# Creating maximally entangled states by gluing

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 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 - 2 , $$m+n-1$$ m + n - 1 , or $$m+n$$ 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 $$k'$$ k ′ -uniform state of n qudits, the resulting state will be a $$\hbox {min}(k,k')$$ min ( k , k ′ ) -uniform of $$m+n$$ m + n qudits. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

# Creating maximally entangled states by gluing

, Volume 16 (3) – Feb 9, 2017
16 pages
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Publisher
Springer US
Copyright
Copyright © 2017 by Springer Science+Business Media New York
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-017-1535-9
Publisher site
See Article on Publisher Site

### Abstract

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 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 - 2 , $$m+n-1$$ m + n - 1 , or $$m+n$$ 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 $$k'$$ k ′ -uniform state of n qudits, the resulting state will be a $$\hbox {min}(k,k')$$ min ( k , k ′ ) -uniform of $$m+n$$ m + n qudits.

### Journal

Quantum Information ProcessingSpringer Journals

Published: Feb 9, 2017

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