Crypto-Unitary Forms of Quantum Evolution Operators

Quadratic Forms in Unitary Operators

Pseudo-Unitary Operators and Pseudo-Unitary Quantum Dynamics

We consider pseudo-unitary quantum systems and discuss various properties of pseudounitary operators. In particular we prove a characterization theorem for block-diagonalizable pseudo-unitary operators with finite-dimensional diagonal blocks. Furthermore, we show that every pseudo-unitary matrix is the exponential of i = √ −1 times a pseudo-Hermitian matrix, and determine the structure of the L...

ON QUANTUM GROUP OF UNITARY OPERATORS QUANTUM ‘az + b’ GROUP

The concept of a quantum group of unitary operators is relevant for the theory of non-compact locally compact quantum groups. It plays similar role as the concept of a quantum matrix group in the compact case. To show the usefulness of this notion we present an approach to a construction of quantum ‘az + b’ group based on this idea. A brief survey of the present status of quantum group theory i...

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...

Constructive control of quantum systems using factorization of unitary operators

We demonstrate how structured decompositions of unitary operators can be employed to derive control schemes for finite-level quantum systems that require only sequences of simple control pulses such as square wave pulses with finite rise and decay times or Gaussian wavepackets. To illustrate the technique, it is applied to find control schemes to achieve population transfers for pure-state syst...