Enhancement in Entanglement Growth due to the Breaking of Translational Symmetry

Information, unlike energy or matter, can leak out of a sub-system to its environment not only due to leaking out of particles from the sub-system to the environment, but also due to leaking in of particles to the sub-system from the environment. We show, this leads to a striking phenomenon -- within a simple setup of free-fermions on a one-dimensional lattice, the breaking of the translational symmetry (TS) may lead to enhancement of information leakage from a sub-system to the environment, though the local correlations show slower propagation upon breaking of the TS as expected. We explain this enhanced leakage in terms of enhancement of entanglement between the sub-system and the environment due to additional scattering of the particles back into the system due to the broken TS. At its extreme, an enhanced leakage of information is observed on introduction of {\it random} on-site potentials, as long the size of the sub-system is of the order of the localization length. For weak disorder the localization length can be considerably large, and we provide a quantitative estimate of that, elaborating on the time and length scale in which this phenomenon is observed. Our counter-intuitive results will provide useful insights and caveats in designing secured local quantum information storage devices based on localization.