Genuine entanglement under squeezed generalized amplitude damping channels with memory

Abstract: We study genuine entanglement among $3$-qubits undergoing through a noisy process including dissipation, squeezing and decoherence. We obtain a general solution and analyze the asymptotic quantum states. It turns out that most of these asymptotic states can be genuinely entangled depending upon parameters of channel, memory parameter, and parameters of initial states. We study Greenberger-Horne-Zeilinger (GHZ) states and W states, mixed with white noise and determine the conditions for them to be genuinely entangled at infinity. We find that for these mixtures, it is possible to start with bi-separable state (with specific mixture of white noise as described below) and end up with genuine entangled states. However, the memory parameter $\mu$ must be very high. We find that in contrast to two-qubit case, all three qubit asymptotic states for $n \to \infty$ are not genuinely entangled.