The Geometry of Quantum Teleportation in Phase Space
Abstract
We formulate the standard quantum teleportation protocol within the framework of deformation quantization, employing the Stratonovich--Weyl (SW) correspondence and the associated star product on the coadjoint orbits of SU(2). Each qubit is represented by a spherical phase space S2 endowed with the Kirillov--Kostant--Souriau (KKS) symplectic structure. Within this setting, we explicitly construct the phase space representations of the entangled Bell resource, the controlled-NOT and Hadamard operators, the projective measurements, and the conditional Pauli corrections. We demonstrate how the quantum information initially encoded in the Wigner function for the input qubit is redistributed through bipartite and tripartite phase space correlations. Upon consideration of a conditional unitary transformation, the measurement outcome produces a Wigner function on the receiver's coadjoint orbit that is related to the input by an outcome-dependent rotation, which can subsequently be inverted through the implementation of an appropriate Pauli correction. The covariance of the SW correspondence provides a geometric interpretation of this process, in which quantum information is redistributed and reconstructed without transferring the underlying symplectic geometry. Our formulation can also be extended to study quantum teleportation in more general phase space geometries equipped with suitable star products.
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BibTeX
@misc{berramontiel2026geometry,
title = {{The Geometry of Quantum Teleportation in Phase Space}},
author = {Jasel Berra-Montiel and Alberto Molgado and Mar Sánchez-Córdova},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37861},
eprint = {2610.37861},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37861},
}
RIS
TY - UNPB
TI - The Geometry of Quantum Teleportation in Phase Space
AU - Jasel Berra-Montiel
AU - Alberto Molgado
AU - Mar Sánchez-Córdova
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37861
UR - https://arxiv.org/abs/2610.37861
AB - We formulate the standard quantum teleportation protocol within the framework of deformation quantization, employing the Stratonovich--Weyl (SW) correspondence and the associated star product on the coadjoint orbits of SU(2). Each qubit is represented by a spherical phase space S^2 endowed with the Kirillov--Kostant--Souriau (KKS) symplectic structure. Within this setting, we explicitly construct the phase space representations of the entangled Bell resource, the controlled-NOT and Hadamard operators, the projective measurements, and the conditional Pauli corrections. We demonstrate how the quantum information initially encoded in the Wigner function for the input qubit is redistributed through bipartite and tripartite phase space correlations. Upon consideration of a conditional unitary transformation, the measurement outcome produces a Wigner function on the receiver's coadjoint orbit that is related to the input by an outcome-dependent rotation, which can subsequently be inverted through the implementation of an appropriate Pauli correction. The covariance of the SW correspondence provides a geometric interpretation of this process, in which quantum information is redistributed and reconstructed without transferring the underlying symplectic geometry. Our formulation can also be extended to study quantum teleportation in more general phase space geometries equipped with suitable star products.
ER -