Quantum Probability and Decision Theory, Revisited

Helstrom's Theory on Quantum Binary Decision Revisited

For a binary system specified by the density operators r0 and r1 and by the prior probabilities q0 and q1, Helstrom's theory permits the evaluation of the optimal measurement operators and of the corresponding maximum correct detection probability. The theory is based on the eigendecomposition (EID) of the operator, given by the difference of the weighted density operators, namely D = q1r1-q0r0. In general, this EID is obtained explicitly only with pure states, whereas with mixed states it must be carried out numerically. In this letter we show that the same evaluation can be performed on the …

重新审视电磁激发的量子振子模型

The quantum oscillator model of electromagnetic excitations revisited

本文重新考察电磁场的量子振子模型，阐明实Maxwell场二次量子化所得Hermitian算符描述局域耦合于费米子物质的光子-反光子对，并指出单光子场应解释为概率幅。

One-dimensional transport revisited: A simple and exact solution for phase disorder

Disordered systems have grown in importance in the past decades, with similar phenomena manifesting themselves in many different physical systems. Because of the difficulty of the topic, theoretical progress has mostly emerged from numerical studies or analytical approximations. Here, we provide an exact, analytical solution to the problem of uniform phase disorder in a system of identical scatterers arranged with varying separations along a line. Relying on a relationship with Legendre functions, we demonstrate a simple approach to computing statistics of the transmission probability (or the …

Quantum Probability from Decision Theory?

Deutsch has recently (in quant-ph/9906015) offered a justification, based only on the non-probabilistic axioms of quantum theory and of classical decision theory, for the use of the standard quantum probability rules. In this note, this justification is examined.

Decisions, Decisions, Decisions: Can Savage Salvage Everettian Probability?

Critics object that the Everett view cannot make sense of quantum probabilities, in one or both of two ways: either it cannot make sense of probability at all, or it cannot explain why probability should be governed by the Born rule. David Deutsch has attempted to meet these objections by appealing to an Everettian version of Savage's rational decision theory. Deutsch argues not only that an analogue of classical decision under uncertainty makes sense in an Everett world; but also that under reasonable assumptions, the betting odds of a rational Everettian agent should be constrained by the Bo…

Quantum Theory of Probability and Decisions

The probabilistic predictions of quantum theory are conventionally obtained from a special probabilistic axiom. But that is unnecessary because all the practical consequences of such predictions follow from the remaining, non-probabilistic, axioms of quantum theory, together with the non-probabilistic part of classical decision theory.