Quantum

The Geometry of Quantum Teleportation in Phase Space

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Briefings

A new theoretical framework applies quantum teleportation using deformation quantization and the Stratonovich--Weyl correspondence on $SU(2)$ coadjoint orbits. The study explicitly constructs phase space representations for Bell resources, entangled operators, and measurements, demonstrating how Wigner function information is redistributed via correlations rather than symplectic geometry transfer. The research extends to general phase space geometries with star products.

Key points

• The protocol uses the Stratonovich--Weyl (SW) correspondence and star product on $SU(2)$ coadjoint orbits to represent qubits as spherical phase space $S^2$ with Kirillov--Kostant--Souriau (KKS) symplectic structure.
• The Wigner function for the input qubit is redistributed through bipartite and tripartite phase space correlations, with conditional unitary transformations producing outcome-dependent rotations on the receiver's coadjoint orbit.

Context

This research advances quantum teleportation by reformulating it within deformation quantization, offering a geometric interpretation of information redistribution without direct symplectic geometry transfer. It provides a framework applicable to general phase space geometries with star products.

Limitations

The study is a preprint (arXiv:2610.37861v1) with limited experimental validation. Theoretical claims regarding generalization to other geometries remain unverified, and specific numerical results for operational fidelity are not provided.

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