We address measurement-based generation of quantum coherence in continuous variable systems. We consider Gaussian measurements performed on Gaussian states and focus on two scenarios: In the first one, we assume an initially correlated bipartite state shared by two parties and study how correlations may be exploited to remotely create quantum coherence via measurement back action. In particular, we focus on conditional states with zero first moments, so as to address coherence due to properties of the covariance matrix. We consider different classes of bipartite states with incoherent marginals and show that the larger the measurement squeezing, the larger the conditional coherence. Homodyne detection is thus the optimal Gaussian measurement to remotely generate coherence. We also show that for squeezed thermal states there exists a threshold value for the generated coherence which separates entangled and separable states at a fixed energy. Finally, we briefly discuss the tripartite case and the relationship between tripartite correlations and the conditional two-mode coherence. In the second scenario, we address the steady-state coherence of a system interacting with an environment which is continuously monitored. In particular, we discuss the dynamics of an optical parametric oscillator in order to investigate how the coherence of a Gaussian state may be increased by means of time-continuous Gaussian measurement on the interacting environment.
In this work, we prove the generation of genuine tripartite continuous-variable entanglement in the unitary dynamics of the simultaneous measurement process of position and momentum observables raised by Arthurs and Kelly, considering a measurement configuration where the system under examination is a rotated, displaced, and squeezed vacuum state. Under these assumptions, the measurement configuration is entirely described by a Gaussian state. Then, through the positive partial transpose criterion (PPT), we certify genuine tripartite entanglement by testing the non-separability of the three
(1 vs 2)-mode bipartitions of the system. This process allows us to classify the qualitative properties of the entanglement in the category of fully inseparable Gaussian states according to the classification exposed in [Giedke et al., \href{https://link.aps.org/doi/10.1103/PhysRevA.64.052303}{Phys. Rev. A \textbf{64}, 052303 (2001)}]. Besides, we determine the quantitative entanglement properties of the system using the residual tripartite R{é}nyi-2 entanglement as a quantifier measure.
Quantum entanglement is a crucial resource for a wide variety of quantum technologies. However, the current state-of-art methods to generate quantum entanglement in optomechanical systems are not as efficient as all-optical methods utilizing nonlinear crystals. This article proposes a new scheme in which two single-mode squeezed light fields are injected into an optomechanical cavity. We demonstrate through our numerical simulations that the quantum entanglement can be substantially enhanced with the careful selection of squeezing strength and squeezing angle of the two quadrature squeezed light fields. Our results represent a significant improvement in output bipartite photon-photon entanglement over the previously demonstrated schemes using two coherent light fields as inputs. These simulations predict a maximum increase in Gaussian entanglement by a factor of about 6 for lossless input coupling, as well as increases in the quantum noise and non-Gaussianity of the output light. This non-Gaussianity is attributed to tripartite entanglement between the two optical fields and the optomechanical oscillator (OMO). At particular squeezing angles, the Gaussianity can be increased, thus introducing a method of optically controlling the intracavity entanglement. These mechanics can benefit various optical quantum technologies utilizing optomechanical entanglement and continuous variable quantum optics.