*Quantum Bayesianism (QBism): An interpretation of quantum mechanics based on quantum information theory*

Hans Christian von Baeyer, Professor of Physics, emeritus College of William and Mary, Williamsburg, Virginia January 2014 I am honored and proud to be asked by Pedro to inaugurate the tradition of “New Year Lecture” to the FIS community, in the spirit of the Royal Institution’s “Christmas Lectures”, which have been presented in London almost every year since 1825. Those shows were originally intended for a “juvenile audience”, but have always captivated young and old alike. My electronic lecture is not for children, but like many of its famous predecessors it features a mind-boggling experiment. In spite of the scholarly nature my topic – the interpretation of quantum mechanics – my principal message is simple, and I hope relevant to our quest for the meaning of information. I look forward to a lively discussion after my virtual lecture! QBism (with a capital B) is a radical new interpretation of quantum mechanics that resolves many of the paradoxes that have bedeviled the theory since its invention. The technical successes of quantum theory are unchanged and undisputed -- only the meaning of the formalism is re-appraised. The revision has far-reaching implications for the scientific worldview in general. The crucial move for QBism, inspired by quantum information theory, is very simple. It consists of revising the predominant interpretation of probability. Most physicists accept the frequentist interpretation of probability as “favorable outcomes/all possible outcomes”. Even though this definition becomes rigorous only in the unrealistic limit of an infinite number of trials, it is claimed to be objective. QBism is based instead on the older Bayesian interpretation, which defines probability as “degree of belief.” Specifically, the probability that an event will occur is an agent’s personal assignment of betting odds for the occurrence of the event. It is based on all the information available to the agent, and is explicitly subjective. Bayesian probability, unlike frequentist probability, is meaningful for a single, unrepeatable event. Bayesianism is more general than frequentism. In many cases, such as normal laboratory practice, Bayesian probability can be *measured *by conventional frequentist procedures, but the *meaning *of the result remains Bayesian. (Similarly, temperature is measured by a thermometer, but its meaning runs much deeper.) Bayesianism thus absorbs the successes of frequentism. By combining Bayesian probability with conventional quantum mechanics, QBism locates the result of a calculation in the mind of the agent who makes it. The Schrödinger wavefunction, which is a compendium of information about a quantum system, and in turn yields probabilities for the outcomes of future experiments, becomes subjective as well. Input for assigning betting odds comes from the experiments the agent performs herself, added to information she gathers from the written and oral records of science, i.e. from the totality of her personal experiences. Since wavefunctions are not real in this scheme, the problems associated with such phenomena as the “collapse of the wavefunction” (when probability snaps into certainty as a result of a measurement), Schrödinger’s cat, nonlocality, and Bell inequalities, issues that were interminably debated during the twentieth century, all dissolve. The notorious problem of wavefunction collapse, for example, which defies both mathematical description and the relativistic speed limit, is interpreted as the modification of a probability assignment by a measurement. It is a straightforward application of Bayes’ Law (also known as Bayes’ Theorem or Rule) for updating a probability upon the acquisition of new information. In this way QBism provides a natural and convincing explanation of the mysterious collapse. Apparent nonlocality is displayed most dramatically in an experiment suggested in 1989 by Daniel Greenberger, Michael Horne, and Anton Zeilinger (GHZ). The spin of a “spin 1/2 particle” (such as an electron) can be measured along one axis at a time -- say pointing up or down (U/D) along the z axis, or, alternatively, right or left (R/L) along the x axis. Three identical particles are brought into close contact, and prepared in the special GHZ configuration, in which they are said to be “entangled.” They are then separated by large distances and it is found that whenever two of them point in the same horizontal direction, the third one points UP. (DOWN, if the first two point in opposite directions.) Thus LLU, RRU, RLD and LRD are found among the measurement results, but LLD, RRD, RLU and LRU never occur. A mnemonic: If your two index fingers point in the same horizontal direction, one thumb (representing the third particle,) points up. If they point in opposite horizontal directions the thumb points down. In short: thumbs UP for agreement, thumbs DOWN for disagreement. This configuration displays classical correlations, reminiscent of two bar magnets which, when in contact, align north pole to south pole. If the magnets are then separated without rotation, their orientations remain correlated throughout their subsequent histories. Observing one instantly reveals the direction of the other, regardless of their distance of separation. The horizontal and vertical spin directions of particles in a GHZ state could conceivably assume their values during preparation, and retain them as they are separated. GHZ states have, in fact, been assembled, and their properties have been confirmed experimentally. They are robust. Once two horizontal spins have been measured, the third, vertical spin can be predicted with certainty. Einstein would have considered it to be a “real” property of the third particle, pre-existing any observation. Quantum mechanics throws a spanner into the works. Suppose that the experimenter assembles a GHZ state, but measures the first two spins along the z axis, obtaining UU. What is the prediction for the third vertical spin? In any triangular relationship, if two pairs agree, the third pair must agree also (transitivity). Since all three horizontal spins (*if they were measured*) would point in the same direction, the third spin should point UP, so the classical, logical prediction for the allowed state is UUU. Quantum mechanics, however, decrees that UUU is forbidden, and that the result is UUD instead. Experiments confirm this seemingly bizarre prediction. GHZ presents a choice between realism and locality, defined as the absence of spooky action-at-a-distance. The paradox can be resolved in one of two ways. Many physicists insist on realism – believing that theory should describe nature as it really is. This implies that properties predictable with certainty pre-exist the measurement – that they are carried along by the particle. Some realistic interpretations of quantum mechanics require that the Schrödinger wavefunction is nonlocal. In the case of GHZ this means that the first two measurements yielding UU, even though they take place far from the third particle, instantaneously influence its spin and constrain it to point down. The second option for GHZ is to give up realism in favor of locality – the QBist approach. The wavefunction becomes a purely abstract mathematical object designed to predict measurement outcomes. The unmeasured horizontal spins cannot be invoked to make logical inferences: they have no values at all unless they enter an agent’s experience. Once the first two vertical spins are measured, they co-exist at one location – the agent’s mind – where they become input information for the (correct) quantum mechanical calculation. Quoting from the second reference below: “[B]ecause everything any of us knows about the world is constructed out of his or her individual private experience, it can be unwise to rely on a picture of the physical world from which personal experience is explicitly excluded, as it has been from physical science. Schrödinger traces this exclusion back more than two thousand years to the ancient Greeks. It worked for over two millennia and played an important role in the construction of classical science. But when we attempted to understand phenomena not directly accessible to our senses, our ingrained practice of divorcing the objects of our investigations from the subjective experiences they induce in us got us into trouble. While our efforts at dealing with phenomena at these new scales were spectacularly successful, we have just as spectacularly failed for almost a century to reach agreement about the nature or meaning of that success.” QBism, by placing human experience at the center of a new worldview, suggests a way of “restoring the subject-object balance” to science. My popular exposition of QBism was published in the June 2013 issue of SCIENTIFIC AMERICAN and some of its translations. A more sophisticated but non-mathematical primer dated 20 November 2013, by Christopher Fuchs, David Mermin, and Rüdiger Schack, is available gratis at www.arxiv.org with the ID number 1311.5253v1. HAPPY NEW YEAR 2014!

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