88 research outputs found
Fault-ignorant Quantum Search
We investigate the problem of quantum searching on a noisy quantum computer.
Taking a 'fault-ignorant' approach, we analyze quantum algorithms that solve
the task for various different noise strengths, which are possibly unknown
beforehand. We prove lower bounds on the runtime of such algorithms and thereby
find that the quadratic speedup is necessarily lost (in our noise models).
However, for low but constant noise levels the algorithms we provide (based on
Grover's algorithm) still outperform the best noiseless classical search
algorithm.Comment: v1: 15+8 pages, 4 figures; v2: 19+8 pages, 4 figures, published
version (Introduction section significantly expanded, presentation clarified,
results and order unchanged
Hilbert's projective metric in quantum information theory
We introduce and apply Hilbert's projective metric in the context of quantum
information theory. The metric is induced by convex cones such as the sets of
positive, separable or PPT operators. It provides bounds on measures for
statistical distinguishability of quantum states and on the decrease of
entanglement under LOCC protocols or other cone-preserving operations. The
results are formulated in terms of general cones and base norms and lead to
contractivity bounds for quantum channels, for instance improving Ruskai's
trace-norm contraction inequality. A new duality between distinguishability
measures and base norms is provided. For two given pairs of quantum states we
show that the contraction of Hilbert's projective metric is necessary and
sufficient for the existence of a probabilistic quantum operation that maps one
pair onto the other. Inequalities between Hilbert's projective metric and the
Chernoff bound, the fidelity and various norms are proven.Comment: 32 pages including 3 appendices and 3 figures; v2: minor changes,
published versio
Grand unification through gravitational effects
We systematically study the unification of gauge couplings in the presence of
(one or more) effective dimension-5 operators cHGG/4MPl, induced into the grand
unified theory by gravitational interactions at the Planck scale MPl. These
operators alter the usual condition for gauge coupling unification, which can,
depending on the Higgs content H and vacuum expectation value, result in
unification at scales MX significantly different than naively expected. We find
non-supersymmetric models of SU(5) and SO(10) unification, with natural Wilson
coefficients c, that easily satisfy the constraints from proton decay.
Furthermore, gauge coupling unification at scales as high as the Planck scale
seems feasible, possibly hinting at simultaneous unification of gauge and
gravitational interactions. In the Appendix we work out the group theoretical
aspects of this scenario for SU(5) and SO(10) unified groups in detail; this
material is also relevant in the analysis of non-universal gaugino masses
obtained from supergravity.Comment: 27 pages, 5 figures, 8 tables, 1 appendix, revtex; v2: introduction
and conclusion expanded, references added, minor changes, version published
in PR
Monsters, black holes and the statistical mechanics of gravity
We review the construction of monsters in classical general relativity.
Monsters have finite ADM mass and surface area, but potentially unbounded
entropy. From the curved space perspective they are objects with large proper
volume that can be glued on to an asymptotically flat space. At no point is the
curvature or energy density required to be large in Planck units, and quantum
gravitational effects are, in the conventional effective field theory
framework, small everywhere. Since they can have more entropy than a black hole
of equal mass, monsters are problematic for certain interpretations of black
hole entropy and the AdS/CFT duality.
In the second part of the paper we review recent developments in the
foundations of statistical mechanics which make use of properties of
high-dimensional (Hilbert) spaces. These results primarily depend on kinematics
-- essentially, the geometry of Hilbert space -- and are relatively insensitive
to dynamics. We discuss how this approach might be adopted as a basis for the
statistical mechanics of gravity. Interestingly, monsters and other highly
entropic configurations play an important role.Comment: 9 pages, 4 figures, revtex; invited Brief Review to be published in
Modern Physics Letters
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