Given a general d-dimensional unitary operation Ud for which, apart from the dimension, its description is unknown, is it possible to implement its inverse operation with a universal protocol that works for every unitary Ud? How does the situation change when k uses of unitary operation Ud are allowed? In this talk we show that any universal protocol implementing the inverse of a general unitary Ud with a positive heralded probability requires at least d−1 uses of Ud. For the cases where k≥d−1 uses are accessible, we construct a parallel and sequential protocol, whose respective probability of failure decreases linearly and exponentially. We then analyse protocols with indefinite causal order. These more general protocols still cannot yield the inverse of a general d-dimensional unitary operation with kd−1. In this talk we also introduce the notion of delayed input-state protocols and provides a one-to-one correspondence between the unitary learning (unitary store and retrieve) problem and universal parallel protocols for unitary transposition.


Seminar, February 14, 2019, 12:00. ICFO’s Seminar Room

Hosted by Antonio Acín