Coarse-grained quantum state tomography with optimal POVM construction

In a multiqubit system, when a detector's resolution is insufficient to distinguish between qubits, individual qubit measurement becomes impractical. This limitation results in coarse-grained (CG) measurements that dilute system information and, more critically, hinder accurate assessment of qubit correlations, making quantum state tomography (QST) infeasible. To address this issue, we propose a scheme to utilize CG measurements for QST by integrating two-qubit gates and optimizing their corresponding positive operator-valued measures (POVMs) using parametrized quantum circuits. Specifically, we focus on constructing generalized symmetric informationally complete POVMs by maximizing the von Neumann entropy of the Gram matrix of these CG POVMs. Our numerical simulations demonstrate the effectiveness of this approach for QST using a two-qubit model and further verify the scalability of our scheme toward <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>N</a:mi></a:math>-qubit systems.