In close analogy to the fundamental role of random numbers in classical information theory, random operators are a basic component of quantum information theory. Unfortunately, the implementation of random unitary operators on a quantum processor is exponentially hard. Here we introduce a method for generating pseudo-random unitary operators that can reproduce those statistical properties of ra...

A random unitary channel is one that is given by a convex combination of unitary channels. It is shown that the conjectures on the additivity of the minimum output entropy and the multiplicativity of the maximum output p-norm can be equivalently restated in terms of random unitary channels. This is done by constructing a random unitary approximation to a general quantum channel. This approximat...

The QR-algorithm is a renowned method for computing all eigenvalues of an arbitrary matrix. A preliminary unitary similarity transformation to Hessenberg form is indispensible for keeping the computational complexity of the QRalgorithm applied on the resulting Hessenberg matrix under control. The unitary factor Q in the QR-factorization of the Hessenberg matrix H = QR is composed of n − 1 rotat...

Orthogonal sets of idempotents are used to design sets of unitary matrices, known as constellations, such that the modulus of the determinant of the difference of any two distinct elements is greater than 0. It is shown that unitary matrices in general are derived from orthogonal sets of idempotents reducing the design problem to a construction problem of unitary matrices from such sets. The qu...

We analyse when and why unitarity violations might occur in quantum cosmology restricted to minisuperspace. To this end we discuss in detail backscattering transitions between expanding and contracting solutions of the Wheeler-DeWitt equation. We first show that upon neglecting only backscattering, one obtains an intermediate regime in which matter evolves unitarily but which does not correspon...

The unitary rational orbifold conformal field theories in the algebraic quantum field theory and subfactor theory framework are formulated. Under general conditions, it is shown that the orbifold of a given unitary rational conformal field theory generates a unitary modular category. Many new unitary modular categories are obtained. It is also shown that the irreducible representations of orbif...

The quantum circuit is generalized to include non-unitary gates operated by quantum measurement, in order to reduce the number of the overhead of qubits required to ensure fault tolerance. A specific type of one-qubit non-unitary gates, together with the controlled-not gate and all one-qubit unitary gates, is shown to constitute a universal set of gates for the non-unitary quantum circuit. A re...