Deterministic superreplication of one-parameter unitary transformations

TL;DR

This paper demonstrates that it is possible to deterministically produce up to quadratically more copies of an unknown unitary operation from a limited number of initial copies, with broad applicability and without probabilistic success constraints.

Contribution

It introduces a method for deterministic super-replication of one-parameter unitary transformations, extending previous probabilistic results to a deterministic framework.

Findings

Up to N^2 almost perfect copies can be generated from N initial copies.

The method applies to all operations generated by a Hamiltonian with unknown interaction strength.

Multiple copies of unitaries can be emulated by operations on smaller systems.

Abstract

We show that one can deterministically generate out of $N$ copies of an unknown unitary operation up to $N^2$ almost perfect copies. The result holds for all operations generated by a Hamiltonian with an unknown interaction strength. This generalizes a similar result in the context of phase covariant cloning where, however, super-replication comes at the price of an exponentially reduced probability of success. We also show that multiple copies of unitary operations can be emulated by operations acting on a much smaller space, e.g., a magnetic field acting on a single $n$-level system allows one to emulate the action of the field on $n^2$ qubits.