Looking ahead, the work points to adaptive algorithms and scaling strategies to tackle larger, more complex quantum systems while preserving efficiency and accuracy.

The framework also covers collective variants of state, detector, and process tomography, enabling efficient information extraction for collections of quantum objects.

A new generalized collective quantum tomography framework extends state, detector, and process tomography to handle collections of identical or distinct quantum objects simultaneously, improving information extraction efficiency.

Experimental validation with two-copy collective measurements and photonic quantum walks demonstrates practical effectiveness and shows how purity information unavailable to single-copy measurements can be leveraged.

The approach treats each task as a tensor-structured optimization problem and shows that the methods reduce measurement errors and approach fundamental precision limits by effectively using state purity information.

Applications demonstrated include pure quantum states, projective measurements, and unitary processes, indicating broad applicability across quantum characterization tasks.

The collective tomography framework achieves lower mean squared errors than existing methods, using closed-form solutions and sum-of-squares optimization, with a trade-off between accuracy and computational cost.