4,017 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
Perfect Function Transfer in two- and three- dimensions without initialization
We find analytic models that can perfectly transfer, without state
initializati$ or remote collaboration, arbitrary functions in two- and
three-dimensional interacting bosonic and fermionic networks. We elaborate on a
possible implementation of state transfer through bosonic or fermionic atoms
trapped in optical lattices. A significant finding is that the state of a spin
qubit can be perfectly transferred through a fermionic system. Families of
Hamiltonians, both linear and nonlinear, are described which are related to the
linear Boson model and that enable the perfect transfer of arbitrary functions.
This includes entangled states such as decoherence-free subsystems enabling
noise protection of the transferred state.Comment: 4 pages, no figur
Miniature Optical Atomic Clock: Stabilization of a Kerr Comb Oscillator
Mechanical clocks consist of a pendulum and a clockwork that translates the
pendulum period to displayed time. The most advanced clocks utilize optical
transitions in atoms in place of the pendulum and an optical frequency comb
generated by a femtosecond laser as the clockwork. The comb must be stabilized
at two points along its frequency spectrum: one with a laser to lock a comb
line to a transition in the atom, and another through self referencing to
stabilize the frequency interval between the comb lines. This approach requires
advanced techniques, so optical atomic clocks are currently laboratory devices
in specialized labs. In this paper we leverage unique properties of Kerr comb
oscillators for realization of optical atomic clocks in miniature form factors.
In particular, we describe a clock based on D1 transition of 87Rb that fits in
the palm of the hand, and can be further miniaturized to chip scale.Comment: 4 pages, 4 figure
Casimir Invariants for Systems Undergoing Collective Motion
Dicke states are states of a collection of particles which have been under
active investigation for several reasons. One reason is that the decay rates of
these states can be quite different from a set of independently evolving
particles. Another reason is that a particular class of these states are
decoherence-free or noiseless with respect to a set of errors. These noiseless
states, or more generally subsystems, can avoid certain types of errors in
quantum information processing devices. Here we provide a method for
calculating invariants of systems of particles undergoing collective motions.
These invariants can be used to determine a complete set of commuting
observables for a class of Dicke states as well as identify possible logical
operations for decoherence-free/noiseless subsystems. Our method is quite
general and provides results for cases where the constituent particles have
more than two internal states.Comment: 5 page
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