Related papers: Constructing Operator Valued Probability Measures …
Randomized orthogonal projection methods (ROPMs) can be used to speed up the computation of Krylov subspace methods in various contexts. Through a theoretical and numerical investigation, we establish that these methods produce…
The integral of the Wigner function over a subregion of the phase-space of a quantum system may be less than zero or greater than one. It is shown that for systems with one degree of freedom, the problem of determining the best possible…
Covariant affine integral quantization of the half-plane is studied and applied to the motion of a particle on the half-line. We examine the consequences of different quantizer operators built from weight functions on the half-plane. To…
Wigner functions generically attain negative values and hence are not probability densities. We prove an asymptotic expansion of Wigner functions in terms of Hermite spectrograms, which are probability densities. The expansion provides…
It has recently been shown that it is possible to represent the complete quantum state of any system as a phase-space quasi-probability distribution (Wigner function) [Phys Rev Lett 117, 180401]. Such functions take the form of expectation…
In this work we provide a way to introduce a probability measure on the space of minimal fillings of finite additive metric spaces as well as an algorithm for its computation. The values of probability, got from the analytical solution,…
Quantum computation is the suitable orthogonal encoding of possibly holistic functional properties into state vectors, followed by a projective measurement.
Generalized measurements, also called positive operator-valued measures (POVMs), can offer advantages over projective measurements in various quantum information tasks. Here, we realize a generalized measurement of one and two…
Simple minimal but informationally complete positive operator-valued measures are constructed out of the expectation-value representation for qudits. Upon suitable modification, the procedure transforms any set of d^2 linearly independent…
We show that the joint behaviour of an arbitrary pair of quantum observables can be described by quasi-probabilities, which are extensions of the standard probabilities used for describing the behaviour of a single observable. The physical…
In this work we have explored few tools in Quantum State Tomography for Continuous Variable Systems. The concept of quantum states in phase space representation is introduced in a simple manner by using a few statistical concepts. Unlike…
We introduce a quasi-probability phase space distribution with two pairs of azimuthal-angular coordinates. This representation is well adapted to describe quantum systems with discrete symmetry. Quantum error correction of states encoded in…
We consider the convex sets of QO's (quantum operations) and POVM's (positive operator valued measures) which are covariant under a general finite-dimensional unitary representation of a group. We derive necessary and sufficient conditions…
A quantum state is fully characterized by its density matrix or equivalently by its quasiprobabilities in phase space. A scheme to identify the quasiprobabilities of a quantum state is an important tool in the recent development of quantum…
Many prominent quantum computing algorithms with applications in fields such as chemistry and materials science require a large number of measurements, which represents an important roadblock for future real-world use cases. We introduce a…
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…
We provide a definition of POVM in terms of abstract tensor structure only. It is justified in two distinct manners. i. At this abstract level we are still able to prove Naimark's theorem, hence establishing a bijective correspondence…
Decomposable models and Bayesian networks can be defined as sequences of oligo-dimensional probability measures connected with operators of composition. The preliminary results suggest that the probabilistic models allowing for effective…
Suppose we measure the time-dependent spectrum of a single photon. That is, we first send the photon through a set of frequency filters (which we assume to have different filter frequencies but the same finite bandwidth $\Gamma$), and then…
Approximation properties of multivariate quasi-projection operators are studied in the paper. Wide classes of such operators are considered, including the sampling and the Kantorovich-Kotelnikov type operators generated by different…