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Higher-Order Quantum Operations

Mar 12, 2025

106 pages

e-Print:

2503.09693 [quant-ph]

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Abstract: (arXiv)

An operational description of quantum phenomena concerns developing models that describe experimentally observed behaviour. \textit{Higher-order quantum operations}\unicode{x2014}quantum operations that transform quantum operations\unicode{x2014}are fundamental to modern quantum theory, extending beyond basic state preparations, evolutions, and measurements described by the Born rule. These operations naturally emerge in quantum circuit architectures, correlated open dynamics, and investigations of quantum causality, to name but a few fields of application. This Review Article provides both a pedagogical introduction to the framework of higher-order quantum operations and a comprehensive survey of current literature, illustrated through physical examples. We conclude by identifying open problems and future research directions in this rapidly evolving field.

Note:

106 page Review Article (65 pages Tutorial, 41 pages Review) including 566 references. Comments welcome!

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