Nice Error Basis and Quantum Channel

Article Type

Research Article

Publication Title

Open Systems and Information Dynamics

Abstract

The Weyl operators give a convenient basis of Mn(C) which is also orthonormal with respect to the Hilbert-Schmidt inner product. The properties of such a basis can be generalised to the notion of a nice error basis (NEB), as introduced by E. Knill [3]. We can use an NEB of Mn(C) to construct an NEB for Lin(Mn(C)), the space of linear maps on Mn(C). Any linear map will then correspond to a n2 × n2 coefficient matrix in the basis decomposition with respect to such an NEB of Lin(Mn(C)). Positivity, complete (co)positivity or other properties of a linear map can be characterised in terms of such a coefficient matrix

DOI

10.1142/S1230161224500033

Publication Date

3-1-2024

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