Quantum channels function as the operational primitives of quantum theory, while superchannels describe the most general transformations acting upon them. Yet the prevailing framework for superchannels is both internally inconsistent, owing to the coexistence of distinct Choi operator constructions, and structurally incomplete, lacking the analogue of representations that ground channel theory. We resolve these issues by combining tensor-network methods with a generalized Occam's razor introduced here, establishing a unified foundation for superchannels. Our framework establishes the connections between competing Choi formulations, develops the Kraus, Stinespring, and Liouville representations for superchannels, and provides a simplified derivation of the realization theorem that identifies the minimal memory required to implement a given transformation. These structural tools also enable characterizations of superchannels that destroy quantum correlations or causal structure, opening a systematic route to non-Markovian quantum dynamics.

Biography

Yunlong Xiao earned his Ph.D. in Mathematical Physics from the Max Planck Institute for Mathematics in the Sciences (MiS) in Leipzig, Germany, and a second Ph.D. in Pure Mathematics from South China University of Technology. He subsequently held a Postdoctoral Fellowship at the Institute for Quantum Science and Technology at the University of Calgary until August 2019, followed by a Research Fellowship at the Quantum Hub in the School of Physical and Mathematical Sciences at Nanyang Technological University, Singapore. He is now a Senior Scientist at the Institute of High Performance Computing (IHPC), Agency for Science, Technology and Research (A*STAR), Singapore. His research spans quantum foundations, quantum causal inference, quantum resource theory, and quantum communication, with publications in Physical Review Letters, Physical Review Research, Physical Review D, Light: Science & Applications, npj Quantum Information, Communications Physics, Quantum Science and Technology, and New Journal of Physics. His broader impact includes long talks and contributed talks at major international venues such as APS March Meeting, AQIS, QPL, and QIP.

Inviter: Dong-Sheng Wang