3 research outputs found
Irreversible Quantum Baker Map
We propose a generalization of the model of classical baker map on the torus,
in which the images of two parts of the phase space do overlap. This
transformation is irreversible and cannot be quantized by means of a unitary
Floquet operator. A corresponding quantum system is constructed as a completely
positive map acting in the space of density matrices. We investigate spectral
properties of this super-operator and their link with the increase of the
entropy of initially pure states.Comment: 4 pages, 3 figures include
Quantum computers in phase space
We represent both the states and the evolution of a quantum computer in phase
space using the discrete Wigner function. We study properties of the phase
space representation of quantum algorithms: apart from analyzing important
examples, such as the Fourier Transform and Grover's search, we examine the
conditions for the existence of a direct correspondence between quantum and
classical evolutions in phase space. Finally, we describe how to directly
measure the Wigner function in a given phase space point by means of a
tomographic method that, itself, can be interpreted as a simple quantum
algorithm.Comment: 16 pages, 7 figures, to appear in Phys Rev