17 research outputs found
Quantum theory from four of Hardy's axioms
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 necessary for his derivation. By reformulating Hardy's assumptions, and
modifying a part of his proof, in terms of Bayesian probabilities, we show that
his work can be easily reconciled with a Bayesian interpretation of quantum
probability.Comment: 5 page
Hypothesis elimination on a quantum computer
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
distributions encoded on a register of qubits, and establish a lower bound on
the required computational resources.Comment: 8 page
Unknown Quantum States and Operations, a Bayesian View
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 this paper, we motivate and review two results that generalize de
Finetti's theorem to the quantum mechanical setting: Namely a de Finetti
theorem for quantum states and a de Finetti theorem for quantum operations. The
quantum-state theorem, in a closely analogous fashion to the original de
Finetti theorem, deals with exchangeable density-operator assignments and
provides an operational definition of the concept of an "unknown quantum state"
in quantum-state tomography. Similarly, the quantum-operation theorem gives an
operational definition of an "unknown quantum operation" in quantum-process
tomography. These results are especially important for a Bayesian
interpretation of quantum mechanics, where quantum states and (at least some)
quantum operations are taken to be states of belief rather than states of
nature.Comment: 37 pages, 3 figures, to appear in "Quantum Estimation Theory," edited
by M.G.A. Paris and J. Rehacek (Springer-Verlag, Berlin, 2004