Properties of QBist State Spaces

TL;DR

This paper explores the structure of quantum state space represented as probability distributions over SIC measurement outcomes, highlighting bounds on inner products and features consistent with quantum theory.

Contribution

It advances the understanding of quantum state space by analyzing bounds on probabilities and features of extreme points, building on prior SIC measurement frameworks.

Findings

Inner products of probabilities are bounded within quantum state space

Identified new features of quantum state space consistent with quantum theory

No complete characterization of quantum state space achieved

Abstract

Every quantum state can be represented as a probability distribution over the outcomes of an informationally complete measurement. But not all probability distributions correspond to quantum states. Quantum state space may thus be thought of as a restricted subset of all potentially available probabilities. A recent publication [1] advocates such a representation using symmetric informationally complete (SIC) measurements. Building upon this work we study how this subset--quantum-state space--might be characterized. Our leading characteristic is that the inner products of the probabilities are bounded, a simple condition with nontrivial consequences. To get quantum-state space something more detailed about the extreme points is needed. No definitive characterization is reached, but we see several new interesting features over those in [1], and all in conformity with quantum theory.