4,093 research outputs found
Implications of Qudit Superselection rules for the Theory of Decoherence-free Subsystems
The use of d-state systems, or qudits, in quantum information processing is
discussed. Three-state and higher dimensional quantum systems are known to have
very different properties from two-state systems, i.e., qubits. In particular
there exist qudit states which are not equivalent under local unitary
transformations unless a selection rule is violated. This observation is shown
to be an important factor in the theory of decoherence-free, or noiseless,
subsystems. Experimentally observable consequences and methods for
distinguishing these states are also provided, including the explicit
construction of new decoherence-free or noiseless subsystems from qutrits.
Implications for simulating quantum systems with quantum systems are also
discussed.Comment: 13 pages, 1 figures, Version 2: Typos corrected, references fixed and
new ones added, also includes referees suggested changes and a new exampl
Universal Leakage Elimination
``Leakage'' errors are particularly serious errors which couple states within
a code subspace to states outside of that subspace thus destroying the error
protection benefit afforded by an encoded state. We generalize an earlier
method for producing leakage elimination decoupling operations and examine the
effects of the leakage eliminating operations on decoherence-free or noiseless
subsystems which encode one logical, or protected qubit into three or four
qubits. We find that by eliminating the large class of leakage errors, under
some circumstances, we can create the conditions for a decoherence free
evolution. In other cases we identify a combination decoherence-free and
quantum error correcting code which could eliminate errors in solid-state
qubits with anisotropic exchange interaction Hamiltonians and enable universal
quantum computing with only these interactions.Comment: 14 pages, no figures, new version has references updated/fixe
A graph of dark energy significance on different spatial and mass scales
The current cosmological paradigm sees the formation and evolution of the
cosmic large-scale structure as governed by the gravitational attraction of the
Dark Matter (DM) and the repulsion of the Dark Energy (DE).
We characterize the relative importance of uniform and constant dark energy,
as given by the Lambda term in the standard LCDM cosmology, in galaxy systems
of different scales, from groups to superclusters.
An instructive "Lambda significance graph" is introduced where the matter-DE
density ratio /rho_Lambda for different galaxy systems is plotted
against the radius R. This presents gravitation and DE dominated regions and
shows directly the zero velocity radius, the zero-gravity radius, and the
Einstein-Straus radius for any fixed value of mass.
Example galaxy groups and clusters from the local universe illustrate the use
of the Lambda significance graph. These are generally located deep in the
gravity-dominated region /rho_Lambda > 2, being virialized. Extended
clusters and main bodies of superclusters can reach down near the border line
between gravity-dominated and DE dominated regions /rho_Lambda = 2. The
scale--mass relation from the standard 2-point correlation function intersects
this balance line near the correlation lenght.
The log /rho_Lambda vs. log R diagram is a useful and versatile way to
characterize the dynamical state of systems of galaxies within the Lambda
dominated expanding universe.Comment: 4 pages, 2 figure
Topological structures of adiabatic phase for multi-level quantum systems
The topological properties of adiabatic gauge fields for multi-level
(three-level in particular) quantum systems are studied in detail. Similar to
the result that the adiabatic gauge field for SU(2) systems (e.g. two-level
quantum system or angular momentum systems, etc) have a monopole structure, the
curvature two-forms of the adiabatic holonomies for SU(3) three-level and SU(3)
eight-level quantum systems are shown to have monopole-like (for all levels) or
instanton-like (for the degenerate levels) structures.Comment: 15 pages, no figures. Accepted by J.Phys.
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