Theoretical framework for Higher-Order Quantum Theory

Understand

Higher-order quantum theory is an extension of quantum theory where one introduces transformations whose input and output are transformations, thus generalizing the notion of channels and quantum operations.

• The generalization then goes recursively, with the construction of a full hierarchy of maps of increasingly higher order.
• The analysis of special cases already showed that higher-order quantum functions exhibit features that cannot be tracked down to the usual circuits, such as indefinite causal structures, providing provable advantages over circuital maps.
• The present treatment provides a general framework where this kind of analysis can be carried out in full generality.