Manuscript Oai272-A@1 · Oai272-A.tex · example · a40828a0

Example: An entangled full-range state

Stage 4: hypothesis changes and named-model tests › Product-free range is sufficient, not necessary · lines 1798–1811

For $1/3 < t < 1$ , the two-qubit state

ω_{t} = t ∣ Φ_{2} ⟩ ⟨ Φ_{2} ∣ + (1 - t) I_{4} /4

has full range, so its range contains every product vector. It is entangled because its Bell overlap is

(1 + 3 t) /4 > 1/2,

whereas every separable two-qubit state has Bell overlap at most $1/2$ . This example is not PPT and is not a proposed zero-key state.

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