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.