Quantum Protocols within Spekkens' Toy Model
Friday, 27 May. 2016, 15:00 - 16:00
Presenter: Leonardo Disilvestro
Host: Zizhu Wang
Where: IQOQI Seminar Room, 2nd Floor, Boltzmanngasse 3, 1090 Vienna
Quantum theory is believed to provide improvements both in computational power and se- curity with respect to classical information theory. In order to better understand the origin of these improvements, we translate emblematic quantum protocols to Spekkens' toy mo- del - a local hidden variable theory which is phenomenologically very close to quantum theory. Despite the toy model non being able to provide any computational speed up with respect to quantum theory, we see that it can still provide similar security statements as in the quantum case. We notice how the existence of anticommutation relations between toy measurements and toy transformations and the existence of `toy purifications' seems to be sufficient to implement many quantum protocols within the toy model. In particular, we show that error correction, secret sharing, and blind and verified computation are indeed possible in the toy model along with providing a proof of the impossibility of toy-bit com- mitment. Our results firstly suggest that purifications and anticommutaiton relations pro- vide the structure behind the existence of these protocols within quantum theory; and se- condly, the ability to perform blind and verified computation in the toy model strongly suggest that not only steering is a sufficient property for such a protocol, but that any pro- babilistic theory featuring purification is indeed apt to implement blind and verified computation.