Physical foundations of information processing

The quantum theory is the most accurate and successful theory that we have. Still its set of axioms describes the mathematical formalism used rather than reasons for why the theory is as it is. This is one of the reasons that leads to our problems with understanding the world at microscale. Since every experiment can be viewed as an information processing protocol (with settings being the inputs and the results being the outputs), finding the principles that govern the processing of the information by quantum systems is equivalent to finding the principles underlying the quantum theory.To this end we must complete three steps. First, the candidates for such principles should be identified. Then the resources allowed by chosen principles must be fully characterized. By this we mean describing the set of all the possible probability distributions of outcomes conditioned on the settings. Finally we must compare these resources with the ones allowed by quantum mechanics. If they are identical then we have successfully derived quantum mechanics from information theoretic principles. My research is concentrated on these three steps.While identifying candidates for principles that underlie quantum mechanics the choice is made according to some rules. First, the principle should be reasonable. Otherwise one always can choose the world is such that the quantum mechanics must be true as a principle. Second, it should be true in our universe. Finally, it has to impose nontrivial requirements on acceptable probability distributions.In the second step characterization of resources is done. This is highly nontrivial task and, usually, the better principle the harder. Each principle can be connected with some corresponding task and the violation of this principle is equivalent to performing this task with better than critical efficiency. Often the only known way to put restrictions on resources available is to propose a protocol which uses them and tries to complete this task. Therefore the main objective of this step is to find protocols which are optimal for testing chosen principles.Even if we have good characterization of the resources allowed by each principle in consideration comparing them with quantum ones is not easy. The reason for this is the lack of good characterization of the quantum resources. The only know algorithm for deciding if the resource is allowed by quantum mechanics gives only negative answers in finite time (if the resource is quantum one has to wait infinitely long for the answer). Therefore, other methods of comparison must be devised.

The main beneficiaries of the research on the foundations of physics are the academic ones. Their benefits are obvious as any advancement in the understanding of the universe and the laws of Nature benefits them. More precisely, my research will provide: New information processing protocols devised for generalized probabilistic theories can be also used by quantum information scientists. This protocols may open whole new fields of quantum information theory as it has been in the case of communication complexity. Better understanding of the behavior of the information at the quantum scale leads directly to better understanding how to keep it secret. Study of no-signaling and monogamy principles has been of particular usefulness here in the past. My research will provide tools not only for construction of new cryptographic protocols but can be used in applied cryptography to analyze the security of the existing ones. Experimental scientists will benefit from new protocols derived during the course of research as they can be implemented as experiments. They will also provide a new tools for the analysis of the existing experimental data. Finally, better characterization of quantum resources has impact on mathematics as it may lead to establishing better bounds on various versions of the Grothendieck constant. The influence of the research in theoretical physics on industry works on much longer timescale and is harder to predict. One thing is certain: Any advancements in quantum cryptography are of immediate use for the companies that already build systems based on this technology. The results obtained in objective 1.3 will be most welcome by companies working on data security as lower physical requirements for the same amount security mean cheaper equipment of the same quality. Objective 1.2c, through supplying new useful monogamy tradeoffs, will provide tools for the analysis of existing and the future cryptosystems. Objective 2.1 will provide new key distribution protocols. Some of them may find application in commercial products.