642 research outputs found
Teleportation as a Depolarizing Quantum Channel, Relative Entropy and Classical Capacity
We show that standard teleportation with an arbitrary mixed state resource is
equivalent to a generalized depolarizing channel with probabilities given by
the maximally entangled components of the resource. This enables the usage of
any quantum channel as a generalized depolarizing channel without additional
twirling operations. It also provides a nontrivial upper bound on the
entanglement of a class of mixed states. Our result allows a consistent and
statistically motivated quantification of teleportation success in terms of the
relative entropy and this quantification can be related to a classical
capacity.Comment: Version published in Phys. Rev. Let
Unitarily localizable entanglement of Gaussian states
We consider generic -mode bipartitions of continuous variable
systems, and study the associated bisymmetric multimode Gaussian states. They
are defined as -mode Gaussian states invariant under local mode
permutations on the -mode and -mode subsystems. We prove that such states
are equivalent, under local unitary transformations, to the tensor product of a
two-mode state and of uncorrelated single-mode states. The entanglement
between the -mode and the -mode blocks can then be completely
concentrated on a single pair of modes by means of local unitary operations
alone. This result allows to prove that the PPT (positivity of the partial
transpose) condition is necessary and sufficient for the separability of -mode bisymmetric Gaussian states. We determine exactly their negativity and
identify a subset of bisymmetric states whose multimode entanglement of
formation can be computed analytically. We consider explicit examples of pure
and mixed bisymmetric states and study their entanglement scaling with the
number of modes.Comment: 10 pages, 2 figure
Entanglement Cost of Nonlocal Measurements
For certain joint measurements on a pair of spatially separated particles, we
ask how much entanglement is needed to carry out the measurement exactly. For a
class of orthogonal measurements on two qubits with partially entangled
eigenstates, we present upper and lower bounds on the entanglement cost. The
upper bound is based on a recent result by D. Berry [Phys. Rev. A 75, 032349
(2007)]. The lower bound, based on the entanglement production capacity of the
measurement, implies that for almost all measurements in the class we consider,
the entanglement required to perform the measurement is strictly greater than
the average entanglement of its eigenstates. On the other hand, we show that
for any complete measurement in d x d dimensions that is invariant under all
local Pauli operations, the cost of the measurement is exactly equal to the
average entanglement of the states associated with the outcomes.Comment: 14 pages; new result in v4: cost of an arbitrary measurement
invariant under local Pauli operation
Entanglement in continuous variable systems: Recent advances and current perspectives
We review the theory of continuous-variable entanglement with special
emphasis on foundational aspects, conceptual structures, and mathematical
methods. Much attention is devoted to the discussion of separability criteria
and entanglement properties of Gaussian states, for their great practical
relevance in applications to quantum optics and quantum information, as well as
for the very clean framework that they allow for the study of the structure of
nonlocal correlations. We give a self-contained introduction to phase-space and
symplectic methods in the study of Gaussian states of infinite-dimensional
bosonic systems. We review the most important results on the separability and
distillability of Gaussian states and discuss the main properties of bipartite
entanglement. These include the extremal entanglement, minimal and maximal, of
two-mode mixed Gaussian states, the ordering of two-mode Gaussian states
according to different measures of entanglement, the unitary (reversible)
localization, and the scaling of bipartite entanglement in multimode Gaussian
states. We then discuss recent advances in the understanding of entanglement
sharing in multimode Gaussian states, including the proof of the monogamy
inequality of distributed entanglement for all Gaussian states, and its
consequences for the characterization of multipartite entanglement. We finally
review recent advances and discuss possible perspectives on the qualification
and quantification of entanglement in non Gaussian states, a field of research
that is to a large extent yet to be explored.Comment: 61 pages, 7 figures, 3 tables; Published as Topical Review in J.
Phys. A, Special Issue on Quantum Information, Communication, Computation and
Cryptography (v3: few typos corrected
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