Marco Túlio QUINTINO

Higher-order quantum operations is a paradigm where operations, such as quantum channels and unitary gates, play the role of a quantum states and are viewed as objects which may be subjected to transformations. In this talk, we show how the framework of higher-order quantum operations provide powerful mathematical methods to tackle several problems in quantum information. We will conduct our talk following two motivating and recurring examples, the problem of designing quantum circuits for inverting an arbitrary unitary operation and how to computationally tackle different strategies for discriminating quantum operations. In the end of the talk, we will also discuss the constraints imposed by causality and how strategies without a definite causal order may be used as a resource in quantum information processing.

This talk will cover results from various papers, such as:

https://arxiv.org/abs/1810.06944
https://arxiv.org/abs/2011.08300
https://arxiv.org/abs/2109.08202
https://arxiv.org/abs/2206.00107