Weight-based measure of quantum memory as a universal and operational benchmark

Quantum memory plays a critical role in quantum communication, sensing, and computation. However, studies on quantum memory under a unified benchmarking framework remain scarce. In this paper we propose a weight-based quantifier as a benchmarking method to evaluate the performance advantage of quantum memory in nonlocal exclusion tasks. We establish a general lower bound for the weight-based measure of quantum memory. Moreover, this measure provides fundamental theoretical bounds for transforming a general channel into an ideal quantum memory. Finally, we present explicit calculations of the weight-based quantifier for various channels, including unitary channels, depolarizing channels, maximal replacement channels, stochastic damping channels, and erasure channels.