  Consider a quantum system with $m$ subsystems with $n$ qubits each, and
suppose the state of the system is living in the symmetric subspace. It is
known that, in the limit of $m\to\infty$, entanglement between any two
subsystems vanishes.
  In this paper we study asymptotic behavior of the entanglement as $m$ and $n$
grows. Our conjecture is that if $m$ is a polynomially bounded function in $n$,
then the entanglement decreases polynomially.
  The motivation of this study is a study of quantum Merlin-Arthur game. If
this conjecture is ture, we can prove that bipartite separable certificate does
not increase the computational power of the proof system. protocol.
  In the paper, we provide two evidences which support the conjecture. First,
if $m$ is an exponential function, then entanglement decreases exponentially
fast. Second, in case of a maximally entangled state, our conjecture is true.
