The Optimal Pure Gaussian State Associated with Joint Position-Momentum\n Measurements

2012/04/13 by Maurice A. de Gosson, de Gosson, Maurice A.
Computer Science · Decision Sciences · Physics and Astronomy · #Data Analysis #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Scientific Measurement and Uncertainty Evaluation #Statistics and Probability (physics.data-an)

paper · pdf · doi:10.48550/arxiv.1204.2956

openalex publication_date 2012/04/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that given experimental data obtained from joint position and\nmomentum measurements one can construct an optimal pure state approximating the\nobserved quantum state. For that purpose we use a tool from multivariate\nstatistical analysis (the MVE method), which relies on the existence of a\nminimum volume ellipsoid (the John--L "owner ellipsoid) containing a given\nconvex set. This method allows us to determine the shape of the covariance\nellipsoid, which is thereafter calibrated using the expression of the\nuncertainty principle in terms of the notion of symplectic capacity. We finally\nuse the Wigner formalism to produce the best approximating Gaussian state.\n

Citations

• Ellipsoids of maximal volume in convex bodies
• The Symplectic Camel and the Uncertainty Principle: The Tip of an Iceberg?

Related

• Reconstruction of Gaussian Quantum States from Ideal Position Measurements: Beyond Pauli's Problem, I
• Joint estimation of position and momentum with arbitrarily high precision using non-Gaussian states
• Gaussian Formalism: Joint Measurement for Heisenberg's Uncertainty Relation for Errors by Squeezed Coherent States
• Bayesian uncertainty relation for a joint measurement of canonical variables
• Estimating the Degree of Entanglement of Unknown Gaussian States