Typical Gaussian Quantum Information

We investigate different geometries and invariant measures on the space of mixed Gaussian quan- tum states. We show that when the global purity of the state is held fixed, these measures coincide and it is possible, within this constraint, to define a unique notion of volume on the space of mixed Ga...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2018-08
Main Authors: Sohr, Philipp, Link, Valentin, Luoma, Kimmo, Strunz, Walter T
Format: Article
Language:English
Subjects:
Correlation analysis
Invariants
Purity
Quantum computing
Quantum entanglement
Quantum phenomena
Quantum theory
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We investigate different geometries and invariant measures on the space of mixed Gaussian quan- tum states. We show that when the global purity of the state is held fixed, these measures coincide and it is possible, within this constraint, to define a unique notion of volume on the space of mixed Gaussian states. We then use the so defined measure to study typical non-classical correlations of two mode mixed Gaussian quantum states, in particular entanglement and steerability. We show that under the purity constraint alone, typical values for symplectic invariants can be computed very elegantly, irrespectively of the non-compactness of the underlying state space. Then we consider finite volumes by constraining the purity and energy of the Gaussian state and compute typical values of quantum correlations numerically.
ISSN:2331-8422
DOI:10.48550/arxiv.1808.10153