53,528 research outputs found
The trumping relation and the structure of the bipartite entangled states
The majorization relation has been shown to be useful in classifying which
transformations of jointly held quantum states are possible using local
operations and classical communication. In some cases, a direct transformation
between two states is not possible, but it becomes possible in the presence of
another state (known as a catalyst); this situation is described mathematically
by the trumping relation, an extension of majorization. The structure of the
trumping relation is not nearly as well understood as that of majorization. We
give an introduction to this subject and derive some new results. Most notably,
we show that the dimension of the required catalyst is in general unbounded;
there is no integer such that it suffices to consider catalysts of
dimension or less in determining which states can be catalyzed into a given
state. We also show that almost all bipartite entangled states are potentially
useful as catalysts.Comment: 7 pages, RevTe
The Power of LOCCq State Transformations
Reversible state transformations under entanglement non-increasing operations
give rise to entanglement measures. It is well known that asymptotic local
operations and classical communication (LOCC) are required to get a simple
operational measure of bipartite pure state entanglement. For bipartite mixed
states and multipartite pure states it is likely that a more powerful class of
operations will be needed. To this end \cite{BPRST01} have defined more
powerful versions of state transformations (or reducibilities), namely LOCCq
(asymptotic LOCC with a sublinear amount of quantum communication) and CLOCC
(asymptotic LOCC with catalysis). In this paper we show that {\em LOCCq state
transformations are only as powerful as asymptotic LOCC state transformations}
for multipartite pure states. We first generalize the concept of entanglement
gambling from two parties to multiple parties: any pure multipartite entangled
state can be transformed to an EPR pair shared by some pair of parties and that
any irreducible party pure state can be used to create any other
state (pure or mixed), using only local operations and classical communication
(LOCC). We then use this tool to prove the result. We mention some applications
of multipartite entanglement gambling to multipartite distillability and to
characterizations of multipartite minimal entanglement generating sets. Finally
we discuss generalizations of this result to mixed states by defining the class
of {\em cat distillable states}
Laser-like Instabilities in Quantum Nano-electromechanical Systems
We discuss negative damping regimes in quantum nano-electromechanical systems
formed by coupling a mechanical oscillator to a single-electron transistor
(normal or superconducting). Using an analogy to a laser with a tunable
atom-field coupling, we demonstrate how these effects scale with system
parameters. We also discuss the fluctuation physics of both the oscillator and
the single-electron transistor in this regime, and the degree to which the
oscillator motion is coherent.Comment: 4+ pages, 1 figure; reference to the work of Dykman and Krivoglaz
adde
Entanglement of pure states for a single copy
An optimal local conversion strategy between any two pure states of a
bipartite system is presented. It is optimal in that the probability of success
is the largest achievable if the parties which share the system, and which can
communicate classically, are only allowed to act locally on it. The study of
optimal local conversions sheds some light on the entanglement of a single copy
of a pure state. We propose a quantification of such an entanglement by means
of a finite minimal set of new measures from which the optimal probability of
conversion follows.Comment: Revtex, 4 pages, no figures. Minor changes. Appendix remove
An improved bound on distillable entanglement
The best bound known on 2-locally distillable entanglement is that of Vedral
and Plenio, involving a certain measure of entanglement based on relative
entropy. It turns out that a related argument can be used to give an even
stronger bound; we give this bound, and examine some of its properties. In
particular, and in contrast to the earlier bounds, the new bound is not
additive in general. We give an example of a state for which the bound fails to
be additive, as well as a number of states for which the bound is additive.Comment: 14 pages, no figures. A significant erratum in theorems 4 and 5 has
been fixe
Irreversibility in asymptotic manipulations of entanglement
We show that the process of entanglement distillation is irreversible by
showing that the entanglement cost of a bound entangled state is finite. Such
irreversibility remains even if extra pure entanglement is loaned to assist the
distillation process.Comment: RevTex, 3 pages, no figures Result on indistillability of PPT states
under pure entanglement catalytic LOCC adde
A Measure of Stregth of an Unextendible Product Basis
A notion of strength of an unextendible product basis is introduced and a
quantitative measure for it is suggested with a view to providing an indirect
measure for the bound entanglement of formation of the bound entangled mixed
state associated with an unextendible product basis.Comment: 4 pages, Latex, 1 figure, remarks, criticisms welcom
Mixedness and teleportation
We show that on exceeding a certain degree of mixedness (as quantified by the
von Neumann entropy), entangled states become useless for teleporatation. By
increasing the dimension of the entangled systems, this entropy threshold can
be made arbitrarily close to maximal. This entropy is found to exceed the
entropy threshold sufficient to ensure the failure of dense coding.Comment: 6 pages, no figure
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