LOCC distinguishability of unilaterally transformable quantum states

We consider the question of perfect local distinguishability of mutually orthogonal bipartite quantum states, with the property that every state can be specified by a unitary operator acting on the local Hilbert space of Bob. We show that if the states can be exactly discriminated by one-way LOCC where Alice goes first, then the unitary operators can also be perfectly distinguished by an orthogonal measurement on Bob's Hilbert space. We give examples of sets of N<=d maximally entangled states in $d \otimes d$ for d=4,5,6 that are not perfectly distinguishable by one-way LOCC. Interestingly for d=5,6 our examples consist of four and five states respectively. We conjecture that these states cannot be perfectly discriminated by two-way LOCC.Comment: Revised version, new proofs added; to appear in New Journal of Physic

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 $t=3$ and $t=4$ . 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