  In 1999 Raz demonstrated a partial function that had an efficient quantum
two-way communication protocol but no efficient classical two-way protocol and
asked, whether there existed a function with an efficient quantum one-way
protocol, but still no efficient classical two-way protocol. In 2010 Klartag
and Regev demonstrated such a function and asked, whether there existed a
function with an efficient quantum simultaneous-messages protocol, but still no
efficient classical two-way protocol.
  In this work we answer the latter question affirmatively and present a
partial function Shape, which can be computed by a protocol sending entangled
simultaneous messages of poly-logarithmic size, and whose classical two-way
complexity is lower bounded by a polynomial.
