Quantum

Second-level termination of the PPT entanglement-cost hierarchy for two qutrits

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Based on a feed excerpt; full article content has not been acquired. Source evidence retrieved 11/11/2026, 05:13:24 UTC.

Briefings

A new arXiv preprint proves that the PPT entanglement-cost hierarchy for two-qutrit states terminates at the second level, allowing zero-error asymptotic entanglement cost calculation via a semidefinite program with three Hermitian matrix variables. This establishes a unified terminating level for two-qutrit systems, contrasting with the lack of such a level for all dimensions.

Key points

• The PPT entanglement-cost hierarchy terminates at the second level for arbitrary two-qutrit quantum states.
• The zero-error asymptotic entanglement cost can be computed using a semidefinite program with only three Hermitian matrix variables.

Context

This result provides a unified terminating level for two-qutrit systems, resolving a long-standing open problem in quantum information theory regarding the termination of the hierarchy for all dimensions.

Limitations

The evidence is an arXiv preprint (arXiv:2611.12993v1) from November 2026, meaning the results are unverified and subject to potential revision. The study covers only two-qutrit systems, not all dimensions, and relies on exact rational arithmetic and analytic estimates near parameter boundaries.

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