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

Zeitschrift:: Quantum Information Processing > Ausgabe 6/2015

Autoren:: Yao-Min Di, Hai-Rui Wei, Ya Cao, Li Liu, Chun-Hong Zhou

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 \(U\) gates, uniformly controlled \(U\) 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 \(X\) (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 \(k\) can be prepared from a product state by using \(k-1\) GCX gates, and any two-qudit state can be transformed into any other by using at most \(d-1\) 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 (\(d=4\)) 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.

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Titel: Entangling capability of multivalued bipartite gates and optimal preparation of multivalued bipartite quantum states
Autoren:: Yao-Min Di
Hai-Rui Wei
Ya Cao
Li Liu
Chun-Hong Zhou
Publikationsdatum: 01.06.2015
DOI: https://doi.org/10.1007/s11128-015-0955-7
Verlag: Springer US
Zeitschrift: Quantum Information Processing
Ausgabe 6/2015
Print ISSN: 1570-0755
Elektronische ISSN: 1573-1332

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