Abstract
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.
Highlights
The superposition principle is one of the axioms and most distinctive features of quantum mechanics and it is responsible for the presence of coherence in quantum states [1]
It is useful to introduce the concept of local coherence that is present in the state π( ) to be distinguished from genuine multipartite effects [32, 35]
Uloc where the minimum is taken over the set local unitaries. To summarize, when it comes to characterize a quantum state, the mutual information is not necessarily an adequate indicator, for it fails to take into account the coherence properties of the state itself
Summary
The superposition principle is one of the axioms and most distinctive features of quantum mechanics and it is responsible for the presence of coherence in quantum states [1]. In analogy to what has been done in different contexts, such as entanglement theory ([2, 12, 13]) or quantum thermodynamics ([14, 15]), a resource theory for quantum coherence was proposed in Refs. Given the fact that quantum correlations and coherences are both useful resources in quantum information and computing, it appears very relevant to find a way to completely characterize the overall computational power of a state exhibiting both aspects of quantumness through the introduction of a global quantifier Is our scheme useful to give a comprehensive approach to quantumness through coherence, but it allows one to explain the incongruent lack of closure emerging in the framework of Ref. [37], showing the indissoluble connexion between local and global quantum effects
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