2:28 p.m.
Dear friends,
This Thursday at 11:00 in D5.01 we will be visited by Yelena Guryanova, who will give a
talk about cloning quantum channels. Title and abstract below.
Hope to see you there,
Will Schober
Title: Cloning Quantum Channels
Abstract: We consider the problem of deterministically cloning quantum channels with
respect to the best attainable rate and the highest quality, so-called optimal cloning. We
demonstrate that cloning quantum states is, in-fact, equivalent to cloning the
trash-and-replace channel and therefore the former is a special case of the more general
problem. By appealing to higher-order quantum operations (quantum processes) we construct
a unified framework to deal with the most general cloning tasks and establish necessary
conditions for a family of channels to exhibit super-replication -- a quadratic cloning
rate with vanishing error. We find that noisy phase-gate channels satisfy these
conditions, and we construct the explicit super-replicating process for the task.
Conversely, we find that the criteria are not met by the full set of noisy unitary gates;
classical noise channels; or amplitude damping channels, whose respective cloning rates
are at most linear. In this paradigm, we not only derive new results, but also refigure
known ones. We derive a strong converse for state cloning, and for unitary channels we
construct an alternative super-replication process to that of Dür et al. [PRL 114, 120503
(2015)] and Chiribella et al. [PRL 114, 120504 (2015)] based on a measure-and-prepare
process, which allows us to establish a direct connection between optimal channel cloning
and Bayesian channel estimation. Finally we give an SDP algorithm to search for optimal
cloning processes and study the advantage of coherent vs measure-and-prepare protocols on
concrete examples.