for the…
Recently, a novel framework for semi-device-independent quantum prepare-and-measure protocols has been proposed, based on the assumption of a limited distinguishability between the prepared quantum states. Here, we discuss the problem of…
We study informationally overcomplete measurements for quantum state estimation so as to clarify their tomographic significance as compared with minimal informationally complete measurements. We show that informationally overcomplete…
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…
Several finite dimensional quasi-probability representations of quantum states have been proposed to study various problems in quantum information theory and quantum foundations. These representations are often defined only on restricted…
Informationally complete measurements allow the estimation of expectation values of any operator on a quantum system, by changing only the data-processing of the measurement outcomes. In particular, an informationally complete measurement…
The process of cavity mode quantum state photodetection subject to a nonideal measurement device is under consideration. A set of nonorthogonal probabilistic operator valued measures (POVMs) describing the photodetection process is…
We investigate unitary and state $t$-designs from a computational complexity perspective. First, we address the problems of computing frame potentials that characterize (approximate) $t$-designs. We present a quantum algorithm for computing…
It is a well-known fact that the optimal POVM for quantum state tomography is the symmetric, informationally complete, positive operator valued measure (SIC-POVM). We investigate the same problem only in the case when there are some a…