  We prove the difference between the minimal entanglement costs in quantum
state merging under one-way and two-way communication in a one-shot scenario,
whereas they have been known to coincide asymptotically. While the minimal
entanglement cost in state merging under one-way communication is
conventionally interpreted to characterize partial quantum information
conditioned by quantum side information, we introduce a notion of spread
quantum information evaluated by the corresponding cost under two-way
communication. Spread quantum information quantitatively characterizes how
nonlocally one-shot quantum information is spread, and it cannot be interpreted
as partial quantum information.
