1,690 research outputs found
Transformations of -Type Entangled States
The transformations of -type entangled states by using local operations
assisted with classical communication are investigated. For this purpose, a
parametrization of the -type states which remains invariant under local
unitary transformations is proposed and a complete characterization of the
local operations carried out by a single party is given. These are used for
deriving the necessary and sufficient conditions for deterministic
transformations. A convenient upper bound for the maximum probability of
distillation of arbitrary target states is also found.Comment: 7 page
On the Geometric Measures of Entanglement
The geometric measure of entanglement, which expresses the minimum distance
to product states, has been generalized to distances to sets that remain
invariant under the stochastic reducibility relation. For each such set, an
associated entanglement monotone can be defined. The explicit analytical forms
of these measures are obtained for bipartite entangled states. Moreover, the
three qubit case is discussed and argued that the distance to the W states is a
new monotone.Comment: 7 pages, 1 figures, minor content change, references added, 1 figure
adde
Poisson Algebra of Wilson Loops in Four-Dimensional Yang-Mills Theory
We formulate the canonical structure of Yang--Mills theory in terms of
Poisson brackets of gauge invariant observables analogous to Wilson loops. This
algebra is non--trivial and tractable in a light--cone formulation. For U(N)
gauge theories the result is a Lie algebra while for SU(N) gauge theories it is
a quadratic algebra. We also study the identities satsfied by the gauge
invariant observables. We suggest that the phase space of a Yang--Mills theory
is a co--adjoint orbit of our Poisson algebra; some partial results in this
direction are obtained.Comment: 32 Pages, 7 figures upon reques
Geometric Quantization and Two Dimensional QCD
In this article, we will discuss geometric quantization of 2d QCD with
fermionic and bosonic matter fields. We identify the respective large-N_c phase
spaces as the infinite dimensional Grassmannian and the infinite dimensional
Disc. The Hamiltonians are quadratic functions, and the resulting equations of
motion for these classical systems are nonlinear. In a previous publication,
the first author has shown that the linearization of the equations of motion
for the Grassmannian gave the `t Hooft equation. We will see that the
linearization in the bosonic case leads to the scalar analog of the `t Hooft
equation found by Tomaras.Comment: 46 pages, Latex, no figure
Deterministic Transformations of Multipartite Entangled States with Tensor Rank 2
Transformations involving only local operations assisted with classical
communication are investigated for multipartite entangled pure states having
tensor rank 2. All necessary and sufficient conditions for the possibility of
deterministically converting truly multipartite, rank-2 states into each other
are given. Furthermore, a chain of local operations that successfully achieves
the transformation has been identified for all allowed transformations. The
identified chains have two nice features: (1) each party needs to carry out at
most one local operation and (2) all of these local operations are also
deterministic transformations by themselves. Finally, it is found that there
are disjoint classes of states, all of which can be identified by a single real
parameter, which remain invariant under deterministic transformations.Comment: 27 pages, 1 figure; added new references and improved the
presentatio
Relations between Entropies Produced in Nondeterministic Thermodynamic Processes
Landauer's erasure principle is generalized to nondeterministic processes on
systems having an arbitrary number of non-symmetrical logical states. The
condition that the process is applied in the same way, irrespective of the
initial logical state, imposes some restrictions on the individual heat
exchanges associated with each possible transition. The complete set of such
restrictions are derived by a statistical analysis of the phase-space flow
induced by the process. Landauer's erasure principle can be derived from and is
a special case of these.Comment: 12 pages with one figure; a final major revision in presentation;
physical assumptions are clarified no
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