2023/05/23 by B. V. Rajarama Bhat, Bhat, B. V. Rajarama, Purbayan Chakraborty +3
Computer Science · Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Matrix Theory and Algorithms #Operator Algebras (math.OA) #Quantum Physics (quant-ph) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2305.14274
openalex publication_date 2023/05/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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. 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 on Mn(ℂ) 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.