Distributed Phase Tags: A Locality-Preserving Realification Compiler for Misty-State Quantum Programs
Abstract
Complex amplitudes can be simulated over real Hilbert spaces by adjoining a two-dimensional real/imaginary degree of freedom. In a multipartite program, however, one globally shared phase tag is not a locality-preserving program transformation: every party would have to act on the same auxiliary system. We recast the distributed real simulation of multipartite quantum mechanics as a syntax-directed compiler into a real misty-state intermediate language. For n parties we give explicit phase-reference codewords |0⟩Pn and |1⟩Pn on n local tags and prove that the same real operator J=XZ on any single tag realizes the logical action of multiplication by i. If a complex party-local gate is A=AR+iAI, its real translation is Âj=AR⊗ I+AI⊗ Jj, which acts only on party j's data and local phase tag. We prove an intertwining theorem for arbitrary finite party-local pure-state circuits, exact preservation of computational-basis measurement probabilities, preservation of the run-time interaction graph, and one-rebit-per-party overhead. For the canonical three-party GHZ program, the translation lies entirely inside the ordinary black-and-white misty gate fragment: controlled-J replaces the complex phase operation, while the invariant JjJk|0⟩P=−|0⟩P transfers the required branch sign. This yields a short correctness proof for all four promised GHZ inputs and explains the earlier 64-path cancellation calculation at a single logical phase-code boundary. We distinguish this program realification problem from the weaker task of finding any real strategy with the same correlations, and state precisely which parts are known real-Hilbert-space simulation and which parts belong to the misty-language compilation layer developed here.
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BibTeX
@misc{german2026distributed,
title = {{Distributed Phase Tags: A Locality-Preserving Realification Compiler for Misty-State Quantum Programs}},
author = {Dan-Adrian German and Tony Newton},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25703},
eprint = {2610.25703},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25703},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Distributed Phase Tags: A Locality-Preserving Realification Compiler for Misty-State Quantum Programs
AU - Dan-Adrian German
AU - Tony Newton
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.25703
UR - https://arxiv.org/abs/2610.25703
AB - Complex amplitudes can be simulated over real Hilbert spaces by adjoining a two-dimensional real/imaginary degree of freedom. In a multipartite program, however, one globally shared phase tag is not a locality-preserving program transformation: every party would have to act on the same auxiliary system. We recast the distributed real simulation of multipartite quantum mechanics as a syntax-directed compiler into a real misty-state intermediate language. For n parties we give explicit phase-reference codewords |0⟩_P_n and |1⟩_P_n on n local tags and prove that the same real operator J=XZ on any single tag realizes the logical action of multiplication by i. If a complex party-local gate is A=A_R+iA_I, its real translation is Â_j=A_R⊗ I+A_I⊗ J_j, which acts only on party j's data and local phase tag. We prove an intertwining theorem for arbitrary finite party-local pure-state circuits, exact preservation of computational-basis measurement probabilities, preservation of the run-time interaction graph, and one-rebit-per-party overhead. For the canonical three-party GHZ program, the translation lies entirely inside the ordinary black-and-white misty gate fragment: controlled-J replaces the complex phase operation, while the invariant J_jJ_k|0⟩_P=−|0⟩_P transfers the required branch sign. This yields a short correctness proof for all four promised GHZ inputs and explains the earlier 64-path cancellation calculation at a single logical phase-code boundary. We distinguish this program realification problem from the weaker task of finding any real strategy with the same correlations, and state precisely which parts are known real-Hilbert-space simulation and which parts belong to the misty-language compilation layer developed here.
ER -