4 Approximate Quantum Cloning
Dagmar Bruß and Chiara Macchiavello
Heinrich‐Heine‐Universität Düsseldorf, Institut für Theoretische Physik III, Universitätsstr. 1, D‐40225 Düsseldorf, Germany
Università degli Studi di Pavia, Dipartimento di Fisica and INFN‐Sezione di Pavia, Via Bassi 6, I‐27100 Pavia, Italy
4.1 Introduction
Perfect cloning of quantum states that are a priori unknown is forbidden by the laws of quantum mechanics (1–3). Perfect cloning is only possible when the input states belong to a known set of orthogonal states. For example, the Controlled‐NOT quantum gate (4), which operates as follows on two qubits (two‐level systems):
where denotes addition modulo two and represent basis states for each qubit, ...
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