Hallmarking quantum states: unified framework for coherence and correlations

Gian Luca Giorgi and Roberta Zambrini

Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (UIB-CSIC), UIB Campus, E-07122 Palma de Mallorca, Spain

Quantum coherence and distributed correlations among subparties are often considered as separate, although operationally linked to each other, properties of a quantum state. Here, we propose a measure able to quantify the contributions derived by both the tensor structure of the multipartite Hilbert space and the presence of coherence inside each of the subparties. Our results hold for any number of partitions of the Hilbert space. Within this unified framework, global coherence of the state is identified as the ingredient responsible for the presence of distributed quantum correlations, while local coherence also contributes to the quantumness of the state. A new quantifier, the "hookup", is introduced within such a framework. We also provide a simple physical interpretation, in terms of coherence, of the difference between total correlations and the sum of classical and quantum correlations obtained using relative-entropy-based quantifiers.

The advantage of quantum systems over their classical counterparts in computing, communication, simulations, sensing, is the consequence of the ability of quantum objects of being at the same time in a superposition of different states. In the case of a single object, superposition is revealed by the presence of quantum coherence. When it comes to more than one quantum object, the superposition principle is still the ingredient that allows quantum states to show inner correlations, such as, for instance, entanglement, beyond any classical probabilistic model.
Building on the common roots of coherence and multipartite correlations, we introduce a quantifier (the quantum hookup) that captures the possible advantages coming from both aspects of quantumness within a unified theoretical framework. Within this framework, we redefine the concepts of quantumness and classicality and also discuss the different properties of local and global coherence.

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