Gaussian states under coarse-grained continuous variable measurements

Abstract

The quantum-to-classical transition of a quantum state is a topic of great interest in fundamental and practical aspects. A coarse-graining in quantum measurement has recently been suggested as its possible account in addition to the usual decoherence model. We here investigate the reconstruction of a Gaussian state (single mode and two modes) by coarse-grained homodyne measurements. To this aim, we employ two methods, the direct reconstruction of the covariance matrix and the maximum likelihood estimation (MLE), respectively, and examine the reconstructed state under each scheme compared to the state interacting with a Gaussian (squeezed thermal) reservoir. We clearly demonstrate that the coarse-graining model, though applied equally to all quadrature amplitudes, is not compatible with the decoherence model by a thermal (phase-insensitive) reservoir. Furthermore, we compare the performance of the direct reconstruction and the MLE methods by investigating the fidelity and the nonclassicality of the reconstructed states and show that the MLE method can generally yield a more reliable reconstruction, particularly without information on a reference frame (phase of input state).

published version, 9 pages, 5 figures

References in corpus (21)

• A computable measure of entanglement
• Decoherence, einselection, and the quantum origins of the classical
• Gaussian Quantum Information
• Continuous-variable optical quantum state tomography
• Quantum state reconstruction of the single-photon Fock state
• Quantum state estimation
• Maximum-likelihood estimation of the density matrix
• A computable measure of nonclassicality for light
• Classical world arising out of quantum physics under the restriction of coarse-grained measurements
• Quantum homodyne tomography of a two-photon Fock state
• Uhlmann fidelity between two-mode Gaussian states
• The conditions for quantum violation of macroscopic realism
• Homodyne tomography characterization and nonlocality of a dual-mode optical qubit
• Experimental generation of multi-photon Fock states
• Violation of Continuous Variable EPR Steering with Discrete Measurements
• Coarsening Measurement References and the Quantum-to-Classical Transition
• Coarse Graining Makes It Hard to See Micro-Macro Entanglement
• Optimal Uncertainty Relations for Extremely Coarse-grained Measurements
• Reliable Entanglement Detection Under Coarse--Grained Measurements
• Instant single-photon Fock state tomography
• Heisenberg Uncertainty Relation for Coarse-grained Observables

Cited by in corpus (10)

• Uncertainty Relations for coarse-grained measurements: an overview
• Macro-to-micro quantum mapping and the emergence of nonlinearity
• Entropic Uncertainty Relations and the Quantum-to-Classical transition
• Verifying single-mode nonclassicality beyond negativity in phase space
• Homodyning the $g^{(2)}(0)$ of Gaussian states
• Classical capacity of Gaussian communication under a single noisy channel
• Continuous-Variable Nonclassicality Detection under Coarse-Grained Measurement
• Mesoscopic and macroscopic quantum correlations in photonic, atomic and optomechanical systems
• Quantum state inference from coarse-grained descriptions: analysis and an application to quantum thermodynamics
• Quantum Metrology under Coarse-Grained Measurement