Lower bounds on communication complexity
Information and Computation
Elements of information theory
Elements of information theory
Rounds in communication complexity revisited
SIAM Journal on Computing
On data structures and asymmetric communication complexity
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
SIAM Journal on Computing
Quantum circuits with mixed states
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Quantum vs. classical communication and computation
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Why quantum bit commitment and ideal quantum coin tossing are impossible
PhysComp96 Proceedings of the fourth workshop on Physics and computation
Exponential separation of quantum and classical communication complexity
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
The communication complexity of pointer chasing: applications of entropy and sampling
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
On quantum and probabilistic communication: Las Vegas and one-way protocols
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
A new protocol and lower bounds for quantum coin flipping
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Lower Bounds for Computation with Limited Nondeterminism
COCO '98 Proceedings of the Thirteenth Annual IEEE Conference on Computational Complexity
The Quantum Communication Complexity of Sampling
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Optimal Lower Bounds for Quantum Automata and Random Access Codes
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Communication Complexity Lower Bounds by Polynomials
CCC '01 Proceedings of the 16th Annual Conference on Computational Complexity
Cryptographic distinguishability measures for quantum-mechanical states
IEEE Transactions on Information Theory
A new protocol and lower bounds for quantum coin flipping
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
On communication over an entanglement-assisted quantum channel
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Dense quantum coding and quantum finite automata
Journal of the ACM (JACM)
Quantum communication and complexity
Theoretical Computer Science - Natural computing
Improved Quantum Communication Complexity Bounds for Disjointness and Equality
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
On Quantum and Approximate Privacy
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
The Quantum Communication Complexity of the Pointer Chasing Problem: The Bit Version
FST TCS '02 Proceedings of the 22nd Conference Kanpur on Foundations of Software Technology and Theoretical Computer Science
Exponential lower bound for 2-query locally decodable codes via a quantum argument
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
A new protocol and lower bounds for quantum coin flipping
Journal of Computer and System Sciences - STOC 2001
Exponential lower bound for 2-query locally decodable codes via a quantum argument
Journal of Computer and System Sciences - Special issue: STOC 2003
Limits on the ability of quantum states to convey classical messages
Journal of the ACM (JACM)
Lower bounds for predecessor searching in the cell probe model
Journal of Computer and System Sciences
The pattern matrix method for lower bounds on quantum communication
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Robust lower bounds for communication and stream computation
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
SIAM Journal on Computing
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One of the most intriguing facts about communication using quantum states is that these states cannot be used to transmit more classical bits than the number of qubits used, yet in some scenarios there are ways of conveying information with exponentially fewer qubits than possible classically [3, 26]. Moreover, these methods have a very simple structure---they involve only few message exchanges between the communicating parties.We consider the question as to whether every classical protocol may be transformed to a “simpler” quantum protocol---one that has similar efficiency, but uses fewer message exchanges. We show that for any constant k, there is a problem such that its k+1 message classical communication complexity is exponentially smaller than its k message quantum communication complexity, thus answering the above question in the negative. This in particular proves a round hierarchy theorem for quantum communication complexity, and implies via a simple reduction, an \Omega(N^{1/k}) lower bound for k message protocols for Set Disjointness for constant~k.Our result builds on two primitives, local transitions in bi-partite states (based on previous work) and average encoding which may be of significance in other contexts as well.