154 research outputs found
Positive-partial-transpose distinguishability for lattice-type maximally entangled states
We study the distinguishability of a particular type of maximally entangled
states -- the "lattice states" using a new approach of semidefinite program.
With this, we successfully construct all sets of four ququad-ququad orthogonal
maximally entangled states that are locally indistinguishable and find some
curious sets of six states having interesting property of distinguishability.
Also, some of the problems arose from \cite{CosentinoR14} about the
PPT-distinguishability of "lattice" maximally entangled states can be answered.Comment: It's rewritten. We deleted the original section II about
PPT-distinguishability of three ququad-ququad MESs. Moreover, we have joined
new section V which discuss PPT-distinguishability of lattice MESs for cases
and . As a result, the sequence of the theorems in our article
has been changed. And we revised the title of our articl
Local indistinguishability: more nonlocality with less entanglement
We provide a first operational method for checking indistinguishability of
orthogonal states by local operations and classical communication (LOCC). This
method originates from the one introduced by Ghosh et al. (Phys. Rev. Lett. 87,
5807 (2001) (quant-ph/0106148)), though we deal with pure states. We apply our
method to show that an arbitrary complete multipartite orthogonal basis is
indistinguishable by LOCC, if it contains at least one entangled state. We also
show that probabilistic local distinguishing is possible for full basis if and
only if all vectors are product. We employ our method to prove local
indistinguishability in an example with sets of pure states of 3X3, which shows
that one can have ``more nonlocality with less entanglement'', where ``more
nonlocality'' is in the sense of ``increased local indistinguishability of
orthogonal states''. This example also provides, to our knowledge, the only
known example where d orthogonal states in dXd are locally indistinguishable.Comment: 4 pages, no figures, RevTeX4, partially supersedes quant-ph/0204116,
to appear in Phys. Rev. Let
Distinguishing Bipartitite Orthogonal States using LOCC: Best and Worst Cases
Two types of results are presented for distinguishing pure bipartite quantum
states using Local Operations and Classical Communications. We examine sets of
states that can be perfectly distinguished, in particular showing that any
three orthogonal maximally entangled states in C^3 tensor C^3 form such a set.
In cases where orthogonal states cannot be distinguished, we obtain upper
bounds for the probability of error using LOCC taken over all sets of k
orthogonal states in C^n tensor C^m. In the process of proving these bounds, we
identify some sets of orthogonal states for which perfect distinguishability is
not possible.Comment: 22 pages, published version. Some proofs rewritten for clarit
- …