A Quantum-Bayesian Route to Quantum-State Space

TL;DR

This paper derives the structure of quantum-state space using a quantum Bayesian framework, showing how the Born rule can be seen as a modification of classical probability laws based on minimal Bayesian assumptions.

Contribution

It provides a novel derivation of quantum-state space structure from Bayesian principles and the Born rule's interpretation as a probability modification.

Findings

Quantum states represented via SIC measurements.

Born rule as a modification of total probability.

Derivation of quantum-state space from Bayesian assumptions.

Abstract

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 usual probability rules as required by Dutch-book coherence, but quantum mechanics imposes additional constraints upon them. In this paper, we explore the question of deriving the structure of quantum-state space from a set of assumptions in the spirit of quantum Bayesianism. The starting point is the representation of quantum states induced by a symmetric informationally complete measurement or SIC. In this representation, the Born rule takes the form of a particularly simple modification of the law of total probability. We show how to derive key features of quantum-state space from (i) the requirement that the Born rule arises as a simple modification of the law of total probability and (ii) a limited number of additional assumptions of a strong Bayesian flavor.