entangled states. We construct sets of fewer than d orthogonal maximally entangled states which are not distinguished by one-way local operations and classical communication (LOCC) in the Hilbert space of d ⊗ d. The proof, based on the Fourier transform of an additive group, is very simple but quite effective. Simultaneously, our results give a general unified upper bound for the minimum number of one-way LOCC indistinguishable maximally entangled states. This improves previous results which only showed sets of N  d − 2 such states. Finally, our results also show that previous conjectures in Zhang et al. [Z.-C. Zhang, Q.-Y. Wen, F. Gao, G.-J. Tian, and T.-Q. Cao, Quant. Info. Proc. 13, 795 (2014)] are indeed correct.

The purpose of this paper is to solve a problem posed by Strominger in constructing smooth models of superstring theory with flux. These are given by non-K¨ahler manifolds with torsion

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Connected sequences of functors whose domain, is the category of morphisms of an arbitrary abelian category$A$and whose range category$B$is also abelian are compared with the composition functors of Eckmann and Hilton acting between the same categories Sequences of functors of both types are obtained from any half-exact functor$A→B$if$A$has enough injectives and projectives.

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