1,291 research outputs found
Mixed state geometric phases, entangled systems, and local unitary transformations
The geometric phase for a pure quantal state undergoing an arbitrary
evolution is a ``memory'' of the geometry of the path in the projective Hilbert
space of the system. We find that Uhlmann's geometric phase for a mixed quantal
state undergoing unitary evolution not only depends on the geometry of the path
of the system alone but also on a constrained bi-local unitary evolution of the
purified entangled state. We analyze this in general, illustrate it for the
qubit case, and propose an experiment to test this effect. We also show that
the mixed state geometric phase proposed recently in the context of
interferometry requires uni-local transformations and is therefore essentially
a property of the system alone.Comment: minor changes, journal reference adde
Thermoacoustic tomography arising in brain imaging
We study the mathematical model of thermoacoustic and photoacoustic
tomography when the sound speed has a jump across a smooth surface. This models
the change of the sound speed in the skull when trying to image the human
brain. We derive an explicit inversion formula in the form of a convergent
Neumann series under the assumptions that all singularities from the support of
the source reach the boundary
Optimal manipulations with qubits: Universal quantum entanglers
We analyze various scenarios for entangling two initially unentangled qubits.
In particular, we propose an optimal universal entangler which entangles a
qubit in unknown state with a qubit in a reference (known) state
. That is, our entangler generates the output state which is as close as
possible to the pure (symmetrized) state . The most
attractive feature of this entangling machine, is that the fidelity of its
performance (i.e. the distance between the output and the ideally entangled --
symmetrized state) does not depend on the input and takes the constant value
. We also analyze how to optimally generate
from a single qubit initially prepared in an unknown state |\Psi\r a two
qubit entangled system which is as close as possible to a Bell state
, where \l\Psi|\Psi^\perp\r =0.Comment: 11 pages, 3 eps figures, accepted for publication in Phys. Rev.
Temperature effects on mixed state geometric phase
Geometric phase of an open quantum system that is interacting with a thermal
environment (bath) is studied through some simple examples. The system is
considered to be a simple spin-half particle which is weakly coupled to the
bath. It is seen that even in this regime the geometric phase can vary with
temperature. In addition, we also consider the system under an adiabatically
time-varying magnetic field which is weakly coupled to the bath. An important
feature of this model is that it reveals existence of a temperature-scale in
which adiabaticity condition is preserved and beyond which the geometric phase
is varying quite rapidly with temperature. This temperature is exactly the one
in which the geometric phase vanishes. This analysis has some implications in
realistic implementations of geometric quantum computation.Comment: 5 page
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