Spin-orbit-coupled quantum memory of a double quantum dot

The concept of quantum memory plays an incisive role in the quantum information theory. As confirmed by the several recent rigorous mathematical studies, the quantum memory inmate in the bipartite system ρAB can reduce the uncertainty about part B, after measurements done on part A. In the present work, we extend this concept to systems with a spin-orbit coupling and introduce the notion of spin-orbit quantum memory. We self-consistently explore the Uhlmann fidelity, the pre- and the post-measurement entanglement entropy, and the post-measurement conditional quantum entropy of the system with spin-orbit coupling and show that measurement performed on the spin subsystem decreases the uncertainty of the orbital part. The uncovered effect enhances with the strength of the spin-orbit coupling. We study the concept of macroscopic realism introduced by Leggett and Garg [Phys. Rev. Lett. 54, 857 (1985)] and observe that POVM measurements done on the system under the particular protocol are noninvasive. For the extended system, we perform quantum Monte Carlo calculations and consider the reshuffling of the electron densities due to an external electric field.