Inverse Problem of Alchemical Resource Theory: Replication and Universal Simulation Single Out Imaginarity and Parity Asymmetry
Abstract
Quantum resource theories usually begin with a prescribed free structure and ask what tasks become possible when a resource is supplied. We study the inverse problem of alchemical resource theories, which we define as resource theories admitting a resource that can both replicate itself exactly and universally simulate quantum instruments. Under natural consistency assumptions and branchwise complete freeness, we show that for multi-qubit systems only two nontrivial theories survive, up to a common local unitary change of basis: parity asymmetry and imaginarity. We further show that exact universality exhibits an all-or-nothing trade-off: any nonmaximal resource state can exactly simulate only free unitaries. These results demonstrate that prescribed operational capabilities can strongly constrain the underlying resource structure and reveal a fundamental trade-off between computational capability and the precision required for physical implementation.
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BibTeX
@misc{nakayama2026inverse,
title = {{Inverse Problem of Alchemical Resource Theory: Replication and Universal Simulation Single Out Imaginarity and Parity Asymmetry}},
author = {Yasuaki Nakayama and Hayato Arai},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.12988},
eprint = {2609.12988},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.12988},
}
RIS
TY - UNPB
TI - Inverse Problem of Alchemical Resource Theory: Replication and Universal Simulation Single Out Imaginarity and Parity Asymmetry
AU - Yasuaki Nakayama
AU - Hayato Arai
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2609.12988
UR - https://arxiv.org/abs/2609.12988
AB - Quantum resource theories usually begin with a prescribed free structure and ask what tasks become possible when a resource is supplied. We study the inverse problem of alchemical resource theories, which we define as resource theories admitting a resource that can both replicate itself exactly and universally simulate quantum instruments. Under natural consistency assumptions and branchwise complete freeness, we show that for multi-qubit systems only two nontrivial theories survive, up to a common local unitary change of basis: parity asymmetry and imaginarity. We further show that exact universality exhibits an all-or-nothing trade-off: any nonmaximal resource state can exactly simulate only free unitaries. These results demonstrate that prescribed operational capabilities can strongly constrain the underlying resource structure and reveal a fundamental trade-off between computational capability and the precision required for physical implementation.
ER -