Quantum Bayesianism---Something Old, Something New

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Quantum Bayesianism is a point of view on quantum foundations that says that there is no such thing as a “measurement problem” because there is no such THING as a quantum state: Quantum states are not things---instead information. But the view doesn’t stop there; it starts there! Taking the idea seriously over the last 15 years has been the direct motivation for a number of theorems and objects in quantum information theory: from the no-broadcasting theorem, to the quantum de Finetti theorem, and even some quantum cryptographic alphabets. I will review some of this, and then move on to the holy grail of present efforts: Finding an efficient representation of quantum states in terms of a singular probability function. Doing so leads to the hard technical problem of demonstrating the existence of a certain very symmetric sets of quantum states, and holds out the hope of understanding the amount of “quantum stuff” in a physical system in terms of a single parameter. (I.e., there is the THING that the quantum state is not).