We study unextendible maximally entangled bases (UMEBs) in (d < d′). An operational method to construct UMEBs containing d(d′ − 1) maximally entangled vectors is established, and two UMEBs in and are given as examples. Furthermore, a systematic way of constructing UMEBs containing d(d′ − r) maximally entangled vectors in is presented for r = 1, 2, …, d − 1. Correspondingly, two UMEBs in are obtained.
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