Annals of Physics Classical impurities and boundary Majorana zero
... barrier which blocks its further propagation. Mixing of the boundary Majorana states located at the
opposite boundaries thus becomes impossible; hence an exact Z2 degeneracy of the ground state.
Let us make this statement more precise. Consider a QIC with a zero-h impurity, say at n = 0:
Understanding the Mach-Zehnder Interferometer (MZI)
... For simplicity, we will assume that a photon can only reflect from one of the two surfaces of the identical
half-silvered mirrors (beam splitters) BS1 and BS2 because of anti-reflection coatings.
The detectors D1 and D2 are point detectors located symmetrically with respect to the other components
Compact operator on Hilbert space
In functional analysis, compact operators on Hilbert spaces are a direct extension of matrices: in the Hilbert spaces, they are precisely the closure of finite-rank operators in the uniform operator topology. As such, results from matrix theory can sometimes be extended to compact operators using similar arguments. In contrast, the study of general operators on infinite-dimensional spaces often requires a genuinely different approach.For example, the spectral theory of compact operators on Banach spaces takes a form that is very similar to the Jordan canonical form of matrices. In the context of Hilbert spaces, a square matrix is unitarily diagonalizable if and only if it is normal. A corresponding result holds for normal compact operators on Hilbert spaces. (More generally, the compactness assumption can be dropped. But, as stated above, the techniques used are less routine.)This article will discuss a few results for compact operators on Hilbert space, starting with general properties before considering subclasses of compact operators.