Ancilla-assisted discrimination of quantum gates

Abstract

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 basic 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}rc^{\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.

Distinguishing unitary gates on the IBM quantum processor

“…The discrimination of quantum operations asks to identify an unknown quantum operation from a set of known ones. As a fundamental task in quantum information and computation, many interesting aspects have been discovered over the last two decades, see [1][2][3][4][5][6][7][8][9] (and references therein) for a partial list. As applications, the discrimination of quantum operations plays important roles in the design of classical data hiding protocols [5] and the study of quantum reading capacity [10].…”

Optimal Perfect Distinguishability between Unitaries and Quantum Operations

“…Although perfect distinguishability between quantum states is completely characterized by orthogonality, perfect distinguishability of quantum operations is sharply different [1]. Consequently, the problem arouses people's great interests and a series of results are obtained [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19], especially [5,6,7,15,16,17,18] solve perfect distinguishability between unitaries and [19] solves perfect distinguishability between projective measurements.…”