"BROOKLYN QUANTUM" CONSIDERS QBISM

This week we'll be discussing yet another interpretation of quantum mechanics: QBism aka "Quantum Bayesianism" aka "Quantum Bettabilitarianism" (in a nod to Oliver Wendell Holmes, Jr.). Like any good interpretation, QBism has both a mathematical component and a philosophical component. We'll begin with the former, discussing POVM's (positive operator valued measures), which provide a generalized notion of measurement in quantum mechanics, and which can be thought of as an entangling operation with an auxiliary system and a standard measurement on the latter. QBists love, in particular, SIC-POVM's (symmetric informationally complete positive operator valued measures), since the probabilities for each outcome of such a measurement suffice to completely nail down the quantum state! Using them, one can formulate quantum mechanics in a way that looks ridiculously close to normal probability theory (no amplitudes in sight!) with, of course, a twist. Philosophically, QBists apply the subjectivist, personalist notion of probability to quantum states: quantum states don't represent reality, but rather are collections of probabilities representing beliefs, and Born's Rule appears in a new and elegant guise as a consistency criterion for those beliefs across different experiments. More radically, QBists also hold that the very outcomes of measurements themselves are subjective, and that quantum mechanics is not a theory of the objective physical world as such, but is instead a first person theory by which one may predict the future consequences of one's own actions in experience. In making this move, they harken back to the old American pragmatists, like William James, who advocated what he called "radical empiricism," which meant grounding all philosophy in experience itself. QBists also appeal to work of John Wheeler, who famously speculated, in words that echo those of James himself, that we live in a unfinished world, whose creation is ongoing, incessant, and ceaseless, and that this profound openendedness is the real meaning behind "quantum indeterminism."