Talk by Mio Murao, Tue. Feb. 19, 11 am at the IQOQI seminar room

Higher order quantum operations of blackbox unitaries and causal structure of the blackboxes

Supermaps are functions taking maps as input.  Quantum mechanically implementable supermaps are called quantum supermaps and their general properties are formulated by the framework of quantum networks and quantum combs proposed by Chiribella et al. We consider the implementability of supermaps in quantum mechanics when the input maps are unitaries given as blackboxes and the unitary blackboxes can be used multiple but finite times. We regard such direct implementations of supermaps for blackbox quantum operations with multiple uses of the blackboxes as higher order quantum operations.  We investigate how the causal structure of these unitary blackboxes affects their performance in implementing higher order quantum operations.  We analyze two tasks, inversion of blackbox unitaries and controllization of divisible blackbox unitaries.  We study three types of causal structure of blackboxes, parallel, sequential and indefinite causal order.