Unitary realizations of the ideal phase measurement

2 00 3 Unitary realizations of the ideal phase measurement

We explicitly construct a large class of unitary transformations that allow to perform the ideal estimation of the phase-shift on a single-mode radiation field. The ideal phase distribution is obtained by heterodyne detection on two radiation modes after the interaction. The quantum estimation of an unknown phase shift—the so called quantum phase measurement—is the essential problem of high sen...

Unitary Realizations of the q-Oszillator Algebra

We give a classification of the unitary irreducible realizations of the q-oscillator algebra and present their explicit construction. Besides standard representations, we obtain a new one with continuous spectrum absent in the non-deformed case. ∗Part of Project Nr. P8916-PHY of the “Fonds zur Förderung der wissenschaftlichen Forschung in Österreich”.

Unitary Shift-Register Realizations of Sequential Machines

Optimal realizations of controlled unitary gates

The controlled-not gate and the single qubit gates are considered elementary gates in quantum computing. It is natural to ask how many such elementary gates are needed to implement more elaborate gates or circuits. Recall that a controlled-U gate can be realized with two controlled-not gates and four single qubit gates. We prove that this implementation is optimal if and only if the matrix U sa...

Lattice Realizations of Unitary Minimal Modular Invariant Partition Functions

The conformal spectra of the critical dilute A–D–E lattice models are studied numerically. The results strongly indicate that, in branches 1 and 2, these models provide realizations of the complete A–D–E classification of unitary minimal modular invariant partition functions given by Cappelli, Itzykson and Zuber. In branches 3 and 4 the results indicate that the modular invariant partition func...