23,610 research outputs found
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}
Research investigation directed toward extending the useful range of the electromagnetic spectrum Progress report, 1 May - 31 Oct. 1968
Microwave frequency probes of ionized helium, rubidium lasers, cesium spectrum, and ruby crystal
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
A new class of entanglement measures
We introduce new entanglement measures on the set of density operators on
tensor product Hilbert spaces. These measures are based on the greatest cross
norm on the tensor product of the sets of trace class operators on Hilbert
space. We show that they satisfy the basic requirements on entanglement
measures discussed in the literature, including convexity, invariance under
local unitary operations and non-increase under local quantum operations and
classical communication.Comment: Revised version accepted by J Math Phys, 12 pages, LaTeX, contains
Sections 1-5 & 7 of the previous version. The previous Section 6 is now in
quant-ph/0105104 and the previous Section 8 is superseded by quant-ph/010501
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
Remote information concentration using a bound entangled state
Remote information concentration, the reverse process of quantum telecloning,
is presented. In this scheme, quantum information originally from a single
qubit, but now distributed into three spatially separated qubits, is remotely
concentrated back to a single qubit via an initially shared entangled state
without performing any global operations. This entangled state is an unlockable
bound entangled state and we analyze its properties.Comment: 4 pages, 2 figure
Entanglement sharing among qudits
Consider a system consisting of n d-dimensional quantum particles (qudits),
and suppose that we want to optimize the entanglement between each pair. One
can ask the following basic question regarding the sharing of entanglement:
what is the largest possible value Emax(n,d) of the minimum entanglement
between any two particles in the system? (Here we take the entanglement of
formation as our measure of entanglement.) For n=3 and d=2, that is, for a
system of three qubits, the answer is known: Emax(3,2) = 0.550. In this paper
we consider first a system of d qudits and show that Emax(d,d) is greater than
or equal to 1. We then consider a system of three particles, with three
different values of d. Our results for the three-particle case suggest that as
the dimension d increases, the particles can share a greater fraction of their
entanglement capacity.Comment: 4 pages; v2 contains a new result for 3 qudits with d=
Extracting Classical Correlations from a Bipartite Quantum System
In this paper we discuss the problem of splitting the total correlations for
a bipartite quantum state described by the Von Neumann mutual information into
classical and quantum parts. We propose a measure of the classical correlations
as the difference between the Von Neumann mutual information and the relative
entropy of entanglement. We compare this measure with different measures
proposed in the literature.Comment: 5 pages, 1 figur
Entanglement splitting of pure bipartite quantum states
The concept of entanglement splitting is introduced by asking whether it is
possible for a party possessing half of a pure bipartite quantum state to
transfer some of his entanglement with the other party to a third party. We
describe the unitary local transformation for symmetric and isotropic splitting
of a singlet into two branches that leads to the highest entanglement of the
output. The capacity of the resulting quantum channels is discussed. Using the
same transformation for less than maximally entangled pure states, the
entanglement of the resulting states is found. We discuss whether they can be
used to do teleportation and to test the Bell inequality. Finally we generalize
to entanglement splitting into more than two branches.Comment: 6 pages, 2 figures, extended version, to be published in Phys. Rev.
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