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

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• Fundamental limits on quantum cloning from the no-signalling principle
• Universal adjointation of isometry operations using conversion of quantum supermaps
• Experimental replication of single-qubit quantum phase gates
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• Virtual Cloning of Quantum States