Harnessing non-equilibrium environments to reduce the entropic uncertainty bound

The uncertainty in the measurement of two conjugate physical quantities of a quantum system can be reduced in the presence of a quantum memory, which can be investigated using the quantum memory-assisted entropic uncertainty relation (QMA-EUR). While the inevitable exposure of quantum systems to dephasing and decohering environments represents a major challenge to the realization of practical quantum information processing systems, we show how they can be harnessed to reduce the measurement uncertainty. We study the impact of local nonequilibrium dephasing environments versus a common one on the dynamics of a bipartite composite system made of measured and memory quantum systems. We investigate how the competition between non-equilibrium and non-Markovianity can control the entropic uncertainty bound (EUB) in weak- and strong-coupling regimes. We show that the non-equilibrium effect provides an efficient mean for controlling the EUB in either regime without the need to act on the measured system, where the EUB can be reduced considerably in the common bath compared with the local baths. Moreover, we study another setup where only the quantum memory is exposed to a nonequilibrium dephasing environment with an Ohmic-class spectrum. This environment is defined in terms of a dynamic random function that can be varied by engineering the initial phases of the bath modes. We demonstrate how this setup can be utilized to significantly suppress the maximum steady-state value of the EUB for any Ohmic spectral density.