20 research outputs found
A "Square-root" Method for the Density Matrix and its Applications to Lindblad Operators
The evolution of open systems, subject to both Hamiltonian and dissipative
forces, is studied by writing the element of the time () dependent
density matrix in the form \ber \rho_{nm}(t)&=& \frac {1}{A} \sum_{\alpha=1}^A
\gamma ^{\alpha}_n (t)\gamma^{\alpha *}_m (t) \enr The so called "square root
factors", the 's, are non-square matrices and are averaged over
systems () of the ensemble. This square-root description is exact.
Evolution equations are then postulated for the factors, such as to
reduce to the Lindblad-type evolution equations for the diagonal terms in the
density matrix. For the off-diagonal terms they differ from the
Lindblad-equations. The "square root factors" are not unique and
the equations for the 's depend on the specific representation
chosen. Two criteria can be suggested for fixing the choice of 's
one is simplicity of the resulting equations and the other has to do with the
reduction of the difference between the formalism and the
Lindblad-equations.Comment: 36 pages, 7 figure
On unified-entropy characterization of quantum channels
We consider properties of quantum channels with use of unified entropies.
Extremal unravelings of quantum channel with respect to these entropies are
examined. The concept of map entropy is extended in terms of the unified
entropies. The map -entropy is naturally defined as the unified
-entropy of rescaled dynamical matrix of given quantum channel.
Inequalities of Fannes type are obtained for introduced entropies in terms of
both the trace and Frobenius norms of difference between corresponding
dynamical matrices. Additivity properties of introduced map entropies are
discussed. The known inequality of Lindblad with the entropy exchange is
generalized to many of the unified entropies. For tensor product of a pair of
quantum channels, we derive two-sided estimating of the output entropy of a
maximally entangled input state.Comment: 12 pages, no figures. Typos are fixed. One lemma is extended and
removed to Appendi