Related papers: Tight informationally complete quantum measurement…
We characterize the asymptotic performance of a class of positive operator valued measurements (POVMs) where the only task is to make measurements on independent and identically distributed quantum states on finite-dimensional systems. The…
We put forward a reconstruction scheme prompted by the relation between a von Neumann measurement and the corresponding informationally complete measurement induced in a relevant reconstruction subspace. This method is specially suited for…
Reconstructing quantum states from measurement data represents a formidable challenge in quantum information science, especially as system sizes grow beyond the reach of traditional tomography methods. While recent studies have explored…
We demonstrate that incomplete quantum tomography can give conclusive information in experimental realizations. We divide the state space into a union of multiple disjoint subsets and determine conclusively which of the subsets a system,…
We show that any unitary transformation performed on the quantum state of a closed quantum system, describes an inner, reversible, generalized quantum measurement. We also show that under some specific conditions it is possible to perform a…
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…
Quantum measurements are important tools in quantum information, represented by positive, operator-valued measures. A wide class of symmetric measurements is given via generalized equiangular measurements that form conical 2-designs. We…
Smooth entropies are a tool for quantifying resource trade-offs in (quantum) information theory and cryptography. In typical bi- and multi-partite problems, however, some of the sub-systems are often left unchanged and this is not reflected…
There has been much interest in so-called SIC-POVMs: rank 1 symmetric informationally complete positive operator valued measures. In this paper we discuss the larger class of POVMs which are symmetric and informationally complete but not…
The tight frames can be regarded as a particular case of POVMs (positive operator-valued measures describing generalized measurements), namely the case when all the operators are rank-one. Each orthonormal basis is a tight frame, and every…
We consider the problem of designing a measurement to minimize the probability of a detection error when distinguishing between a collection of possibly non-orthogonal mixed quantum states. We show that if the quantum state ensemble…
As quantum technologies advance, the ability to generate increasingly large quantum states has experienced rapid development. In this context, the verification and estimation of large entangled systems represents one of the main challenges…
Starting from a new principle inspired by quantum tomography rather than from Born's rule, this paper gives a self-contained deductive approach to quantum mechanics and quantum measurement. A suggestive notion for what constitutes a quantum…
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…
Complex projective t-designs, particularly SICs and full sets of MUBs, play an important role in quantum information. We introduce a generalization which we call conical t-designs. They include arbitrary rank symmetric informationally…
We propose an operational measure of distance of two quantum states, which conversely tells us their closeness. This is defined as a sum of differences in partial knowledge over a complete set of mutually complementary measurements for the…
Quantum statistical models (i.e., families of normalized density matrices) and quantum measurements (i.e., positive operator-valued measures) can be regarded as linear maps: the former, mapping the space of effects to the space of…
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…
Finite tight frames are interesting in various topics including questions of quantum information. Each complex tight frame leads to a resolution of the identity in the Hilbert space. Symmetric informationally complete measurements are a…
Quantum state estimation (or state tomography) is an indispensable task in quantum information processing. Because full state tomography that determines all elements of the density matrix is computationally demanding, one usually takes the…