Quantum Physics

Following Stefan Wolf’s talk, we address the doubts expressed on fundamental space-time causality. Usually it is assumed that causal structures represent a definite partial ordering of events. By relaxing that notion one risks problems of logical nature. Yet, as we show, there exists a logically consistent world beyond the causal, even in the classical realm where quantum theory is not invoked. We explore the classical correlations within and the computational limits of that world. It turns out that relaxing causality in that fashion does not allow for efficient computation of NP-hard problems. These results are related to closed time-like curves: Contrary to previous models of time travel, which necessitate quantum theory and violate the NP-hardness assumption, we obtain a computationally tame model for classical and reversible time travel where freedom of choice is unrestricted.

Landauer's principle claims that "Information is Physical." Its conceptual antipode, Wheeler's "It from Bit," has since long been popular among computer scientists in the form of the Church-Turing hypothesis: All natural processes can be simulated by a universal Turing machine. Switching back and forth between the two paradigms, motivated by quantum-physical Bell correlations and the doubts they raise about fundamental space-time causality, we look for an intrinsic, physical randomness notion and find one, namely complexity, around the second law of thermodynamics. Bell correlations combined with Kolmogorov complexity in the role of randomness imply an all-or-nothing nature of the Church-Turing hypothesis: Either beyond-Turing computations are physically impossible, or they can be carried out by "devices" as simple as individual photons. This latter result demonstrates in an exemplary way the fruitful interplay between physical and informational-computational principles.

An important ingredient of the scientific method is the ability to test alternative hypotheses on the causal relations relating a given set of variables. In the classical world, this task can be achieved with a variety of statistical, information-theoretic, and computational techniques. In this talk I will address the extension from the classical scenario to the quantum scenario, and, more generally, to general probabilistic theories. After introducing the basic hypothesis testing framework, I will focus on a concrete example, where the task is to identify the causal intermediary of a given variable, under the promise that the causal intermediary belongs to a given set of candidate variables. In this problem, I will show that quantum physics offers an exponential advantage over the best classical strategies, with a doubling of the exponential decay of the error probability. The source of the advantage can be found in the combination of two quantum features: the complementarity between the information on the causal structure and other properties of the cause effect relation, and the ability to perform multiple tests in a quantum superposition. An interesting possibility is that one of the "hidden principles" of quantum theory could be on our ability to test alternative causal hypotheses.

I discuss how we might go about about performing a Bell experiment in which humans are used to decide the settings at each end. To get a sufficiently high rate of switching at both ends, I suggest an experiment over a distance of about 100km with 100 people at each end wearing EEG headsets, with the signals from these headsets being used to switch the settings. The radical possibility we wish to investigate is that, when humans are used to decide the settings (rather than various types of random number generators), we might then expect to see a violation of Quantum Theory in agreement with the relevant Bell inequality. Such a result, while very unlikely, would be tremendously significant for our understanding of the world (and I will discuss some interpretations). Possible radical implications aside, performing an experiment like this would push the development of new technologies. The biggest problem would be to get sufficiently high rates wherein there has been a human induced switch at each end before a signal as to the new value of the setting could be communicated to the other end and, at the same time, a photon pair is detected. It looks like an experiment like this, while challenging, is just about feasible with current technologies.