Design and Optimization of Adaptive Diversity Schemes in Quantum MIMO Channels

Abstract

As quantum networks evolve toward a full quantum Internet, reliable transmission in quantum multiple-input multiple-output (QuMIMO) settings becomes essential, yet remains difficult due to noise, crosstalk, and the mixing of quantum information across subchannels. To improve reliability in such settings, we study an adaptive diversity strategy for discrete-variable QuMIMO systems based on universal asymmetric cloning at the transmitter and probabilistic purification at the receiver. An input qubit is encoded into M approximate clones, transmitted over an N x N multi-mode quantum channel, and recovered through a purification map optimized using available channel state information (CSI). For the given cloning asymmetry parameters, we derive an eigenvalue-based expression for the decoder-optimal end-to-end fidelity in the form of a generalized Rayleigh quotient, which enables efficient tuning of the cloner without iterative optimization. As a design choice, we employ semidefinite program (SDP) to construct the purification map for only a targeted success probability p. This numerical framework is used to study fixed-noise, dimension-scaling noise, and stochastic depolarization regimes. A cloning asymmetry index is introduced to quantify the distribution of quantum information across the multiple subchannels across these operating conditions. The results show that the proposed scheme yields significant fidelity gains in crosstalk-dominated settings and automatically adapts to channel symmetry and channel conditions. This work provides design guidelines for future QuMIMO systems and establishes a robust baseline for more advanced transmission and decoding strategies.