474 research outputs found
Information gain versus state disturbance for a single qubit
The trade-off between the information gain and the state disturbance is
derived for quantum operations on a single qubit prepared in a uniformly
distributed pure state. The derivation is valid for a class of measures
quantifying the state disturbance and the information gain which satisfy
certain invariance conditions. This class includes in particular the Shannon
entropy versus the operation fidelity. The central role in the derivation is
played by efficient quantum operations, which leave the system in a pure output
state for any measurement outcome. It is pointed out that the optimality of
efficient quantum operations among those inducing a given operator-valued
measure is related to Davies' characterization of convex invariant functions on
hermitian operators.Comment: 17 pages, LaTeX, osid.sty. Substantially expanded and generalize
Connections and Metrics Respecting Standard Purification
Standard purification interlaces Hermitian and Riemannian metrics on the
space of density operators with metrics and connections on the purifying
Hilbert-Schmidt space. We discuss connections and metrics which are well
adopted to purification, and present a selected set of relations between them.
A connection, as well as a metric on state space, can be obtained from a metric
on the purification space. We include a condition, with which this
correspondence becomes one-to-one. Our methods are borrowed from elementary
*-representation and fibre space theory. We lift, as an example, solutions of a
von Neumann equation, write down holonomy invariants for cyclic ones, and ``add
noise'' to a curve of pure states.Comment: Latex, 27 page
Adapting Quality Assurance to Adaptive Systems: The Scenario Coevolution Paradigm
From formal and practical analysis, we identify new challenges that
self-adaptive systems pose to the process of quality assurance. When tackling
these, the effort spent on various tasks in the process of software engineering
is naturally re-distributed. We claim that all steps related to testing need to
become self-adaptive to match the capabilities of the self-adaptive
system-under-test. Otherwise, the adaptive system's behavior might elude
traditional variants of quality assurance. We thus propose the paradigm of
scenario coevolution, which describes a pool of test cases and other
constraints on system behavior that evolves in parallel to the (in part
autonomous) development of behavior in the system-under-test. Scenario
coevolution offers a simple structure for the organization of adaptive testing
that allows for both human-controlled and autonomous intervention, supporting
software engineering for adaptive systems on a procedural as well as technical
level.Comment: 17 pages, published at ISOLA 201
New measure of electron correlation
We propose to quantify the "correlation" inherent in a many-electron (or
many-fermion) wavefunction by comparing it to the unique uncorrelated state
that has the same single-particle density operator as it does.Comment: Final version to appear in PR
Off-diagonal geometric phase for mixed states
We extend the off-diagonal geometric phase [Phys. Rev. Lett. {\bf 85}, 3067
(2000)] to mixed quantal states. The nodal structure of this phase in the qubit
(two-level) case is compared with that of the diagonal mixed state geometric
phase [Phys. Rev. Lett. {\bf 85}, 2845 (2000)]. Extension to higher dimensional
Hilbert spaces is delineated. A physical scenario for the off-diagonal mixed
state geometric phase in polarization-entangled two-photon interferometry is
proposed.Comment: small corrections; journal reference adde
Lower and upper bounds on the fidelity susceptibility
We derive upper and lower bounds on the fidelity susceptibility in terms of
macroscopic thermodynamical quantities, like susceptibilities and thermal
average values. The quality of the bounds is checked by the exact expressions
for a single spin in an external magnetic field. Their usefulness is
illustrated by two examples of many-particle models which are exactly solved in
the thermodynamic limit: the Dicke superradiance model and the single impurity
Kondo model. It is shown that as far as divergent behavior is considered, the
fidelity susceptibility and the thermodynamic susceptibility are equivalent for
a large class of models exhibiting critical behavior.Comment: 19 page
Fixing All Moduli in a Simple F-Theory Compactification
We discuss a simple example of an F-theory compactification on a Calabi-Yau
fourfold where background fluxes, together with nonperturbative effects from
Euclidean D3 instantons and gauge dynamics on D7 branes, allow us to fix all
closed and open string moduli. We explicitly check that the known higher order
corrections to the potential, which we neglect in our leading approximation,
only shift the results by a small amount. In our exploration of the model, we
encounter interesting new phenomena, including examples of transitions where D7
branes absorb O3 planes, while changing topology to preserve the net D3 charge.Comment: 68 pages, 19 figures; v2: references adde
Statistical distinguishability between unitary operations
The problem of distinguishing two unitary transformations, or quantum gates,
is analyzed and a function reflecting their statistical distinguishability is
found. Given two unitary operations, and , it is proved that there
always exists a finite number such that and are perfectly distinguishable, although they were not in the single-copy
case. This result can be extended to any finite set of unitary transformations.
Finally, a fidelity for one-qubit gates, which satisfies many useful properties
from the point of view of quantum information theory, is presented.Comment: 6 pages, REVTEX. The perfect distinguishability result is extended to
any finite set of gate
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