Quantum speedup in testing causal hypotheses

          @misc{ pirsa_PIRSA:18040122,
            doi = {10.48660/18040122},
            url = {https://pirsa.org/18040122},
            author = {Chiribella, Giulio},
            keywords = {Quantum Foundations},
            language = {en},
            title = {Quantum speedup in testing causal hypotheses},
            publisher = {Perimeter Institute},
            year = {2018},
            month = {apr},
            note = {PIRSA:18040122 see, \url{https://pirsa.org}}
          }
          

Abstract

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.