Partial-measurement-enhanced high-dimensional superdense coding in amplitude damping channel with memory

We study the performance of high-dimensional superdense coding (HD-SDC) over an amplitude damping (AD) channel with memory and propose a protocol that leverages partial measurement and its reversal to enhance the channel capacity. By considering a two-qutrit system, we model the memory AD noise using a convex mixture of memoryless and perfectly memory AD channels. We demonstrate that the memory effect alone can mitigate the decay of the SDC capacity under noise. More significantly, we show that the application of partial measurement before the channel and its reversal after the channel can not only recover the capacity degraded by noise but, for certain non-maximally entangled initial states, even amplify it beyond the initial capacity. This amplification effect is governed by three key factors: the ground-state probability in the initial entangled state, the memory strength, and the partial measurement strength. Our results provide a practical strategy for enhancing quantum communication protocols in realistic noisy environments and highlight the synergistic benefits of memory noise and measurement-based control.