Natasha Oughton (Somerville College): ‘Quantum, In Principle’
The standard rules of quantum mechanics concern abstract entities such as vectors in Hilbert space, which do not obviously relate to physical quantities out there in the world. It has been speculated that this is in part responsible for our lack of insight into some of the foundational questions of quantum mechanics. Motivated by this thought, and by the success of quantum information theory, there have been attempts to recapture the quantum formalism from the starting point of principles involving the possibilities of various operational tasks. I will discuss one such attempt, which uses a “black box'' approach to search for a principle that, in conjunction with the existence of Bell-inequality violation, successfully singles out quantum mechanical correlations from other correlations. A proposed principle, which has received significant attention, is the information causality principle. Information causality limits the amount of information gained after the sending of a number of classical bits, if two observers have access to a particular kind of black box. However, I argue that the information causality principle is flawed. Firstly, I argue that an attempt to justify it by appealing to Einstein’s principle of mutually independent existence fails. Secondly, I argue that although the informal, non-mathematical statement of the principle seems natural and intuitive, the mathematical result rests on the choice of the Shannon entropy as the correct measure of information sent. I demonstrate that using an alternative measure of entropy results in the information causality principle failing to single out quantum correlations. I further argue that Shannon entropy is not the unique natural choice here, thus undermining the status of the principle.
