Entangling capability of multivalued bipartite gates and optimal preparation of multivalued bipartite quantum states

Entangling capability of multivalued bipartite gates and optimal preparation of multivalued... We investigate the entangling capability of various types of two-qudit gates in both the no-ancilla case and the ancilla-assisted case. The investigation involves controlled $$U$$ U gates, uniformly controlled $$U$$ U gates and some high-rank two-qudit gates. The optimal input states for these gates to generate entanglement are also given. By comparison of some important two-qudit gates, the generalized controlled $$X$$ X (GCX) gate shows the excellent properties. Based on the GCX gate, we study the preparation of arbitrary two-qudit quantum states and the transformation of such states. Any two-qudit state with Schmidt number $$k$$ k can be prepared from a product state by using $$k-1$$ k - 1 GCX gates, and any two-qudit state can be transformed into any other by using at most $$d-1$$ d - 1 GCX gates. The result reveals that using multivalued quantum systems has obviously advantages over the binary systems in these respects. The best known result for a four-qubit state preparation is that it needs at most nine CNOT gates. A two-ququart state ( $$d=4$$ d = 4 ) corresponds to a four-qubit state; its preparation and transformation only need at most three GCX gates. Using other gates as the two-qudit elementary gate of multivalued quantum computing, the advantages no longer hold. This once again illustrates that it is reasonable to choose the GCX gate as the two-qudit elementary gate of multivalued quantum computing. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Entangling capability of multivalued bipartite gates and optimal preparation of multivalued bipartite quantum states

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Publisher
Springer US
Copyright
Copyright © 2015 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/s11128-015-0955-7
Publisher site
See Article on Publisher Site

Abstract

We investigate the entangling capability of various types of two-qudit gates in both the no-ancilla case and the ancilla-assisted case. The investigation involves controlled $$U$$ U gates, uniformly controlled $$U$$ U gates and some high-rank two-qudit gates. The optimal input states for these gates to generate entanglement are also given. By comparison of some important two-qudit gates, the generalized controlled $$X$$ X (GCX) gate shows the excellent properties. Based on the GCX gate, we study the preparation of arbitrary two-qudit quantum states and the transformation of such states. Any two-qudit state with Schmidt number $$k$$ k can be prepared from a product state by using $$k-1$$ k - 1 GCX gates, and any two-qudit state can be transformed into any other by using at most $$d-1$$ d - 1 GCX gates. The result reveals that using multivalued quantum systems has obviously advantages over the binary systems in these respects. The best known result for a four-qubit state preparation is that it needs at most nine CNOT gates. A two-ququart state ( $$d=4$$ d = 4 ) corresponds to a four-qubit state; its preparation and transformation only need at most three GCX gates. Using other gates as the two-qudit elementary gate of multivalued quantum computing, the advantages no longer hold. This once again illustrates that it is reasonable to choose the GCX gate as the two-qudit elementary gate of multivalued quantum computing.

Journal

Quantum Information ProcessingSpringer Journals

Published: Feb 27, 2015

References

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