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Robust self-testing with applications to device-independent cryptography

Periodic Reporting for period 1 - ROSETTA (Robust self-testing with applications to device-independent cryptography)

Reporting period: 2017-03-01 to 2019-02-28

"Quantum technologies is a new branch of the information industry which promises significant advantages over the standard (classical) information processing technologies in terms of, for instance, computational power or security. One of the major challenges is to manufacture and control quantum devices of increasing power and complexity and devising efficient and robust testing procedures is a necessary step towards that goal. In this project we have focused on designing new testing procedures for quantum devices which can be applied under minimal assumptions (the so-called ""device-independent"" model). These procedures are based on the fact that quantum systems can exhibit stronger correlations than classical systems and these correlations can be directly observed in an experiment, a phenomenon known as Bell nonlocality. This is precisely what we use to certify the quantumness nature of the devices.

The overarching goal of our research is to provide procedures that allow us to certify any quantum device that might be useful from the practical point of view. In particular, this includes highly complex devices consisting of many qubits (qubit is the quantum equivalent of a bit, a classical unit of information/memory) as well as devices correlated with multiple other devices.

Our procedures have already been used to certify quantum devices and we are actively encouraging experimental groups to take advantage of them. This will allow them to improve the design and manufacturing process which in the long-term will speed up the development of powerful and useful quantum devices. Once these are available we can use them to build a quantum computer (superior computational power) or connect them in a network (the ""quantum internet"") to provide safer and more efficient communication."
"The first project focused on certifying quantum measurements with two outcomes (so-called binary measurements). We used a simple mathematical approach to design robust self-testing procedures for pairs of binary measurements, which can be applied to every pair of binary measurements. The results were published in Physical Review A.

The second project was a big international collaboration with researchers from Canada, Hungary, Taiwan and Singapore. We posed many important and fundamental questions about the nature of quantum correlations and answered them. The results were published in Physical Review A.

The next two projects resulted from a fruitful collaboration with the Group of Applied Physics at the University of Geneva. We have realised that some techniques developed previously can be applied to new scenarios. In particular, we have developed a procedure for certifying states and measurements in the prepare-and-measure scenario (related to the so-called ""quantum random access codes"") and a procedure for certifying entangled measurements in the bilocality scenario (two independent quantum sources). The results are available at an online repository (the arXiv) and are currently under review.

The last project was a collaboration with Institute for Photonic Sciences (Barcelona, Spain) and Center for Theoretical Physics (Warsaw, Poland). We have provided a procedure to certify the maximally entangled state of two qutrits and a particular type of important quantum measurements acting on it (three ""mutually unbiased bases""). We are currently working on generalising this approach to higher-dimensional systems. The results are available at an online repository (the arXiv) and will be submitted to a journal soon."
The project had significant impact on the field of self-testing and device-independent certification. From the practical point of view we have developed new explicit robust testing procedures for quantum devices. What is particularly important is that we have extended the notion of self-testing to new scenarios: prepare-and-measure and bilocality. On a more fundamental level we have discovered several surprising features about the nature of quantum correlations and the limit of what can be certified in a device-independent manner. Moreover, the Fellow had the opportunity to work within the QMATH Center at the University of Copenhagen which has significantly advanced his academic career.
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