Ruediger Schack on quantum Bayesianism

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Ruediger Schack portrait Ruediger Schack is a Professor at the Department of Mathematics at Royal Holloway, University of London. He obtained his PhD in Theoretical Physics at the University of Munich in 1991 and held postdoctoral positions at the Max Planck Institute for Quantum Optics, the University of Southern California, the University of New Mexico, and Queen Mary and Westfield College before joining Royal Holloway in 1995. His research interests are quantum information theory, quantum cryptography and quantum Bayesianism.

Luke Muehlhauser: In Fuchs et al. (2013), you and your co-authors provide an introduction to quantum Bayesianism aka “QBism,” which you more or less co-invented with Carlton Caves and Christopher Fuchs. But before I ask about QBism, let me ask one of the questions asked of the interviewees in Elegance and Enigma: The Quantum Interviews (including Fuchs): “What first stimulated your interest in the foundations of quantum mechanics?”

Ruediger Schack: I can trace the beginning of my interest in quantum foundations to reading one paper: “Where do we stand on maximum entropy?” by Ed Jaynes, and one book: Du Microscopique au Macroscopique by Roger Balian. Jaynes’s paper introduced me to Bayesian probability theory, and Balian’s book taught me that one can think of quantum states as representing Bayesian probabilities.

Luke: What is your own summary of the message of QBism? And what do you think its practical import for the world could be?

Ruediger: In two words the message of QBism is that people matter. According to QBism, quantum mechanics is a theory that any agent can use to organize his experience. More precisely, quantum mechanics permits any agent to quantify, on the basis of his past experiences, his probabilistic expectations for his future experiences. QBism takes measurement outcomes as well as quantum states to be personal to the agent using the theory. Quantum mechanics does therefore not provide an objective, agent-independent description of the world – it rules out a “view from nowhere”. By clarifying thus the role of quantum mechanics and of science in general, QBism avoids all the interpretational difficulties usually associated with quantum foundations. In QBism, there are no objective elements of reality that determine either measurement outcomes or probabilities of measurement outcomes. Rather, every quantum measurement is an action on the world by an agent that results in the creation of something entirely new. QBism holds this to be true not only for laboratory measurements on microscopic systems, but for any action an agent takes on the world to elicit a new experience. It is in this sense that agents – people – have a fundamental creative role in the world.

Any interpretation of quantum mechanics by definition makes the same predictions as quantum mechanics. Nevertheless, I expect QBism to have practical import for the world. By shifting the focus away from interpretations that regard quantum states as real, QBism opens up new possibilities: in the search for a compelling physical principle that would explain the quantum formalism, and in the search for new physics.

Luke: I heard that Fuchs, at least, thinks that the case for QBism would be more compelling if it turns out that SIC-POVMs (symmetric informationally complete positive operator-valued measures) existed in every finite Hilbert space dimension, which is currently an unsolved question. Is that your understanding as well? If so, what’s the reasoning?

Ruediger: QBism as an interpretation of quantum mechanics is independent of the existence of SICs and can be formulated without referring to SICs. But QBism is also a program, ultimately with the aim of discovering new physics. A more immediate goal is to find a simple and compelling physical principle underpinning the quantum formalism. Now one of QBism’s central tenets is that a measurement does not reveal a preexisting outcome but results in the creation of something new. In the quantum formalism, this idea finds a simple expression in the fact that the classical probability sum rule does not apply to the – necessarily hypothetical – outcomes of an unperformed experiment. For instance, in the double-slit experiment the probability distribution for the measured particle position on the screen cannot be obtained by adding the weighted probabilities given the particle goes through one or the other slit.

So far this is a purely negative statement. If a SIC exists in every finite Hilbert-space dimension, it turns into a powerful positive statement. If the hypothetical measurement is a SIC measurement, the Born rule takes the form of a very simple modification of the probability sum rule. What is more, from the modified probability sum rule, a large part of the structure of quantum mechanics can be derived. In this picture, instead of the purely negative statement that the probability sum rule cannot be used, we would have a simple physically motivated principle that implies a substantial part of the quantum formalism. In that sense, the existence of SICs in all dimensions would strengthen the case for QBism.

Luke: Roughly how many people are actively advocating or contributing to QBism? Do you think it’s particularly difficult to draw funding and cognitive talent toward this work because of its theoretical nature, or for other reasons?

Ruediger: As a matter of fact, the mathematical aspects of QBism (such as the structure of the SICs or the quantum de Finetti theorems) have attracted significant funding over the years. At present, however, only a small number of people are actively contributing to QBism. When QBism holds that science is as much about the scientist as it is about the world external to the scientist, it challenges one of the most deeply held prejudices that most physicists subscribe to. This prejudice is exemplified by the following quote from Landau and Lifshitz: “By measurement, in quantum mechanics, we understand any process of interaction between classical and quantum objects occurring apart from and independently of any observer.” Another commonly held prejudice is that a probability-1 assignment implies the existence of an objective mechanism that brings about the event. Physicists find it very hard to accept the QBist principle that probability-1 judgments are still judgments, like any other probability assignments. Let me finish with a prediction: In twenty-five years when a new generation of scientists have been exposed to QBist ideas, QBism will be taken for granted and quantum foundations will have disappeared as a problem.

Luke: Thanks, Ruediger!