Creating Maximally Entangled States by Gluing

We introduce a general method of gluing multi-partite states and show that entanglement swapping is a special class of a wider range of gluing operations. The gluing operation of two m and n qudit states consists of an entangling operation on two given qudits of the the two states followed by operations of measurements of the two qudits in the computational basis. Depending on how many qudits (two, one or zero) we measure, we have three classes of gluing operation, resulting respectively in m+n-2, m+n-1 or m+n qudit states. Entanglement swapping belongs to the first class and has been widely studied, while the other two classes are presented and studied here. In particular we study how larger GHZ and W states can be constructed when we glue the smaller GHZ and W states by the second method. Finally we prove that when we glue two states by the third method, the k-uniformity of the states is preserved. That is when a k-uniform state of m qudits is glued to a k'-uniform state of n qudits, the resulting state will be a min(k,k')-uniform of m+n qudits.