Two dice lie in different rooms. If they are 'entangled,' a roll of one instantly determines the outcome of the other — even at a distance. In the quantum world, such a link is called steering: one party, by performing measurements on their side, seems to dictate the state of the partner. But what happens when the dice are slightly 'shaken'—their state is not perfectly pure but mixed with a dose of chaos? For a long time, it was suspected that steering could disappear even if entanglement persists.
The authors of the new work showed that for states described by just two 'flavors' of mixture (rank two), this does not happen. They proved that any such state is necessarily steerable in at least one direction — one particle can influence the other. If the 'sizes' of the systems match, steering works in both directions. The proof does not rely on complex inequality calculations but on the geometry of the boundary that separates admissible quantum states from impossible ones. When a state touches this boundary, a 'certificate' of nonclassicality automatically appears in its structure, like a crack in the shell that reveals the contents.
This result builds a hierarchy: the rank of the mixture determines how difficult it is to 'steal' steerability from entanglement. Rank two is the first step where mixture is already present but steerability is not yet lost. Practically, this means that even imperfect sources of entangled particles can be suitable for quantum cryptography or teleportation: you don't need to chase perfect purity. The geometric approach opens the way to quick verification: just look at the shape of the boundary, not solve mile-long equations. So two dice, even slightly shaken, remain a reliable tool: their link is not so easy to break.
Steering is a term introduced by Erwin Schrödinger in 1935, while discussing the famous Einstein-Podolsky-Rosen paradox. He considered this ability 'magical' and doubted it could be realized.
In Hannu Rajaniemi's novel 'The Quantum Thief,' steering is used for instantaneous communication and control over remote devices — exactly what this theoretical work promises.