Ancilla-assisted discrimination of quantum gates

  • Authors:

  • Jianxin Chen;Mingsheng Ying

  • Affiliations:

  • State Key Laboratory of Intelligent Technology and Systems, Department of Computer Science and Technology, Tsinghua University, Beijing, China;State Key Laboratory of Intelligent Techn. and Systems, Department of Computer Science and Techn., Tsinghua Univ., Beijing, China and Center for Quantum Computation and Intelligent Systems, Facult ...

  • Venue:
  • Quantum Information & Computation
  • Year:
  • 2010

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Abstract

The intrinsic idea of superdense coding is to find as many gates as possible such thatthey can be perfectly discriminated. In this paper, we consider a basic scheme of dis-crimination of quantum gates, called ancilla-assisted discrimination, in which a set ofquantum gates on a d-dimensional system are perfectly discriminated with assistancefrom an r-dimensional ancilla system. The main contribution of the present paper istwo-fold: (1) The number of quantum gates that can be discriminated in this scheme isevaluated. We prove that any rd + 1 quantum gates cannot be perfectly discriminatedwith assistance from the ancilla, and there exist rd quantum gates which can be perfectlydiscriminated with assistance from the ancilla. (2) The dimensionality of the minimalancilla system is estimated. We prove that there exists a constant positive number c suchthat for any k ≤ cr quantum gates, if they are d-assisted discriminable, then they arealso r-assisted discriminable, and there are c'r (c' c) different quantum gates whichcan be discriminated with a d-dimensional ancilla, but they cannot be discriminated ifthe ancilla is reduced to an r-dimensional system. Thus, the order O(r) of the numberof quantum gates that can be discriminated with assistance from an r-dimensional an-cilla is optimal. The results reported in this paper represent a preliminary step towardunderstanding the role ancilla system plays in discrimination of quantum gates as wellas the power and limit of superdense coding.