Ruediger Schack
QBism has long recognized quantum states, POVM elements, Kraus operators, and even unitary operations to be cut from the same cloth: They express aspects of an agent's belief system concerning the consequences (for her) of actions she might…
According to QBism, quantum states, unitary evolutions, and measurement operators are all understood as personal judgments of the agent using the formalism. Meanwhile, quantum measurement outcomes are understood as the personal experiences…
In a recent paper [e-print quant-ph/0101012], Hardy has given a derivation of "quantum theory from five reasonable axioms." Here we show that Hardy's first axiom, which identifies probability with limiting frequency in an ensemble, is not…
The classical de Finetti theorem provides an operational definition of the concept of an unknown probability in Bayesian probability theory, where probabilities are taken to be degrees of belief instead of objective states of nature. In…
We present an elementary proof of the quantum de Finetti representation theorem, a quantum analogue of de Finetti's classical theorem on exchangeable probability assignments. This contrasts with the original proof of Hudson and Moody [Z.…
Consider a joint quantum state of a system and its environment. A measurement on the environment induces a decomposition of the system state. Using algorithmic information theory, we define the preparation information of a pure or mixed…
In QBism (or Quantum Bayesianism) a quantum state does not represent an element of physical reality but an agent's personal probability assignments, reflecting his subjective degrees of belief about the future content of his experience. In…
We give an introduction to the QBist interpretation of quantum mechanics. We note that it removes the paradoxes, conundra, and pseudo-problems that have plagued quantum foundations for the past nine decades. As an example, we show in detail…
In the Quantum-Bayesian interpretation of quantum theory (or QBism), the Born Rule cannot be interpreted as a rule for setting measurement-outcome probabilities from an objective quantum state. But if not, what is the role of the rule? In…
The probabilities a Bayesian agent assigns to a set of events typically change with time, for instance when the agent updates them in the light of new data. In this paper we address the question of how an agent's probabilities at different…
In the quantum-Bayesian approach to quantum foundations, a quantum state is viewed as an expression of an agent's personalist Bayesian degrees of belief, or probabilities, concerning the results of measurements. These probabilities obey the…
In quantum Bayesian inference problems, any conclusions drawn from a finite number of measurements depend not only on the outcomes of the measurements but also on a prior. Here we show that, in general, the prior remains important even in…
This is a reply to Michael Nauenberg's arXiv:1502.00123, to be published in the American Journal of Physics, in which he comments critically on our paper "An introduction to QBism with an application to the locality of quantum mechanics",…
In the quantum Bayesian (or QBist) conception of quantum theory, "quantum measurement" is understood not as a comparison of something pre-existent with a standard, but instead indicative of the creation of something new in the universe:…
By numerically simulating an implementation of the quantum baker's map on a 3-qubit NMR quantum computer based on the molecule trichloroethylene, we demonstrate the feasibility of quantum chaos experiments on present-day quantum computers.…
We investigate the problem of Bayesian updating of a probability distribution encoded in the quantum state of n qubits. The updating procedure takes the form of a quantum algorithm that prepares the quantum register in the state…
We investigate how classical predictability of the coarse-grained evolution of the quantum baker's map depends on the character of the coarse-graining. Our analysis extends earlier work by Brun and Hartle [Phys. Rev. D 60, 123503 (1999)] to…
Hypothesis elimination is a special case of Bayesian updating, where each piece of new data rules out a set of prior hypotheses. We describe how to use Grover's algorithm to perform hypothesis elimination for a class of probability…
In a previous paper [quant-ph/0408045] we described a quantum algorithm to prepare an arbitrary state of a quantum register with arbitrary fidelity. Here we present an alternative algorithm which uses a small number of quantum oracles…
We review the properties of the frequency operator for an infinite number of systems and disprove claims in the literature that the quantum probability postulate can be derived from these properties.