Typical Gaussian Quantum Information
arXiv:1808.10153 · doi:10.1088/1751-8121/aaf365
Abstract
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.
arXiv comment22 pages, 4 figures
References in corpus (26)
- Quantum information with continuous variables
- Gaussian Quantum Information
- Peres-Horodecki separability criterion for continuous variable systems
- Steering, Entanglement, Nonlocality, and the EPR Paradox
- The logarithmic negativity: A full entanglement monotone that is not convex
- On the volume of the set of mixed entangled states
- Continuous variable quantum information: Gaussian states and beyond
- Entanglement in continuous variable systems: Recent advances and current perspectives
- Entanglement, EPR-correlations, Bell-nonlocality, and Steering
- Quantification of Gaussian quantum steering
- Aspects of generic entanglement
- On the volume of the set of mixed entangled states II
- Determination of continuous variable entanglement by purity measurements
- Random quantum correlations and density operator distributions
- Typical fast thermalization processes in closed many-body systems
- Quantum Systems Equilibrate Rapidly for Most Observables
- How to measure squeezing and entanglement of Gaussian states without homodyning
- Information geometry of Gaussian channels
- Continuous variable steering and incompatibility via state-channel duality
- Quantum characterization of bipartite Gaussian states
- Optimal detection of losses by thermal probes
- On the Choi-Jamiolkowski Correspondence in Infinite Dimensions
- Canonical and micro-canonical typical entanglement of continuous variable systems
- Volumes of conditioned bipartite state spaces
- The volume of Gaussian states by information geometry
- Invariant measures on multimode quantum Gaussian states