Resource Preservability

@article{Hsieh2020ResourceP,
  title={Resource Preservability},
  author={Chung-Yun Hsieh},
  journal={Quantum},
  year={2020},
  volume={4},
  pages={244}
}
Resource theory is a general, model-independent approach aiming to understand the qualitative notion of resource quantitatively. In a given resource theory, free operations are physical processes that do not create the resource and are considered zero-cost. This brings the following natural question: For a given free operation, what is its ability to preserve a resource? We axiomatically formulate this ability as the resource preservability, which is constructed as a channel resource theory… 

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References

SHOWING 1-10 OF 101 REFERENCES
Quantifying Resources in General Resource Theory with Catalysts.
TLDR
This work shows that, in a general resource-theoretic framework that allows the use of free states as catalysts, the amount of "resources" contained in a given state, in the asymptotic scenario, is equal to the regularized relative entropy of a resource of that state.
Resource Destroying Maps.
TLDR
This Letter proposes a general scheme for analyzing resource theories based on resource destroying maps, and defines a class of simple resource measures that can be calculated without optimization, and that are monotone nonincreasing under operations that commute with the resource destroying map.
Reversible Framework for Quantum Resource Theories.
TLDR
The general structure of QRTs is discussed, and it is shown that under a few assumptions, a QRT is asymptotically reversible if its set of allowed operations is maximal, that is, if the allowed operations are the set of all operations that do not generate (asymptotical) a resource.
Quantum resource theories in the single-shot regime
One of the main goals of any resource theory such as entanglement, quantum thermodynamics, quantum coherence, and asymmetry, is to find necessary and sufficient conditions (NSC) that determine
Resource theories of knowledge
TLDR
The extended framework introduced here enables us to formalize new tasks in the language of resource theories, ranging from tomography, cryptography, thermodynamics and foundational questions, both within and beyond quantum theory.
Resource theory of coherence: Beyond states
We generalize the recently proposed resource theory of coherence (or superposition) [Baumgratz, Cramer & Plenio, Phys. Rev. Lett. 113:140401; Winter & Yang, Phys. Rev. Lett. 116:120404] to the
One-Shot Operational Quantum Resource Theory.
TLDR
This work analyzes, from a resource-nonspecific standpoint, the optimal efficiency of resource formation and distillation tasks with only a single copy of the given quantum state, thereby establishing a unified framework of one-shot quantum resource manipulation.
Quantifying Bell: the Resource Theory of Nonclassicality of Common-Cause Boxes
TLDR
This work proves that the set of free operations forms a polytope, which allows us to derive an efficient algorithm for deciding whether one resource can be converted to another, and defines two distinct monotones with simple closed-form expressions in the two-party binary-setting binary-outcome scenario, and reveals various properties of the pre-order of resources.
Operational resource theory of quantum channels
TLDR
This Letter proposes a general resource framework for quantum channels and introduces resource monotones based on general distance quantifiers of channels, and studies the interplay between channel and state resource theories by relating resourceMonotones of a quantum channel to its manipulation power of the state resource.
QUANTUMNESS IN THE CONTEXT OF) RESOURCE THEORIES
We review the basic idea behind resource theories, where we quantify quantum resources by specifying a restricted class of operations. This divides the state space into various sets, including states
...
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