Quantum weakly nondeterministic communication complexity

Quantum Weakly Nondeterministic Communication Complexity

In this paper, we study a weak version of quantum nondeterministic communication complexity, corresponding to the most natural generalization of classical nondeterminism, in which a classical proof has to be checked with probability one by a quantum protocol. Another stronger definition of quantum nondeterminism has already been extensively studied, corresponding to the view of quantum nondeter...

Exponential Quantum-Classical Gaps in Multiparty Nondeterministic Communication Complexity

There are three different types of nondeterminism in quantum communication: i) NQP-communication, ii) QMA-communication, and iii) QCMA-communication. In this paper we show that multiparty NQP-communication can be exponentially stronger than QCMA-communication. This also implies an exponential separation with respect to classical multiparty nondeterministic communication complexity. We argue tha...

Nondeterministic Quantum Query and Quantum Communication Complexities

We study nondeterministic quantum algorithms for Boolean functions f. Such algorithms have positive acceptance probability on input x iff f (x) = 1. In the setting of query complexity, we show that the nondeterministic quantum complexity of a Boolean function is equal to its " nondeterministic polynomial " degree. We also prove a quantum-vs.-classical gap of 1 vs. n for nondeterministic query c...

Nondeterministic Quantum Query and Communication Complexities

Nondeterministic Quantum Communication Complexity: the Cyclic Equality Game and Iterated Matrix Multiplication

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 suppor...