Differential Parametric Formalism for the Evolution of Gaussian States: Nonunitary Evolution and Invariant States
arXiv:2005.11497 · doi:10.3390/e22050586
Abstract
In a differential approach elaborated, we study the evolution of the parameters of Gaussian, mixed, continuous variable density matrices, whose dynamics are given by Hermitian Hamiltonians expressed as quadratic forms of the position and momentum operators or quadrature components. Specifically, we obtain in generic form the differential equations for the covariance matrix, the mean values, and the density matrix parameters of a multipartite Gaussian state, unitarily evolving according to a Hamiltonian . We also present the corresponding differential equations which describe the nonunitary evolution of the subsystems. The resulting nonlinear equations are used to solve the dynamics of the system instead of the Schrödinger equation. The formalism elaborated allows us to define new specific invariant and quasi-invariant states, as well as states with invariant covariance matrices, i.e., states were only the mean values evolve according to the classical Hamilton equations. By using density matrices in the position and in the tomographic-probability representations, we study examples of these properties. As examples, we present novel invariant states for the two-mode frequency converter and quasi-invariant states for the bipartite parametric amplifier.
References in corpus (20)
- Continuous variable quantum information: Gaussian states and beyond
- Quantum Illumination with Gaussian States
- Unconditional optimality of Gaussian attacks against continuous-variable QKD
- Gaussian quantum discord
- Symplectic tomography as classical approach to quantum systems
- Gaussian transformations and distillation of entangled Gaussian states
- Quantum information with Gaussian states
- Extremality of Gaussian quantum states
- Symplectic invariants, entropic measures and correlations of Gaussian states
- Classical-Like Description of Quantum Dynamics by Means of Symplectic Tomography
- Purity of Gaussian states: measurement schemes and time-evolution in noisy channels
- Gaussian entanglement revisited
- Time-evolution of quantum systems via a complex nonlinear Riccati equation. I. Conservative systems with time-independent Hamiltonian
- Optimal measurements for quantum fidelity between Gaussian states and its relevance to quantum metrology
- Nonclassicality Invariant of General Two-Mode Gaussian States
- Time-evolution of quantum systems via a complex nonlinear Riccati equation II. Dissipative systems
- Dynamics of a harmonic oscillator coupled with a Glauber amplifier
- Linear response theory for quantum Gaussian processes
- Evolution and entanglement of Gaussian states in the parametric amplifier
- General superposition states associated to the rotational and inversion symmetries in the phase space