The volume of Gaussian states by information geometry

Abstract

We formulate the problem of determining the volume of the set of Gaussian physical states in the framework of information geometry. That is, by considering phase space probability distributions parametrized by the covariances and supplying this resulting statistical manifold with the Fisher-Rao metric. We then evaluate the volume of classical, quantum and quantum entangled states for two-mode systems showing chains of strict inclusion.

References in corpus (4)

• Classical and Quantum Fisher Information in the Geometrical Formulation of Quantum Mechanics
• The volume of separable states is super-doubly-exponentially small
• Entanglement Typicality
• Quantum States and Hardy's Formulation of the Uncertainty Principle : a Symplectic Approach

Cited by in corpus (7)

• Metric on the space of quantum states from relative entropy. Tomographic reconstruction
• Information geometric methods for complexity
• Complexity of mixed Gaussian states from Fisher information geometry
• The Volume of Two-Qubit States by Information Geometry
• Geometry on the manifold of Gaussian quantum channels
• Catching homologies by geometric entropy
• Typical Gaussian Quantum Information