Diagonal unitary covariant superchannels
Dariusz Chruściński, Vivek Pandey, Sohail
Source abstract
We present a complete characterization of diagonal unitary covariant (DU-covariant) superchannels, i.e., higher-order transformations transforming quantum channels into themselves. Necessary and sufficient conditions for complete positivity and trace preservation are derived and the canonical decomposition describing DU-covariant superchannels is provided. The presented framework unifies and extends known families of covariant quantum channels and enables explicit analysis of their action on physically relevant examples, including amplitude-damping, bit-flip, and Pauli channels. Our results provide a practical toolbox for symmetry-restricted higher-order quantum processes and offer a setting for exploring open problems such as the celebrated positive partial transpose-squared conjecture.
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