Information-based approach towards a unified resource theory
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Information-based approach towards a unified resource theory A. C. S. Costa1
· R. M. Angelo1
Received: 30 March 2020 / Accepted: 17 August 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Resource theories play an important role in quantum information theory, as they identify resourceful states and channels that are potentially useful for the accomplishment of tasks that would be otherwise unreachable. The elementary structure of such theories, which is based on the definition of free states and free operations, successfully accommodates different nonclassical aspects, such as quantum coherence and entanglement, but it is still not clear whether and how far such formal framework can be extended. In this work, by taking information as the most primitive quantum resource and defining resource-destroying operations, we develop a unifying approach that proves able to encompass several nonclassical aspects, including the newly developed concepts of quantum irreality and realism-based nonlocality. Keywords Resource theory · Quantum information · Quantum correlations · Quantum irreality · Realism-based nonlocality
1 Introduction Resource theory is a formal framework developed to investigate and analyse the properties of physical systems that can be viewed as resources for certain tasks under restrictive operations [1]. The most common example of a quantum resource is entanglement [2], which is the basic element of many quantum information processing tasks and formally emerges as a distinctive operational advantage when one is restricted to local operations and classical communication. The basic structure of a resource theory relies on the definition of the following elements: (i) free states, (ii) resource states,
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A. C. S. Costa [email protected] R. M. Angelo [email protected]
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Department of Physics, Federal University of Paraná, P.O. Box 19044, Curitiba, Paraná 81531-980, Brazil 0123456789().: V,-vol
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A. C. S. Costa, R. M. Angelo
and (iii) free operations arising from natural restrictions on physical systems. In addition, within this formal structure, it is naturally required that no resource state can be created from any free state via free operations. The resource theory framework has been applied to various concepts of quantum information science, such as entanglement [2], purity [3], coherence [4,5], informational equilibrium in quantum thermodynamics [6,7], and quantum discord [11]. The search for a unifying framework of resource theories has attracted much interest in the last few years [8–13]. In particular, in Ref. [11], the authors developed a general scheme based on resource-destroying maps for the analysis of resource theories. These maps have the property of maintaining free states unchanged and suppressing all the resource from resourceful states. Recently, new quantifiers of nonclassicality were introduced with basis on an operational scheme to assess elements of reality [14]. In a protocol involving preparation, unrevealed measu
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