On the Use of Minimum Volume Ellipsoids and Symplectic Capacities for Studying Classical Uncertainties for Joint Position-Momentum Measurements

Abstract

We study the minimum volume ellipsoid estimator associates to a cloud of points in phase space. Using as a natural measure of uncertainty the symplectic capacity of the covariance ellipsoid we find that classical uncertainties obey relations similar to those found in non-standard quantum mechanics.

References in corpus (2)

• High-Breakdown Robust Multivariate Methods
• Quantum States and Hardy's Formulation of the Uncertainty Principle : a Symplectic Approach

Cited by in corpus (3)

• Quantum Blobs
• Paths of Canonical Transformations and their Quantization
• Toward a relative q-entropy