Characterization of two-qubit perfect entanglers
Abstract
Here we consider perfect entanglers from another perspective. It is shown that there are some special perfect entanglers which can maximally entangle a full product basis. We have explicitly constructed a one-parameter family of such entanglers together with the proper product basis that they maximally entangle. This special family of perfect entanglers contains some well-known operators such as cnot and dcnot, but not swap. In addition, it is shown that all perfect entanglers with entangling power equal to the maximal value, 2/9, are also special perfect entanglers. It is proved that the one-parameter family is the only possible set of special perfect entanglers. Also we provide an analytic way to implement any arbitrary two-qubit gate, given a proper special perfect entangler supplemented with single-qubit gates. Such these gates are shown to provide a minimum universal gate construction in that just two of them are necessary and sufficient in implementation of a generic two-qubit gate.
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