Optimal heralded negativity from steerable Gaussian states

Determine the optimal average Wigner negativity that Bob can herald on Alice’s subsystem from a steerable Gaussian shared state under the one-sided Gaussian-protocol framework.

Background

The paper introduces the steered negativity as a monotone that upper-bounds the average Wigner negativity Bob can herald on Alice’s side. For Gaussian states, the logarithm of this quantity equals Gaussian steerability, but the bound need not be attainable by any measurement. In the example of a lossy two-mode squeezed vacuum, photon counting achieves only a fraction of the available negativity budget, motivating the unresolved optimization problem of identifying the best possible measurement and protocol.

References

In particular, the optimal average negativity that Bob can herald from a steerable Gaussian state is unknown, as is whether a catalyst can amplify it when the steering constraint is already satisfied.

— Exact Catalysis Cannot Overcome the Gaussian-Steering Barrier for Remote Wigner Negativity  (2610.08509 - Chakrabarty, 6 Oct 2026) in Discussion section

In particular, the optimal average negativity that Bob can herald from a steerable Gaussian state is unknown, as is whether a catalyst can amplify it when the steering constraint is already satisfied.

— Exact Catalysis Cannot Overcome the Gaussian-Steering Barrier for Remote Wigner Negativity  (2610.08509 - Chakrabarty, 6 Oct 2026) in Discussion section

Whether another measurement comes closer is open.

— Exact Catalysis Cannot Overcome the Gaussian-Steering Barrier for Remote Wigner Negativity  (2610.08509 - Chakrabarty, 6 Oct 2026) in Section “Steered negativity,” paragraph following Eq.~(\ref{eq:lossy})