10 research outputs found
Convergence to equilibrium under a random Hamiltonian
We analyze equilibration times of subsystems of a larger system under a
random total Hamiltonian, in which the basis of the Hamiltonian is drawn from
the Haar measure. We obtain that the time of equilibration is of the order of
the inverse of the arithmetic average of the Bohr frequencies. To compute the
average over a random basis, we compute the inverse of a matrix of overlaps of
operators which permute four systems. We first obtain results on such a matrix
for a representation of an arbitrary finite group and then apply it to the
particular representation of the permutation group under consideration.Comment: 11 pages, 1 figure, v1-v3: some minor errors and typos corrected and
new references added; v4: results for the degenerated spectrum added; v5:
reorganized and rewritten version; to appear in PR
Region of fidelities for a 1 -> N universal qubit quantum cloner
We analyze a region of fidelities for qubit which is obtained after an
application of a 1 -> N universal quantum cloner. We express the allowed region
for fidelities in terms of overlaps of pure states with irreps of S(n) (n =
N+1) showing that the pure states can be taken with real coefficients only.
Subsequently, the case n = 4, corresponding to a 1 -> 3 cloner is studied in
more detail as an illustrative example. To obtain the main result, we make a
convex hull of possible ranges of fidelities related to a given irrep. The
formalism allows to construct the state giving rise to a given N-tuple of
fidelities.Comment: 13 pages, 3 figures, final version to appear in Physics Letters