Quantum lower bounds by quantum arguments
STOC '00 Proceedings of the thirty-second 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
Interaction in quantum communication and the complexity of set disjointness
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
Quantum lower bounds by quantum arguments
Journal of Computer and System Sciences - Special issue on STOC 2000
Limits on the ability of quantum states to convey classical messages
Journal of the ACM (JACM)
The pattern matrix method for lower bounds on quantum communication
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
A lower bound for agnostically learning disjunctions
COLT'07 Proceedings of the 20th annual conference on Learning theory
Unbounded-error classical and quantum communication complexity
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Strong direct product theorems for quantum communication and query complexity
Proceedings of the forty-third annual ACM symposium on Theory of computing
On quantum-classical equivalence for composed communication problems
Quantum Information & Computation
Non-local box complexity and secure function evaluation
Quantum Information & Computation
Quantum communication complexity of block-composed functions
Quantum Information & Computation
A note on quantum algorithms and the minimal degree of ε-error polynomials for symmetric functions
Quantum Information & Computation
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Making polynomials robust to noise
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
SIAM Journal on Computing
Tensor rank and strong quantum nondeterminism in multiparty communication
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
A lower bound on entanglement-assisted quantum communication complexity
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
The approximate rank of a matrix and its algorithmic applications: approximate rank
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
| Hi-index | 0.00 |
Abstract: The quantum version of communication complexity allows the two communicating parties to exchange qubits and/or to make use of prior entanglement (shared EPR-pairs). Some lower bound techniques are available for qubit communication complexity, but except for the inner product function, no bounds are known for the model with unlimited prior entanglement. We show that the "log rank" lower bound extends to the strongest variant of quantum communication complexity (qubit communication + unlimited prior entanglement). By relating the rank of the communication matrix to properties of polynomials, we are able to derive some strong bounds for exact protocols. In particular, we prove both the "log rank conjecture" and the polynomial equivalence of quantum and classical communication complexity for various classes of functions. We also derive some weaker bounds for bounded-error quantum protocols.