  The class MA consists of languages that can be efficiently verified by
classical probabilistic verifiers using a single classical certificate, and the
class QMA consists of languages that can be efficiently verified by quantum
verifiers using a single quantum certificate. Suppose that a verifier receives
not only one but multiple certificates. In the classical setting, it is obvious
that a classical verifier with multiple classical certificates is essentially
the same with the one with a single classical certificate. However, in the
quantum setting where a quantum verifier is given a set of quantum certificates
in tensor product form (i.e. each quantum certificate is not entangled with
others), the situation is different, because the quantum verifier might utilize
the structure of the tensor product form. This suggests a possibility of
another hierarchy of complexity classes, namely the QMA hierarchy. From this
point of view, we extend the definition of QMA to QMA(k) for the case quantum
verifiers use k quantum certificates, and analyze the properties of QMA(k).
  To compare the power of QMA(2) with that of QMA(1) = QMA, we show one
interesting property of ``quantum indistinguishability''. This gives a strong
evidence that QMA(2) is more powerful than QMA(1). Furthermore, we show that,
for any fixed positive integer $k \geq 2$, if a language L has a one-sided
bounded error QMA(k) protocol with a quantum verifier using k quantum
certificates, L necessarily has a one-sided bounded error QMA(2) protocol with
a quantum verifier using only two quantum certificates.
