777 research outputs found
Elliptical orbits in the Bloch sphere
As is well known, when an SU(2) operation acts on a two-level system, its
Bloch vector rotates without change of magnitude. Considering a system composed
of two two-level systems, it is proven that for a class of nonlocal
interactions of the two subsystems including \sigma_i\otimes\sigma_j (with i,j
\in {x,y,z}) and the Heisenberg interaction, the geometric description of the
motion is particularly simple: each of the two Bloch vectors follows an
elliptical orbit within the Bloch sphere. The utility of this result is
demonstrated in two applications, the first of which bears on quantum control
via quantum interfaces. By employing nonunitary control operations, we extend
the idea of controllability to a set of points which are not necessarily
connected by unitary transformations. The second application shows how the
orbit of the coherence vector can be used to assess the entangling power of
Heisenberg exchange interaction.Comment: 9 pages, 4 figures, few corrections, J. Opt. B: Quantum Semiclass.
Opt. 7 (2005) S1-S
Decoherence Control and Purification of Two-dimensional Quantum Density Matrices under Lindblad Dissipation
Control of quantum dissipative systems can be challenging because control
variables are typically part of the system Hamiltonian, which can only generate
motion along unitary orbits of the system. To transit between orbits, one must
harness the dissipation super-operator. To separate the inter-orbit dynamics
from the Hamiltonian dynamics for a generic two-dimensional system, we project
the Lindblad master equation onto the set of spectra of the density matrix, and
we interpret the location along the orbit to be a new control variable. The
resulting differential equation allows us to analyze the controllability of a
general two-dimensional Lindblad system, particularly systems where the
dissipative term has an anti-symmetric part. We extend this to categorize the
possible purifiable systems in two dimensions.Comment: 10 pages, 2 figure
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