Error Basis and Quantum Channel

B. V. Rajarama Bhat; Purbayan Chakraborty; Uwe Franz

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arXiv · 2305.14274

Error Basis and Quantum Channel

B. V. Rajarama Bhat·Purbayan Chakraborty·Uwe Franz

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Abstract

The Weyl operators give a convenient basis of $M_n(\mathbb{C})$ 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 $M_n(\mathbb{C})$ to construct an NEB for $Lin(M_n(\mathbb{C}))$, the space of linear maps on $M_n(\mathbb{C})$. Any linear map on $M_n(\mathbb{C})$ will then correspond to a $n^2\times n^2$ coefficient matrix in the basis decomposition with respect to such an NEB of $Lin(M_n(\mathbb{C}))$. Positivity, complete (co)positivity or other properties of a linear map can be characterised in terms of such a coefficient matrix.

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B. V. Rajarama Bhat, Purbayan Chakraborty, Uwe Franz. 2023-05-23. Error Basis and Quantum Channel. https://arxiv.org/abs/2305.14274

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