Process Tensor Framework

Claim/Theorem

Pollock, Rodriguez-Rosario, Frauenheim, Paternostro, and Modi give a complete operational framework for non-Markovian quantum processes in terms of a process tensor: a multilinear object, equivalently a generalized Choi state, that determines the statistics of any allowed sequence of interventions using only experimentally accessible quantities. This provides the natural mathematical language for replacing a time-correlated noise history by one finite tensor object on the intervention slots.

Dependencies

• None.

Conflicts/Gaps

• This is a representation theorem, not an anticoncentration theorem.
• The framework is completely general and does not by itself encode bounded memory, nonunitality, contraction, or spatial locality.
• To use it in Conjecture 1, one still needs an additional structural restriction, such as finite Markov order or an efficiently compressible tensor-network form.

Sources

• 10.1103/PhysRevA.97.012127