277 research outputs found
Mixed state non-Abelian holonomy for subsystems
Non-Abelian holonomy in dynamical systems may arise in adiabatic transport of
energetically degenerate sets of states. We examine such a holonomy structure
for mixtures of energetically degenerate quantal states. We demonstrate that
this structure has a natural interpretation in terms of the standard
Wilczek-Zee holonomy associated with a certain class of Hamiltonians that
couple the system to an ancilla. The mixed state holonomy is analysed for
holonomic quantum computation using ion traps.Comment: Minor 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
Adiabatic geometric phases in hydrogenlike atoms
We examine the effect of spin-orbit coupling on geometric phases in
hydrogenlike atoms exposed to a slowly varying magnetic field. The marginal
geometric phases associated with the orbital angular momentum and the intrinsic
spin fulfill a sum rule that explicitly relates them to the corresponding
geometric phase of the whole system. The marginal geometric phases in the
Zeeman and Paschen-Back limit are analyzed. We point out the existence of nodal
points in the marginal phases that may be detected by topological means.Comment: Clarifying material added, one figure removed, journal reference
adde
Quantal interferometry with dissipative internal motion
In presence of dissipation, quantal states may acquire complex-valued phase
effects. We suggest a notion of dissipative interferometry that accommodates
this complex-valued structure and that may serve as a tool for analyzing the
effect of certain kinds of external influences on quantal interference. The
concept of mixed-state phase and concomitant gauge invariance is extended to
dissipative internal motion. The resulting complex-valued mixed-state
interference effects lead to well-known results in the unitary limit and in the
case of dissipative motion of pure quantal states. Dissipative interferometry
is applied to fault-tolerant geometric quantum computation.Comment: Slight revision, journal reference adde
Optimal Topological Test for Degeneracies of Real Hamiltonians
We consider adiabatic transport of eigenstates of real Hamiltonians around
loops in parameter space. It is demonstrated that loops that map to nontrivial
loops in the space of eigenbases must encircle degeneracies. Examples from
Jahn-Teller theory are presented to illustrate the test. We show furthermore
that the proposed test is optimal.Comment: Minor corrections, accepted in Phys. Rev. Let
Global asymmetry of many-qubit correlations: A lattice gauge theory approach
We introduce a novel bridge between the familiar gauge field theory
approaches used in many areas of modern physics such as quantum field theory
and the SLOCC protocols familiar in quantum information. Although the
mathematical methods are the same the meaning of the gauge group will be
different. The measure we introduce, `twist', is constructed as a Wilson loop
from a correlation induced holonomy. The measure can be understood as the
global asymmetry of the bipartite correlations in a loop of three or more
qubits; if the holonomy is trivial (the identity matrix), the bipartite
correlations can be globally untwisted using general local qubit operations,
the gauge group of our theory, which turns out to be the group of Lorentz
transformations familiar from special relativity. If it is not possible to
globally untwist the bipartite correlations in a state globally using local
operations, the twistedness is given by a non-trivial element of the Lorentz
group, the correlation induced holonomy. We provide several analytical examples
of twisted and untwisted states for three qubits, the most elementary
non-trivial loop one can imagine.Comment: 13 pages, 3 figures, title changed, results and content remain
unchange
Towards a quantum Hall effect for atoms using electric fields
An atomic analogue of Landau quantization based on the Aharonov-Casher (AC)
interaction is developed. The effect provides a first step towards an atomic
quantum Hall system using electric fields, which may be realized in a
Bose-Einstein condensate
Noncyclic geometric changes of quantum states
Non-Abelian quantum holonomies, i.e., unitary state changes solely induced by
geometric properties of a quantum system, have been much under focus in the
physics community as generalizations of the Abelian Berry phase. Apart from
being a general phenomenon displayed in various subfields of quantum physics,
the use of holonomies has lately been suggested as a robust technique to obtain
quantum gates; the building blocks of quantum computers. Non-Abelian holonomies
are usually associated with cyclic changes of quantum systems, but here we
consider a generalization to noncyclic evolutions. We argue that this open-path
holonomy can be used to construct quantum gates. We also show that a structure
of partially defined holonomies emerges from the open-path holonomy. This
structure has no counterpart in the Abelian setting. We illustrate the general
ideas using an example that may be accessible to tests in various physical
systems.Comment: Extended version, new title, journal reference adde
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
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