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Currencies and knowledge in resource theories

Lídia del Rio ( ETH Zurich )

How may we quantify the value of physical resources, such as entangled quantum states, heat baths or lasers? Existing resource theories give us partial answers; however, these rely on idealizations, like the concept of perfectly independent copies of states used to derive conversion rates. As these idealizations are impossible to implement in practice, such results may be of little consequence for experimentalists.

In the first part of this talk I introduce the general tool of currencies [1] to quantify realistic descriptions of resources, applicable in experimental settings when we do not have perfect control over a physical system, when only the neighbourhood of a state or some of its properties are known, or when there is no obvious way to decompose a global space into subsystems. Currencies are a special set of resources chosen to quantify all others - like Bell pairs in LOCC or a lifted weight in thermodynamics. We will see that from very weak assumptions on the theory we can already find useful currencies that give us both necessary and sufficient conditions for resource conversion, and we can build up more results as we impose further structure.

In the second part of the talk I will explore how we can model the knowledge that agents may have of a physical state, beyond the density operator formalism. We will see how to relate theories that differ in the language used to describe resources, like micro and macroscopic thermodynamics. Finally, we take a top-down approach to locality, in which a subsystem structure is derived from a global theory rather than assumed.

References

[1] Lea Kraemer and LdR, Currencies in resource theories [arXiv:1605.01064]

[2] LdR, Lea Kraemer and Renato Renner, Resource theories of knowledge [arXiv:1511.08818]

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