Validity of the HO GSVD-motivated Ansatz II beyond four-dimensional channels

Investigate and establish the validity of the modified higher-order generalized singular value decomposition (HO GSVD)–motivated Ansatz II for generalized extreme channels when the system or channel dimension exceeds four; determine whether its accuracy and efficiency persist for dimensions greater than four.

Background

Ansatz II is a simplified circuit construction motivated by HO GSVD that achieves lower circuit cost while maintaining high accuracy in numerical tests up to dimension four. The authors explicitly note that its validity for higher dimensions has not been established.

Resolving this question would clarify the scalability of the proposed approach and its applicability to higher-dimensional DA channels or qudit channels.

References

Furthermore, Ansatz II is also motivated by the HO GSVD, which has demonstrated broad applications in field of matrix analysis, while its validity for higher than four dimensional channels remains to be investigated.

— Convex decomposition of dimension-altering quantum channels  (1510.01040 - Wang, 2015) in Section 6 (Discussion and conclusion)