3 research outputs found
Wigner Functions and Separability for Finite Systems
A discussion of discrete Wigner functions in phase space related to mutually
unbiased bases is presented. This approach requires mathematical assumptions
which limits it to systems with density matrices defined on complex Hilbert
spaces of dimension p^n where p is a prime number. With this limitation it is
possible to define a phase space and Wigner functions in close analogy to the
continuous case. That is, we use a phase space that is a direct sum of n
two-dimensional vector spaces each containing p^2 points. This is in contrast
to the more usual choice of a two-dimensional phase space containing p^(2n)
points. A useful aspect of this approach is that we can relate complete
separability of density matrices and their Wigner functions in a natural way.
We discuss this in detail for bipartite systems and present the generalization
to arbitrary numbers of subsystems when p is odd. Special attention is required
for two qubits (p=2) and our technique fails to establish the separability
property for more than two qubits.Comment: Some misprints have been corrected and a proof of the separability of
the A matrices has been adde
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