An important consequence of special relativity, in particular, of the constant and finite speed of light, is that space-like separated regions in spacetime cannot communicate. This fact is often referred to as the “no-signaling principle” in physics.
However, even when signaling is in fact possible, there still are obvious constraints on how signaling can occur: for example, by sending one physical bit, no more than one bit of information can be communicated; by sending two physical bits, no more than two bits of information can be communicated; and so on. Such extra constraints, that by analogy we call “no-hypersignaling,” are not dictated by special relativity, but by the physical theory describing the system being transmitted. If the physical bit is described by classical theory, then the no-hypersignaling principle is true by definition. It is not so in quantum theory, where the validity of the no-hypersignaling principle becomes a non-trivial mathematical theorem relying on a recent result by Péter E. Frenkel and Mihály Weiner (whose proof, using the “supply-demand theorem” for bipartite graphs, is very interesting in itself).
As one may suspect, the no-hypersignaling principle does not hold in general: it is possible to construct artificial worlds in which the no-hypersignaling principle is violated. Such worlds are close relatives of the “box world,” a toy-model theory used to describe conceptual devices called Popescu-Rohrlich boxes. Exploring such alternative box worlds, one further discovers that the no-hypersignaling principle is logically independent of both the conventional no-signaling principle and the information causality principle, however related these two may seem to be with no-hypersignaling.
This means that the no-hypersignaling principle needs to be either assumed from the start, or derived from presently unknown physical principles analogous to the finite and constant speed of light behind Einstein’s no-signaling principle.
Thus I freely admit that in arriving at my proposals I have been guided, in the last analysis, by value judgments and predilections. But I hope that my proposals may be acceptable to those who value not only logical rigour but also freedom from dogmatism; who seek practical applicability, but are even more attracted by the adventure of science, and by discoveries which again and again confront us with new and unexpected questions, challenging us to try out new and hitherto undreamt-of answers.
Karl Popper, The Logic of Scientific Discovery. 2nd Edition (Routledge, 1999), p.38.
I have been recently interviewed by Jesse Casman about why younger students should get a course about quantum foundations and computing, and how IBM’s Quantum Experience and their QISKit can help. Here is the full text.
I was invited to talk at the 3rd International Conference on Quantum Foundations in Patna, the capital city of the Indian state of Bihar. Great hospitality and many brilliant students eager to discuss and interact with the international community. A visit to the remains of the ancient university of Nalanda completed the program.
Next Wednesday, I will be giving an invited lecture at the National Cheng Kung University in Tainan, Taiwan, about all that I’ve learnt concerning the information-disturbance tradeoff in quantum theory. Keeping a unified viewpoint, I will cover many aspects of the problem: from the difference between physical and stochastic reversibility, to qualitative “no information without disturbance” statements and quantitative balance equations, up to the two-observable approach à la Heisenberg.
I recently gave a colloquium at the Department of Applied Mathematics of Hanyang University in Ansan, Korea, in which I tried to introduce the idea of incompatibility of quantum measurements to students that were not all perfectly fluent in quantum theory.
Incompatibility, in the form of uncertainty relations, is available in many flavours: statistical and dynamical, variance-based and entropy-based, state-dependent and state-independent… As I was asked to share the slides, I’m now making them publicly available (click on the cover below):