2025/05/04 by Shilpa Nandi, Nandi, Shilpa, Pinaki Patra +2
Computer Science · Mathematics · #Digital Image Processing Techniques #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Image Processing and 3D Reconstruction #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #Statistical and numerical algorithms
paper · pdf · doi:10.48550/arxiv.2505.02269
openalex publication_date 2025/05/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
The Fisher-Rao (FR) information matrix is a central object in multiparameter quantum estimation theory. The geometry of a quantum state can be envisaged through the Riemannian manifold generated by the FR-metric corresponding to the quantum state. Interestingly, any congruence transformation GL(2n,ℝ) in phase space leaves the FR-distance for Gaussian states invariant. In the present paper, we investigate whether this isometry affects the entanglement in the bipartite system. It turns out that the entanglement-generating congruent transformation depends upon the system and background space. To make our study relevant to physical systems, we choose Bopp's shift in phase space as an example of GL(2n,ℝ), so that the results can be interpreted in terms of noncommutative (NC) phase-space deformation. We provide an estimation of the measure of entangled states over separable states for bipartite Gaussian states under a Bopp's shift. Since the dynamics of free oscillators in background NC-space is mathematically equivalent to the dynamics of a charged particle under a homogeneous magnetic field, we provide an outline for a gedankenexperiment through photocurrent measurement in order to determine the effects of congruent transformation on the distinguishibility of Gaussian states.