Hierarchy of continuous-variable quantum resource theories

• URL: http://arxiv.org/abs/2106.11334v1
• Date: Mon, 21 Jun 2021 18:03:26 GMT
• Title: Hierarchy of continuous-variable quantum resource theories
• Authors: Giulio Gianfelici, Hermann Kampermann and Dagmar Bru{\ss}
• Abstract summary: We establish analogous results for continuous-variable systems, in particular Gaussian systems. We show that the maximal Gaussian coherence can be quantified analytically by the relative entropy. We then propose a resource theory of non-uniformity, by considering the purity of a quantum state at fixed energy as resource, and by defining non-uniformity monotones.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Connections between the resource theories of coherence and purity (or non-uniformity) are well known for discrete-variable, finite-dimensional, quantum systems. We establish analogous results for continuous-variable systems, in particular Gaussian systems. To this end, we define the concept of maximal coherence at fixed energy, which is achievable with energy-preserving unitaries. We show that the maximal Gaussian coherence (where states and operations are required to be Gaussian) can be quantified analytically by the relative entropy. We then propose a resource theory of non-uniformity, by considering the purity of a quantum state at fixed energy as resource, and by defining non-uniformity monotones. In the Gaussian case, we prove the equality of Gaussian non-uniformity and maximal Gaussian coherence. Finally, we show a hierarchy for non-uniformity, coherence, discord and entanglement in continuous-variable systems.

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