Generalize the tensor-network approach to optimize parallel quantum channel discrimination

Develop a tensor-network optimization framework for parallel quantum channel discrimination that can efficiently represent and enforce global multi-partite measurement (POVM) constraints—positivity and completeness (summing to identity)—so as to compute optimal parallel discrimination strategies and quantitatively compare their performance with adaptive strategies within the same framework.

Background

The paper introduces a tensor-network-based algorithm that effectively optimizes adaptive quantum channel discrimination strategies (quantum combs) for many channel uses, providing lower bounds on success probabilities beyond the reach of full SDP formulations.

While the method works well for adaptive strategies, the authors point out a gap for parallel strategies, where all channel uses are probed in parallel with a single multipartite input and a global measurement. In quantum metrology, analogous tensor-network methods exist (e.g., matrix product states/operators) to handle parallel settings, but the direct translation to discrimination is hindered by the need to optimize over global POVMs subject to positivity and completeness constraints.

The authors explicitly state that it is not clear how to extend their tensor-network framework to handle optimal parallel discrimination schemes, primarily because representing and optimizing multipartite measurements with the required constraints is challenging in the tensor-network optimization setting. Resolving this would enable numerical observation of the adaptive–parallel gap in channel discrimination.