Non-unitary CMV-decomposition

Cmv: the Unitary Analogue of Jacobi Matrices

Abstract. We discuss a number of properties of CMV matrices, by which we mean the class of unitary matrices recently introduced by Cantero, Moral, and Velazquez. We argue that they play an equivalent role among unitary matrices to that of Jacobi matrices among all Hermitian matrices. In particular, we describe the analogues of well-known properties of Jacobi matrices: foliation by co-adjoint or...

Decomposition of unitary matrices and quantum gates

A general scheme is presented to decompose a d-by-d unitary matrix as the product of two-level unitary matrices with additional structure and prescribed determinants. In particular, the decomposition can be done by using two-level matrices in d − 1 classes, where each class is isomorphic to the group of 2 × 2 unitary matrices. The proposed scheme is easy to apply, and useful in treating problem...

Non Unitary Random Walks

Motivated by the recent refutation of information loss paradox in black hole by Hawking, we investigate the new concept of non unitary random walks. In a non unitary random walk, we consider that the state 0, called the black hole, has a probability weight that decays exponentially in e−λt for some λ > 0. This decaying probabilities affect the probability weight of the other states, so that the...

Non-unitary Valuation Subalgebras

Unitary and Non-Unitary Evolution in Quantum Cosmology

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...