Talks

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.

Microcanonical thermodynamics studies the operations that can be performed on systems with well-defined energy. So far, this approach has been applied to classical and quantum systems. Here we extend it to arbitrary physical theories, proposing two requirements for the development of a general microcanonical framework. We then formulate three resource theories, corresponding to three different choices of basic operations. We focus on a class of physical theories, called sharp theories with purification, where these three sets of operations exhibit remarkable properties. In these theories, a necessary condition for thermodynamic transitions is given by a suitable majorisation criterion. This becomes a sufficient condition in all three resource theories if and only if the dynamics allowed by the theory satisfy a condition that we call "unrestricted reversibility". Under this condition, we derive a duality between the resource theory of microcanonical thermodynamics and the resource theory of pure bipartite entanglement.

Dividing the world into subsystems is an important component of the scientific method. The choice of subsystems, however, is not defined a priori. Typically, it is dictated by our experimental capabilities, and, in general, different agents may have different capabilities. Here we propose a construction that associates every agent with a subsystem, equipped with its set of states and its set of transformations. In quantum theory, this construction accommodates the traditional notion of subsystems as factors of a tensor product, as well as the notion of classical subsystems of quantum systems. We then restrict our attention to systems where all physical transformations act invertibly. For such systems, the future states are a faithful encoding of the past states, in agreement with a requirement known as the Conservation of Information. For systems satisfying the Conservation of Information, we propose a dynamical definition of pure states, and show that all the states of all subsystems admit a canonical purification. This result extends the purification principle to a broader setting, in which coherent superpositions can be interpreted as purifications of incoherent mixtures. As an example, we illustrate the general construction for subsystems associated with group representations.