LAUSR

The construction of unextendible maximally entangled bases is tightly related to quantum information processing like local state discrimination. We put forward two constructions of UMEBs in $${\mathbb {C}}^{pd}\otimes {\mathbb {C}}^{qd}$$Cpd⊗Cqd($$p\le q$$p≤q) based on the constructions of UMEBs in $${\mathbb {C}}^{d}\otimes {\mathbb {C}}^{d}$$Cd⊗Cd and in $${\mathbb {C}}^{p}\otimes {\mathbb {C}}^{q}$$Cp⊗Cq, which generalizes the results in Guo (Phys Rev A 94:052302, 2016) by two approaches. Two different 48-member UMEBs in $${\mathbb {C}}^{6}\otimes {\mathbb {C}}^{9}$$C6⊗C9 have been constructed in detail.