One of the best lower bound methods for the quantum communication complexity of a function H (with or without shared entanglement) is the logarithm of the approximate rank of the communication matrix of H . This measure is essentially equivalent to the approximate γ2 norm and generalized discrepancy, and subsumes several other lower bounds. All known lower bounds on quantum communication comple...

Quantum information processing is at the crossroads of physics, mathematics and computer science. It is concerned with that we can and cannot do with quantum information that goes beyond the abilities of classical information processing devices. Communication complexity is an area of classical computer science that aims at quantifying the amount of communication necessary to solve distributed c...

We prove a general lower bound on the bounded-error entanglement-assisted quantum communication complexity of Boolean functions. The bound is based on the concept that any classical or quantum protocol to evaluate a function on distributed inputs can be turned into a quantum communication protocol. As an application of this bound, we give a very simple proof of the statement that almost all Boo...

We define a quantum model for multiparty communication complexity and prove a simulation theorem between the classical and quantum models. As a result, we show that if the quantum k-party communication complexity of a function f is Ω( n 2k ), then its classical k-party communication is Ω( n 2k/2 ). Finding such an f would allow us to prove strong classical lower bounds for k ≥ log n players and...

Exploiting recent advances in quantum trapped-ion technologies, we propose a scalable, fault-tolerant quantum computing architecture that overcomes the fundamental challenges of building a full-scale quantum computer and leaves the fabrication a daunting but primarily an engineering concern. Using a hierarchical array-based design and a quantum teleportation communication protocol, we are able ...

A major challenge of today’s quantum communication systems lies in the transmission of quantum information with high rates over long distances in the presence of unavoidable losses. Thereby the achievable quantum communication rate is fundamentally limited by the amount of energy that can be transmitted per use of the channel. It is hence vital to develop quantum communication protocols that en...

In STOC 1999, Raz presented a (partial) function for which there is a quantum protocol communicating only O(log n) qubits, but for which any classical (randomized, bounded-error) protocol requires poly(n) bits of communication. That quantum protocol requires two rounds of communication. Ever since Raz’s paper it was open whether the same exponential separation can be achieved with a quantum pro...

This paper studies the three known lower bound methods for one-way quantum communication complexity, namely the Partition Tree method by Nayak, the Trace Distance method by Aaronson, and the two-way quantum communication complexity. It is shown that all these three methods can be exponentially weak for some total Boolean functions. In particular, for a large class of functions generated from Er...

It is known that the classical and quantum query complexities of a total Boolean function f are polynomially related to the degree of its representing polynomial, but the optimal exponents in these relations are unknown. We show that the non-deterministic quantum query complexity of f is linearly related to the degree of a “non-deterministic” polynomial for f . We also prove a quantum-classical...

Communication complexity is an area of classical computer science which studies how much communication is necessary to solve various distributed computational problems. Quantum information processing can be used to reduce the amount of communication required to carry out some distributed problems. We speak of pseudo-telepathy when it is able to completely eliminate the need for communication. S...