  In this paper we study quantum nondeterminism in multiparty communication.
There are three (possibly) different types of nondeterminism in quantum
computation: i) strong, ii) weak with classical proofs, and iii) weak with
quantum proofs. Here we focus on the first one. A strong quantum
nondeterministic protocol accepts a correct input with positive probability,
and rejects an incorrect input with probability 1. In this work we relate
strong quantum nondeterministic multiparty communication complexity to the rank
of the communication tensor in the Number-On-Forehead and Number-In-Hand
models. In particular, by extending the definition proposed by de Wolf to {\it
nondeterministic tensor-rank} ($nrank$), we show that for any boolean function
$f$ when there is no prior shared entanglement between the players, 1) in the
Number-On-Forehead model, the cost is upper-bounded by the logarithm of
$nrank(f)$; 2) in the Number-In-Hand model, the cost is lower-bounded by the
logarithm of $nrank(f)$. Furthermore, we show that when the number of players
is $o(\log\log n)$ we have that $NQP\nsubseteq BQP$ for Number-On-Forehead
communication.
