Nondeterministic quantum communication complexity: the cyclic equality game and iterated matrix multiplication

Understand

We study nondeterministic multiparty quantum communication with a quantum generalization of broadcasts.

• We show that, with number-in-hand classical inputs, the communication complexity of a Boolean function in this communication model equals the logarithm of the support rank of the corresponding tensor, whereas the approximation complexity in this model equals the logarithm of the border support rank.
• This characterisation allows us to prove a log-rank conjecture posed by Villagra et al.
• for nondeterministic multiparty quantum communication with message-passing.