Quantum Inf Process (2015) 14:1997–2012
Entangling capability of multivalued bipartite gates
and optimal preparation of multivalued bipartite
Yao-Min Di · Hai-Rui Wei · Ya Cao · Li Liu ·
Received: 22 September 2014 / Accepted: 18 February 2015 / Published online: 27 February 2015
© Springer Science+Business Media New York 2015
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.
Keywords Entangling capability · Multivalued quantum gate · GCX gate ·
State preparation · Multivalued quantum state
Y.- M. D i (
) · H.-R. Wei · Y. Ca o · L. Liu · C.-H. Zhou
School of Physics and Electronic Engineering, Jiangsu Normal University,
Xuzhou 221116, China
Department of Physics, Beijing Normal University, Beijing 100875, China