The intrinsic idea of superdense coding is to find as many gates as possible

such that they can be perfectly discriminated. In this paper, we consider a new

scheme of discrimination of quantum gates, called ancilla-assisted

discrimination, in which a set of quantum gates on a $d-$dimensional system are

perfectly discriminated with assistance from an $r-$dimensional ancilla system.

The main contribution of the present paper is two-fold: (1) The number of

quantum gates that can be discriminated in this scheme is evaluated. We prove

that any $rd+1$ quantum gates cannot be perfectly discriminated with assistance

from the ancilla, and there exist $rd$ quantum gates which can be perfectly

discriminated with assistance from the ancilla. (2) The dimensionality of the

minimal ancilla system is estimated. We prove that there exists a constant

positive number $c$ such that for any $k\leq cr$ quantum gates, if they are

$d$-assisted discriminable, then they are also $r$-assisted discriminable, and

there are $c^{\prime}r\textrm{}(c^{\prime}>c)$ different quantum gates which

can be discriminated with a $d-$dimensional ancilla, but they cannot be

discriminated if the ancilla is reduced to an $r-$dimensional system. Thus, the

order $O(r)$ of the number of quantum gates that can be discriminated with

assistance from an $r-$dimensional ancilla is optimal. The results reported in

this paper represent a preliminary step toward understanding the role ancilla

system plays in discrimination of quantum gates as well as the power and limit

of superdense coding.