We quantify the measurement-induced nonlocality (Luo and Fu, Phys. Rev. Lett. 106, 1020401, 2011) from the perspective of the relative entropy. This quantification leads to an operational interpretation for the measurement-induced nonlocality, namely, it is the maximal entropy increase after the locally invariant measurements. The relative entropy of nonlocality is upper bounded by the entropy ...

We invert the Fredholm equation representing the light scattered by a single spherical particle or a distribution of spherical particles to obtain the particle size distribution function and refractive index. We obtain the solution by expanding the distribution function as a linear combination of a set of orthonormal basis functions. The set of orthonormal basis functions is composed of Schmidt...

In this paper‎, ‎using the discrete Fourier transform in the finite-dimensional Hilbert space C^n‎, ‎a class of nonRieszable equal norm tight frames is introduced ‎and‎ using this class, a bound for Fiechtinger Conjecture is presented. By the Fiechtinger Conjecture that has been proved recently, for given A,C>0 there exists a universal constant delta>0 independent of $n$ such that every C-equal...

We develop a method for the exact determination of frequency responses for a class of infinite dimensional systems. In particular, we consider distributed systems in which a spatial independent variable belongs to a finite interval, and in which the inputs and outputs are spatially distributed over the same interval. We show that an explicit formula for the Hilbert–Schmidt norm of the operator-...

We review somemore and less recent results concerning bounds on nonlinear eigenvalues NLEV for gradient operators. In particular, we discuss the asymptotic behaviour of NLEV as the norm of the eigenvector tends to zero in bifurcation problems from the line of trivial solutions, considering perturbations of linear self-adjoint operators in a Hilbert space. The proofs are based on the Lusternik-S...

This paper presents a geometric approach to estimating subspaces as elements of complex Grassmann-manifold, with each subspace represented by its unique, complex projection matrix. Variation between the subspaces is modeled by rotating their projection matrices via the action of unitary matrices [elements of the unitary group U( )]. Subspace estimation or tracking then corresponds to inferences...

The spectral problem (A+V (z))ψ = zψ is considered with A, a self-adjoint Hamiltonian of sufficiently arbitrary nature. The perturbation V (z) is assumed to depend on the energy z as resolvent of another self-adjoint operator A ′ : V (z) = −B(A ′ −z) −1 B *. It is supposed that operator B has a finite Hilbert-Schmidt norm and spectra of operators A and A ′ are separated. The conditions are form...

Kernel canonical correlation analysis (KCCA) is a dimensionality reduction technique for paired data. By finding directions that maximize correlation, KCCA learns representations that are more closely tied to the underlying semantics of the data rather than noise. However, meaningful directions are not only those that have high correlation to another modality, but also those that capture the ma...

We develop transportation-entropy inequalities which are saturated by measures such that their log-density with respect to the background measure is an affine function, in setting of uniform on discrete hypercube and exponential measure. In this sense, extends well-known result Talagrand Gaussian case. By duality, these imply a strong integrability inequality for Bernoulli processes. As result,...