Higher-Order Quantum Operations

• URL: http://arxiv.org/abs/2503.09693v1
• Date: Wed, 12 Mar 2025 18:00:01 GMT
• Title: Higher-Order Quantum Operations
• Authors: Philip Taranto, Simon Milz, Mio Murao, Marco Túlio Quintino, Kavan Modi,
• Abstract summary: Outline of quantum operational models that describe experimentally observed quantum phenomena.<n>Describes higher-order quantum operations that transform quantum behaviour.<n> provides a few application fields.
• Score: 1.2815904071470703
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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