Second semester research project within Sorbonne Université’s IQ Master’s degree.
By Hugo Abreu, Fanny Terrier and Hugo Thomas. Supervised by Ivan Šupić.
You can find an HTML version of this document in https://thmhugo.github.io/qi-project/
The subject can be found in the project description.
- Find the relation between two self-testing conditions:
- maximal violation of some Bell inequality
- reproduction of a full-set of measurement correlations
This equates to finding Bell inequalities which are maximally violated by measurement correlations which self-test a corresponding quantum state.
In particular: relate Mayers-Yao self-testing condition to some Bell inequality.
If the first part is successful, try to generalize the Mayers-Yao self-testing condition to larger classes of entangled states.
Self-testing is a method to infer the underlying physics of a quantum experiment in a black box scenario. – Self-testing of quantum systems: a review, p.1
It has both theoretical implications in quantum information theory (as part of the general study of quantum correlations) and practical applications in quantum computing protocols:
- validating quantum systems (device-indepent certification)
- device-independent quantum cryptography
- device-independent randomness generation
- …
Some notations:
-
$\mathcal{L}(\mathcal{H})$ denotes the set of linear operators acting on an Hilbert space$\mathcal{H}$ .
The self-testing scenario (when device-independent, commonly called a Bell test):
- Consider two parties
$A$ and$B$ .
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