Pseudoergotropy without catalysts

Determine whether any reasonable notion of pseudoergotropy can be realized without using catalysts.

Background

Pseudoergotropy is introduced as an analogue of pseudorandomness for extractable work: two keyed families of states and Hamiltonians should be computationally indistinguishable without the key, while exhibiting substantially different catalytic ergotropy when the key is available. The paper constructs such a separation using catalysts and quantum-secure pseudorandom permutations. It explicitly leaves unresolved whether a comparable notion can be achieved without catalysts.

References

It is unclear whether one can realise any reasonable notion of pseudoergotropy without using catalysts.

— Computational Work Extraction: The Complexity of Catalysts  (2609.40323 - Arora et al., 30 Sep 2026) in Section 1, subsection “Pseudoergotropy,” and reiterated in Section 8, “Pseudoergotropy”