The Volume of Two-Qubit States by Information Geometry

Area of Science:

• Quantum Information Theory
• Quantum Many-Body Systems
• Statistical Mechanics

Background:

• Understanding the geometry of quantum states is crucial for quantum information processing.
• Disordered quantum subsystems present unique challenges in characterizing quantum states.
• Information geometry provides a framework for analyzing the structure of quantum state spaces.

Purpose of the Study:

• To determine the volume of two-qubit states with maximally disordered subsystems.
• To investigate the behavior of separable and entangled states with fixed purity within this volume.
• To compare the effectiveness of different quantum Fisher metrics with the classical Fisher metric.

Main Methods:

• Information geometry approach.
• Analysis of sub-manifolds of separable and entangled states.
• Utilizing the classical Fisher metric on phase space probability representation.

Main Results:

• The volume of two-qubit states with maximally disordered subsystems was determined.
• Distinct behaviors were observed for the volumes of separable and entangled states with fixed purity.
• Qualitative agreement was found between the classical Fisher metric and various quantum Fisher metrics.

Conclusions:

• Information geometry offers a powerful tool for quantifying properties of quantum states.
• The study provides insights into the geometric structure of quantum states with disordered subsystems.
• Classical and quantum Fisher metrics yield consistent qualitative results in this context.