Correlations and information processing – quantum and beyond
Paweł Horodecki (Gdańsk University of Technology, Poland)
Quantum mechanics is a very special physical theory where randomness is built in on the ontological level. In particular it allows quantum correlations – also called quantum entanglement – that are stronger than all the correlations we know from our daily lives.
Einstein's ingenious skepticism about this theory gave rise to the fundamental philosophical question - formalized mathematically by John Bell - about the objective existence of properties of quantum particles before measurement. Schrodinger's reflection on quantum entanglement was the beginning of the information-theoretic description of quantum correlations. It this talk we look at those two faces of quantum mechanics - correlation and information – including the outer perspective of possible future physical theories.
From the perspective of Bell test we shall see that on the one hand quantum mechanics look surprisingly powerful and robust – it turns out that, to some extend, its predictions survive even some relaxations of philosophically fundamental "free will assumption". On the other, there still seems to be "space at the top", in the sense of possible extensions of quantum physics that are imaginable without undermining fundamental principle of causality. We shall discuss some of them, including especially intriguing option of jamming of correlations. We shall independently illustrate how some special Bell inequality may behave in tree-particle decays with respect to SM-type interaction.
From the perspective of information processing we shall focus mostly on encoding of information. We shall see that careful quantification of the redundancy in such process in entropic terms can successfully probe some of possible deformations of quantum probabilistic behaviors. We shall argue that this observation as well as long-term questions of limits on linearity of quantum theory supports the recently proposed new paradigm of probing quantum limits namely the quantum input data boxes. Within this paradigm we shall discuss the recent approach to quantum process tomography as a new perspective for high-energy physics. On the one hand the tomography is capable to probe potential extensions of the Standard Model. On the other, it constitutes the foundational test of quantum mechanics itself.