Uniqueness of imaginarity-assisted exact transformation from real orthogonal operations to arbitrary unitary operations
- 1NTT Communication Science Laboratories, NTT, Inc.
- 2Information Technology R&D Center, Mitsubishi Electric Corporation
Abstract
The computational universality with an elementary gate set {H,CCZ} can be transformed to the strict universality by using a maximally imaginary state | +i ⟩ and some non-imaginary ancillary qubits. From the viewpoint of operational resource theory, it would be intriguing to elucidate a resource for the universality transformation. In this paper, we consider the exact universality transformation in which arbitrary real orthogonal matrices can be applied and a supplied resource state is used to simulate unitary operations exactly and deterministically. Within this operational model, we explore a necessary and sufficient condition for resource states to realize the universality transformation under free real operations. We show that | +i ⟩ is a unique resource state up to the free operations. Moreover, we obtain a stronger conclusion. If a given resource state cannot be used for the universality transformation, then realizable quantum gates are restricted to unitary matrices proportional to real orthogonal matrices. Therefore, we can tell that | +i ⟩ is unique (up to the free operations) not only as a state whose resource measure of imaginarity is maximal, but also as a state which empowers real operations with the ability to apply at least one non-real quantum gate (regardless of the magnitudes of its imaginary parts).
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BibTeX
@article{nakayama2026uniqueness,
title = {{Uniqueness of imaginarity-assisted exact transformation from real orthogonal operations to arbitrary unitary operations}},
author = {Yasuaki Nakayama and Yuki Takeuchi and Seiseki Akibue},
journal = {Scientific Reports},
year = {2026},
month = sep,
doi = {10.1038/s41598-026-70782-1},
url = {https://doi.org/10.1038/s41598-026-70782-1},
note = {CC BY},
}
RIS
TY - JOUR
TI - Uniqueness of imaginarity-assisted exact transformation from real orthogonal operations to arbitrary unitary operations
AU - Yasuaki Nakayama
AU - Yuki Takeuchi
AU - Seiseki Akibue
PY - 2026
DA - 2026/09/01
JO - Scientific Reports
DO - 10.1038/s41598-026-70782-1
UR - https://doi.org/10.1038/s41598-026-70782-1
AB - The computational universality with an elementary gate set {H,CCZ} can be transformed to the strict universality by using a maximally imaginary state | +i ⟩ and some non-imaginary ancillary qubits. From the viewpoint of operational resource theory, it would be intriguing to elucidate a resource for the universality transformation. In this paper, we consider the exact universality transformation in which arbitrary real orthogonal matrices can be applied and a supplied resource state is used to simulate unitary operations exactly and deterministically. Within this operational model, we explore a necessary and sufficient condition for resource states to realize the universality transformation under free real operations. We show that | +i ⟩ is a unique resource state up to the free operations. Moreover, we obtain a stronger conclusion. If a given resource state cannot be used for the universality transformation, then realizable quantum gates are restricted to unitary matrices proportional to real orthogonal matrices. Therefore, we can tell that | +i ⟩ is unique (up to the free operations) not only as a state whose resource measure of imaginarity is maximal, but also as a state which empowers real operations with the ability to apply at least one non-real quantum gate (regardless of the magnitudes of its imaginary parts).
SN - 2045-2322
ER -