On a Differential Geometric Viewpoint of Jaynes' Maxent Method and its Quantum Extension

TL;DR

This paper offers a differential geometric perspective on Jaynes' MaxEnt method and its quantum extension, addressing incomplete knowledge and prior biases in quantum state estimation.

Contribution

It introduces a geometric framework for quantum MaxEnt estimation and discusses the incorporation of prior biases and unresolved issues in quantum relative entropy inference.

Findings

Provides a geometric interpretation of quantum MaxEnt estimates

Analyzes the role of prior biases in quantum state inference

Identifies open problems in quantum relative entropy criteria

Abstract

We present a differential geometric viewpoint of the quantum MaxEnt estimate of a density operator when only incomplete knowledge encoded in the expectation values of a set of quantum observables is available. Finally, the additional possibility of considering some prior bias towards a certain density operator (the prior) is taken into account and the unsolved issues with its quantum relative entropic inference criterion are pointed out.