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Generalized qudit Choi maps
Following the linear programming prescription of Ref. \cite{PRA72}, the
Bell diagonal entanglement witnesses are provided. By using
Jamiolkowski isomorphism, it is shown that the corresponding positive maps are
the generalized qudit Choi maps. Also by manipulating particular
Bell diagonal separable states and constructing corresponding bound entangled
states, it is shown that thus obtained BDEW's (consequently qudit
Choi maps) are non-decomposable in certain range of their parameters.Comment: 22 page
Simulation of Gaussian channels via teleportation and error correction of Gaussian states
Gaussian channels are the typical way to model the decoherence introduced by
the environment in continuous-variable quantum states. It is known that those
channels can be simulated by a teleportation protocol using as a resource state
either a maximally entangled state passing through the same channel, i.e., the
Choi-state, or a state that is entangled at least as much as the Choi-state.
Since the construction of the Choi-state requires infinite mean energy and
entanglement, i.e. it is unphysical, we derive instead every physical state
able to simulate a given channel through teleportation with finite resources,
and we further find the optimal ones, i.e., the resource states that require
the minimum energy and entanglement. We show that the optimal resource states
are pure and equally entangled to the Choi-state as measured by the
entanglement of formation. We also show that the same amount of entanglement is
enough to simulate an equally decohering channel, while even more entanglement
can simulate less decohering channels. We, finally, use that fact to generalize
a previously known error correction protocol by making it able to correct noise
coming not only from pure loss but from thermal loss channels as well.Comment: 12 pages, 8 figure
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