Separability Lindblad equation for dynamical open-system entanglement

Abstract

Providing entanglement for the design of quantum technologies in the presence of noise constitutes today's main challenge in quantum information science. A framework is required that assesses the build-up of entanglement in realistic settings. In this work, we put forth a new class of nonlinear quantum master equations in Lindblad form that unambiguously identify dynamical entanglement in open quantum systems via deviations from a separable evolution. This separability Lindblad equation restricts quantum trajectories to classically correlated states only. Unlike many conventional approaches, here the entangling capabilities of a process are not characterized by input-output relations, but separability is imposed at each instant of time. We solve these equations for crucial examples, thereby quantifying the dynamical impact of entanglement in non-equilibrium scenarios. Our results allow to benchmark the engineering of entangled states through dissipation. The separability Lindblad equation provides a unique path to characterizing quantum correlations caused by arbitrary system-bath interactions, specifically tailored for the noisy intermediate-scale quantum era.

Figures (2)

• Figure 1: Schematic representation of the tangential approximation. In general, the unrestricted evolution takes a state outside the manifold of separable states. In the restricted evolution, each infinitesimal time step is projected onto the tangent space of separable states, ensuring the dynamics to contain classical correlations only.
• Figure 2: (a) Scheme of the decay process given in Eq. \ref{['eq:exampleGenerators']}. Comparison between the separable (dotted, purple line) and unrestricted (solid, turquoise line) solutions via Monte Carlo wave function. (b) Entanglement, characterized by the negativity of the partially transposed state. (c) Population of the ground state $\ket{00}$. (d) Probability to occupy one of the intermediate levels $|\Phi_+\rangle$ and $|\Phi_-\rangle$. One standard deviation uncertainty in lighter-colored bands. (Note that that the occupation of the $|11\rangle$ level can be inferred from (c) and (d).) Parameters for the numerical simulation are $\gamma_{11\to\Phi_+}=9=\gamma_{\Phi_-\to00}, \gamma_{11\to\Phi_-}=1=\gamma_{\Phi_+\to00}$, step size $\tau=0.2$, and a sample size of $600$Zenodo.