Reversing unknown quantum transformations: A universal protocol for inverting general unitary operations

Reversing unknown quantum transformations: A universal protocol for inverting general unitary operations

Seminar author:Marco Túlio Quintino

Event date and time:07/10/2019 12:00:pm

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Given a general d-dimensional unitary operation 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? How does the situation change when k uses of unitary operation  are allowed? In this paper we show that any universal protocol implementing the inverse of a general unitary with a positive heralded probability requires at least d−1 uses of this unitary. 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 k<d−1 uses. However we show via a general semidefinite programming that protocols with indefinite causal order attain a higher success probability when k>d−1. We will 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.