Entanglement Spread in Communication Complexity and Many-Body Physics
summary
Defines entanglement spread as the operational width of a Schmidt-weight distribution and proves it both upper- and lower-bounds the qubit communication needed to (unitarily) prepare or test a pure state, with cost given by an L∞ earth mover distance between entanglement distributions. Example: a superposition of product and N‑EPR components requires ~N/2 qubits to make from EPRs. Testing a maximally entangled state uses O(log 1/ε) qubits via quantum expanders. Shows ground‑state spread ≤ boundary size / gap (and a neighborhood √ bound), and that exotic helpers (except embezzlers) don’t beat EPR reducibility for standard communication complexity.
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