238,473 research outputs found
Two-qubit mixed states and teleportation fidelity: Purity, concurrence, and beyond
To explore the properties of a two-qubit mixed state, we consider quantum
teleportation. The fidelity of a teleported state depends on the resource state
purity and entanglement, as characterized by concurrence. Concurrence and
purity are functions of state parameters. However, it turns out that a state
with larger purity and concurrence, may have comparatively smaller fidelity. By
computing teleportation fidelity, concurrence and purity for two-qubit
X-states, we show it explicitly. We further show that fidelity changes
monotonically with respect to functions of parameters - other than concurrence
and purity. A state with smaller concurrence and purity, but larger value of
one of these functions has larger fidelity. These functions, thus characterize
nonlocal classical and/or quantum properties of the state that are not captured
by purity and concurrence alone. In particular, concurrence is not enough to
characterize the entanglement properties of a two-qubit mixed state
Mixed State Entanglement of Assistance and the Generalized Concurrence
We consider the maximum bipartite entanglement that can be distilled from a
single copy of a multipartite mixed entangled state, where we focus mostly on
-dimensional tripartite mixed states. We show that this {\em
assisted entanglement}, when measured in terms of the generalized concurrence
(named G-concurrence) is (tightly) bounded by an entanglement monotone, which
we call the G-concurrence of assistance. The G-concurrence is one of the
possible generalizations of the concurrence to higher dimensions, and for pure
bipartite states it measures the {\em geometric mean} of the Schmidt numbers.
For a large (non-trivial) class of -dimensional mixed states, we are
able to generalize Wootters formula for the concurrence into lower and upper
bounds on the G-concurrence. Moreover, we have found an explicit formula for
the G-concurrence of assistance that generalizes the expression for the
concurrence of assistance for a large class of dimensional
tripartite pure states.Comment: 7 page
Family of Concurrence Monotones and its Applications
We extend the definition of concurrence into a family of entanglement
monotones, which we call concurrence monotones. We discuss their properties and
advantages as computational manageable measures of entanglement, and show that
for pure bipartite states all measures of entanglement can be written as
functions of the concurrence monotones. We then show that the concurrence
monotones provide bounds on quantum information tasks. As an example, we
discuss their applications to remote entanglement distributions (RED) such as
entanglement swapping and remote preparation of bipartite entangled states
(RPBES). We prove a powerful theorem which states what kind of (possibly mixed)
bipartite states or distributions of bipartite states can not be remotely
prepared. The theorem establishes an upper bound on the amount of
-concurrence (one member in the concurrence family) that can be created
between two single-qudit nodes of quantum networks by means of tripartite RED.
For pure bipartite states the bound on the -concurrence can always be
saturated by RPBES.Comment: 8 page
Relation between two measures of entanglement in spin-1/2 and spinless fermion quantum chain systems
The concepts of concurrence and mode concurrence are the measures of
entanglement for spin-1/2 and spinless fermion systems respectively. Based on
the Jordan-Wigner transformation, any spin-1/2 system is always associated with
a fermion system (called counterpart system). The comparison of concurrence and
mode concurrence can be made with the aid of the Marshall's sign rule for the
ground states of spin-1/2 and spinless fermion chain systems. We observe
that there exists an inequality between concurrence and mode concurrence for
the ground states of the two corresponding systems. The spin-1/2 XY chain
system and its spinless fermion counterpart as a realistic example is discussed
to demonstrate the analytical results.Comment: 7 pages, no figures, publication version, to appear in PR
Concurrence for multipartite states
We construct a generalized concurrence for general multipartite states based
on local W-class and GHZ-class operators. We explicitly construct the
corresponding concurrence for three-partite states. The construction of the
concurrence is interesting since it is based on local operators.Comment: 5 page
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