Related papers: Two theorems on the outer product of input and out…
In this study, we explore a form of quantum circuit complexity that extends to open systems. To illustrate our methodology, we focus on a basic model where the projective Hilbert space of states is depicted by the set of orientations in the…
Stokes parameters are a standard tool in quantum optics. They involve averaged intensities at exits of polarizers. If the overall measured intensity fluctuates, as e.g. for states with undefined photon numbers, the instances of its…
We explore the conjectured duality between a class of large $N$ matrix integrals, known as multicritical matrix integrals (MMI), and the series $(2m-1,2)$ of non-unitary minimal models on a fluctuating background. We match the critical…
Sinkhorn proved that every entry-wise positive matrix can be made doubly stochastic by multiplying with two diagonal matrices. In this note we prove a recently conjectured analogue for unitary matrices: every unitary can be decomposed into…
Type-II matrices are a class of matrices used by Jones in his work on spin models. In this paper we show that type-II matrices arise naturally in connection with some interesting combinatorial and geometric structures.
The polarization analysis of the light is typically carried out using modulation schemes. The light of unknown polarization state is passed through a set of known modulation optics and a detector is used to measure the total intensity…
Semi-tensor product(STP) or matrix (M-) product of matrices turns the set of matrices with arbitrary dimensions into a monoid $({\cal M},\ltimes)$. A matrix (M-) addition is defined over subsets of a partition of ${\cal M}$, and a matrix…
The ability to control light polarization state is critically important for diverse applications in information processing, telecommunications, and spectroscopy. Here, we propose that a stack of anisotropic van der Waals materials can…
The basic concepts of exterior calculus for space-time multivectors are presented: interior and exterior products, interior and exterior derivatives, oriented integrals over hypersurfaces, circulation and flux of multivector fields. Two…
An eight stage balanced modulation scheme for dual beam polarimetry is presented in this paper. The four Stokes parameters are weighted equally in all the eight stages of modulation resulting in total polarimetric efficiency of unity. The…
We consider the Stokes phenomenon for the solutions of some partial differential equations with variable coefficients in two complex variables, where initial data are holomorphic. We use the theory of (moment) summability and the theory of…
Symmetry-protected topological (SPT) phases exhibit nontrivial order if symmetry is respected but are adiabatically connected to the trivial product phase if symmetry is not respected. However, unlike the symmetry-breaking phase, there is…
While any two-dimensional mixed state of polarization of light can be represented by a combination of a pure state and a fully random state, any Mueller matrix can be represented by a convex combination of a pure component and three…
We demonstrate that the multipoles associated with the density matrix are truly observable quantities that can be unambiguously determined from intensity moments. Given their correct transformation properties, these multipoles are the…
A Hamiltonian field theory for the macroscopic Maxwell equations with fully general polarization and magnetization is stated in the language of differential forms. The precise procedure for translating the vector calculus formulation into…
We show how to represent a class of expressions involving discrete sums over partitions as matrix models. We apply this technique to the partition functions of 2* theories, i.e. Seiberg-Witten theories with the massive hypermultiplet in the…
In this paper we show how to calculate explicitly the exponential of certain matrices, which are evolution operators governing the interaction of the four level system of atoms and the radiation, etc. We present a consistent method in terms…
The classical problem of computing a complete system of Stokes multipliers of a linear system of ODEs of rank one in terms of some connection coefficients of an associated hypergeometric system of ODEs, is solved with no genericness…
Solving the linear elasticity and Stokes equations by an optimal domain decomposition method derived algebraically involves the use of non standard interface conditions. The one-level domain decomposition preconditioners are based on the…
Matrix-product operators (MPOs) appear throughout the study of integrable lattice models, notably as the transfer matrices. They can also be used as transformations to construct dualities between such models, both invertible (including…