# Copies, currencies and catalysis: beyond the tensor product, pure states and other spherical cows

### APA

del Rio, L. (2016). Copies, currencies and catalysis: beyond the tensor product, pure states and other spherical cows. Perimeter Institute. https://pirsa.org/16010072

### MLA

del Rio, Lidia. Copies, currencies and catalysis: beyond the tensor product, pure states and other spherical cows. Perimeter Institute, Jan. 26, 2016, https://pirsa.org/16010072

### BibTex

@misc{ pirsa_16010072, doi = {10.48660/16010072}, url = {https://pirsa.org/16010072}, author = {del Rio, Lidia}, keywords = {Quantum Foundations}, language = {en}, title = {Copies, currencies and catalysis: beyond the tensor product, pure states and other spherical cows}, publisher = {Perimeter Institute}, year = {2016}, month = {jan}, note = {PIRSA:16010072 see, \url{https://pirsa.org}} }

Lidia del Rio ETH Zurich

## Abstract

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 this talk I introduce tools to quantify realistic descriptions of resources, applicable for example 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 slight correlations cannot be ruled out.

Some resources, like entanglement, can be characterized in terms of copies of local states: we generalize this with operational ways to describe composition and copies of realistic resources, without assuming a tensor product structure. For others, like thermodynamic work, value is seen as a real function on physical states, like the height of a weight. While value is often expected to behave linearly, that simplification excludes many real-life resources: for example, the operational value of money, in terms of what can be done with it, is hardly linear on the amount of coin, and even has catalytic aspects above certain thresholds. We characterize resources that behave linearly and those that allow for investments - in the extreme, catalytic resources.

This work is an application of the framework introduced in arXiv:1511.08818.