Related papers: Effective methods for constructing extreme quantum…
Various forms of optimality for quantum observables described as normalized positive operator valued measures (POVMs) are studied in this paper. We give characterizations for observables that determine the values of the measured quantity…
Uncertainty relations are usually stated as bounds on selected combinations of variances, but the full covariance matrix contains substantially richer information about the geometry of quantum state space and about the operational…
Determining the conditions under which positive operator-valued measures (POVMs), the most general class of quantum measurements, outperform projective measurements remains a challenging and largely unresolved problem. Of particular…
In this paper we discuss the explicit solution of certain extremal problems in Bergman spaces. In order to do this, we develop methods to calculate the Bergman projections of various functions. As a special case, we deal with canonical…
Recent developments in extreme value statistics have established the so-called geometric approach as a powerful modelling tool for multivariate extremes. We tailor these methods to the case of spatial modelling and examine their efficacy at…
Partially observable Markov decision processes (POMDPs) provide an elegant mathematical framework for modeling complex decision and planning problems in stochastic domains in which states of the system are observable only indirectly, via a…
We show that a rank-1 quantum observable (POVM) M is jointly measurable with a quantum observable M' exactly when M' is a smearing of M. If M is extreme, rank-1 and discrete then M and M' are coexistent if and only if they are jointly…
We describe a particular class of pairs of quantum observables which are extremal in the convex set of all pairs of compatible quantum observables. The pairs in this class are constructed as uniformly noisy versions of two mutually unbiased…
Superposition is an essential feature of quantum mechanics. From the Schrodinger's cat to quantum algorithms such as Deutsch-Jorsza algorithm, quantum superposition plays an important role. It is one fundamental and crucial question how to…
We study the closure of the locus of radical ideals in the multigraded Hilbert scheme associated with a standard graded polynomial ring and the Hilbert function of a homogeneous coordinate ring of points in general position in projective…
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…
For a quantum measurement process described by a quantum instrument $\mathcal{I}$ and a system observable corresponding to a positive-operator valued measure (POVM) $E ,$ $\mathcal{I}$ is said to conserve the information of $E$ if the joint…
From an operational point of view, we propose several new entanglement detection criteria using quantum designs. These criteria are constructed by considering the correlations defined with quantum designs. Counter-intuitively, the criteria…
The paper is devoted to studying the image of probability measures on a Hilbert space under finite-dimensional analytic maps. We establish sufficient conditions under which the image of a measure has a density with respect to the Lebesgue…
A non-Hermitian complex symmetric 2x2 matrix toy model is used to study projective Hilbert space structures in the vicinity of exceptional points (EPs). The bi-orthogonal eigenvectors of a diagonalizable matrix are Puiseux-expanded in terms…
The paper contains two natural constructions of extreme hyperspace selections generated by special ordinal decompositions of the underlying space. These constructions are very efficient not only in simplifying arguments but also in…
Possibilistic and qualitative POMDPs (pi-POMDPs) are counterparts of POMDPs used to model situations where the agent's initial belief or observation probabilities are imprecise due to lack of past experiences or insufficient data…
Motivated by the increasing availability of data of functional nature, we develop a general probabilistic and statistical framework for extremes of regularly varying random elements $X$ in $L^2[0,1]$. We place ourselves in a…
This paper investigates an iterative rank-one decomposition scheme for positive operators on a Hilbert space based on a residual-weighted congruence update. At each step the operator is compressed along a chosen unit vector while remaining…
A photodetector may be characterized by various figures of merit such as response time, bandwidth, dark count rate, efficiency, wavelength resolution, and photon-number resolution. On the other hand, quantum theory says that any measurement…