An acoustic cloak can suppress scattered sound energy by 25 decibels. At the design frequency, the coated cylinder reflects almost nothing back to the observer. Energetically, the object is nearly invisible — it disturbs the surrounding field barely more than empty water would.
Sumaya-Martinez and Mulia-Rodriguez then asked a different question: how much can an observer learn about the hidden object from whatever signal remains? They computed the Fisher Information Matrix for the cloaked system — the mathematical object that quantifies how much parameter-estimation precision the residual signal supports. The trace of the Fisher Information Matrix, which bounds the best achievable estimation accuracy through the Cramér-Rao inequality, dropped by only a few decibels.
Twenty-five decibels of energy suppression. A few decibels of information suppression. The cloak is energetically invisible and informationally exposed.
The mechanism is precise. The cloak works by canceling the dominant multipoles — monopole and dipole modes — of the scattered field. These are the modes that carry the most total energy. But the higher-order modes, which carry very little energy, still encode the object's radius, density, and sound speed. An observer using maximum-likelihood estimation on the residual signal can recover the object's properties with nearly the same precision as if the cloak weren't there. The cloak silenced the loud modes and left the informative ones.
This decoupling is not a design failure. It is a theorem about the relationship between energy and information in scattered fields. Total scattered power weights all modes by their amplitude. Fisher information weights all modes by their sensitivity to parameters. These are different weightings of the same signal, and there is no mathematical reason they should track each other. The modes that carry the most energy are not necessarily the modes that carry the most information about the scatterer's properties.
The structural principle: hiding and being unknowable are different operations. A system that minimizes its visible footprint is not necessarily minimizing what can be inferred about it. The energy you suppress may be exactly the energy an adversary does not need. Stealth is not the same as opacity, and the gap between them is formally measurable — it is the difference between the total scattering cross-section and the trace of the Fisher Information Matrix. The ghost is quiet, but it is not unreadable.