Gisin's theorem

In plain terms

Here is a comfortable picture: entanglement comes in degrees, so maybe weak entanglement is effectively classical, and the famous Bell conflict only kicks in past some threshold of strangeness. Below the threshold, ordinary intuitions survive.

Gisin's theorem deletes the comfortable picture, at least for pure states. Any entanglement at all -- any amount, however small -- produces correlations no local account can reproduce, for some choice of measurement settings. The conflict has no threshold and no safe margin. Either a pure state is unentangled and boring, or it is entangled and already in conflict with local realism.

For mixed states, genuinely, the story is more complicated: there are entangled mixed states that violate nothing. The clean dichotomy is a pure-state fact.

In CSD

This matters to the programme because it forbids an economy measure. A substrate account might hope to handle weak entanglement classically and reserve its non-local machinery for the strongly entangled regime. Not allowed: whatever mechanism produces the correlations has to operate at every degree of entanglement, all the way down to almost-product states.

The corpus can express statements of this generality because its CHSH machinery treats the singlet as an instance rather than the subject -- the theorems quantify over states and settings, so universal claims are statable rather than aspirational.

Mathematically

Every pure entangled bipartite state violates the CHSH inequality for some settings. The result genuinely fails for mixed states -- Werner's examples are entangled yet admit a local hidden-variable model -- so entanglement and Bell non-locality are distinct properties there, and conflating them is an error the corpus is built to avoid.

The name

Nicolas Gisin, born 1952, took his doctorate at Geneva and stayed, apart from a stint in industry building fibre-optic instruments -- which turned out to be the perfect apprenticeship. His group's 1997 experiments sent entangled photons through ten kilometres of deployed Swisscom telecom fibre under Lake Geneva, the moment quantum communication stopped being a tabletop subject.

The theorem is from 1991, a two-page paper. He co-founded idQuantique, which sells quantum cryptography commercially, and has written a small book arguing that physics has been too quick to give up on genuine chance.