212 research outputs found
Comment on "Geometric phases for mixed states during cyclic evolutions"
It is shown that a recently suggested concept of mixed state geometric phase
in cyclic evolutions [2004 {\it J. Phys. A} {\bf 37} 3699] is gauge dependent.Comment: Comment to the paper L.-B. Fu and J.-L. Chen, J. Phys. A 37, 3699
(2004); small changes; journal reference adde
Geometric Phases for Mixed States during Cyclic Evolutions
The geometric phases of cyclic evolutions for mixed states are discussed in
the framework of unitary evolution. A canonical one-form is defined whose line
integral gives the geometric phase which is gauge invariant. It reduces to the
Aharonov and Anandan phase in the pure state case. Our definition is consistent
with the phase shift in the proposed experiment [Phys. Rev. Lett. \textbf{85},
2845 (2000)] for a cyclic evolution if the unitary transformation satisfies the
parallel transport condition. A comprehensive geometric interpretation is also
given. It shows that the geometric phases for mixed states share the same
geometric sense with the pure states.Comment: 9 pages, 1 figur
Non-adiabatic holonomic quantum computation
We develop a non-adiabatic generalization of holonomic quantum computation in
which high-speed universal quantum gates can be realized by using non-Abelian
geometric phases. We show how a set of non-adiabatic holonomic one- and
two-qubit gates can be implemented by utilizing optical transitions in a
generic three-level configuration. Our scheme opens up for universal
holonomic quantum computation on qubits characterized by short coherence times.Comment: Some changes, journal reference adde
Kinematic approach to off-diagonal geometric phases of nondegenerate and degenerate mixed states
Off-diagonal geometric phases have been developed in order to provide
information of the geometry of paths that connect noninterfering quantal
states. We propose a kinematic approach to off-diagonal geometric phases for
pure and mixed states. We further extend the mixed state concept proposed in
[Phys. Rev. Lett. {\bf 90}, 050403 (2003)] to degenerate density operators. The
first and second order off-diagonal geometric phases are analyzed for unitarily
evolving pairs of pseudopure states.Comment: New section IV, new figure, journal ref adde
Geometric phases for mixed states in interferometry
We provide a physical prescription based on interferometry for introducing
the total phase of a mixed state undergoing unitary evolution, which has been
an elusive concept in the past. We define the parallel transport condition that
provides a connection-form for obtaining the geometric phase for mixed states.
The expression for the geometric phase for mixed state reduces to well known
formulas in the pure state case when a system undergoes noncyclic and unitary
quantum evolution.Comment: Two column, 4 pages, Latex file, No figures, Few change
Kinematic approach to the mixed state geometric phase in nonunitary evolution
A kinematic approach to the geometric phase for mixed quantal states in
nonunitary evolution is proposed. This phase is manifestly gauge invariant and
can be experimentally tested in interferometry. It leads to well-known results
when the evolution is unitary.Comment: Minor changes; journal reference adde
Reply to `Singularities of the mixed state phase'
The only difference between Bhandari's viewpoint [quant-ph/0108058] and ours
[Phys. Rev. Lett. 85, 2845 (2000)] is that our phase is defined modulo ,
whereas Bhandari argues that two phases that differ by , integer,
may be distinguished experimentally in a history-dependent manner.Comment: 2 page
On the stability of quantum holonomic gates
We provide a unified geometrical description for analyzing the stability of
holonomic quantum gates in the presence of imprecise driving controls
(parametric noise). We consider the situation in which these fluctuations do
not affect the adiabatic evolution but can reduce the logical gate performance.
Using the intrinsic geometric properties of the holonomic gates, we show under
which conditions on noise's correlation time and strength, the fluctuations in
the driving field cancel out. In this way, we provide theoretical support to
previous numerical simulations. We also briefly comment on the error due to the
mismatch between real and nominal time of the period of the driving fields and
show that it can be reduced by suitably increasing the adiabatic time.Comment: 7 page
Generalization of geometric phase to completely positive maps
We generalize the notion of relative phase to completely positive maps with
known unitary representation, based on interferometry. Parallel transport
conditions that define the geometric phase for such maps are introduced. The
interference effect is embodied in a set of interference patterns defined by
flipping the environment state in one of the two paths. We show for the qubit
that this structure gives rise to interesting additional information about the
geometry of the evolution defined by the CP map.Comment: Minor revision. 2 authors added. 4 pages, 2 figures, RevTex
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