Quasi inversion of qubit channels

Abstract

Quantum operations, or quantum channels cannot be inverted in general. An arbitrary state passing through a quantum channel looses its fidelity with the input. Given a quantum channel $\mathcal{E}$, we introduce the concept of its quasi-inverse as a map ${\mathcal{E}}^{qi}$ which when composed with $\mathcal{E}$ increases its average input-output fidelity in an optimal way. The channel ${\mathcal{E}}^{qi}$ comes as close as possible to the inverse of a quantum channel. We give a complete classification of such maps for qubit channels and provide quite a few illustrative examples.

4+5 pages, 4 figures, a few corrections in arguments and improvements in presentation

Cited by in corpus (8)

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• Symmetries of quantum evolutions
• The Near-optimal Performance of Quantum Error Correction Codes
• Qubit noise deconvolution
• Quasi-inversion of quantum and classical channels in finite dimensions
• Protecting quantum correlations in presence of generalised amplitude damping channel: the two-qubit case
• Measurement sharpness and disturbance tradeoff
• Protecting an unknown qubit state by weak measurement