Coherence and correlations represent two related properties of a compound system. The system can be, for instance, the polarization of a photon, which forms part of a polarization-entangled two-photon state, or the spatial shape of a coherent beam, where each spatial mode bears different polarizations. Whereas a local unitary transformation of the system does not affect its coherence, global unitary transformations modifying both the system and its surroundings can enhance its coherence, transforming mutual correlations into coherence. The question naturally arises of what is the best measure that quantifies the correlations that can be turned into coherence, and how much coherence can be extracted. We answer both questions, and illustrate its application for some typical simple systems, with the aim at illuminating the general concept of enhancing coherence by modifying correlations.

Department of Signal Theory and Communications Universitat Politecnica de Catalunya Campus Nord D3 08034 Barcelona Spain

ICFO Institut de Ciencies Fotoniques Mediterranean Technology Park 08860 Castelldefels Barcelona Spain

Palacký University RCPTM Joint Laboratory of Optics 17 listopadu 12 771 46 Olomouc Czech Republic

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