Deterministic superreplication of one-parameter unitary transformations

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.

4 pages, 2 figures. The title has changed from Deterministic Super-replication of unitary operators to Deterministic Superreplication of One-Parameter Unitary Transformations to reflect the title of the published version. Version 2 is the published version

References in corpus (2)

• Optimal cloning of unitary transformations
• Universal super-replication of unitary gates

Cited by in corpus (1)

• Universal super-replication of unitary gates