Private vs. common random bits in communication complexity
Information Processing Letters
Elements of information theory
Elements of information theory
SIAM Review
Public vs. private coin flips in one round communication games (extended abstract)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Communication complexity
On randomized one-round communication complexity
Computational Complexity
Quantum computation and quantum information
Quantum computation and quantum information
Quantum communication and complexity
Theoretical Computer Science - Natural computing
On the power of quantum fingerprinting
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Randomized Simultaneous Messages: Solution Of A Problem Of Yao In Communication Complexity
CCC '97 Proceedings of the 12th Annual IEEE Conference on Computational Complexity
Optimal Lower Bounds for Quantum Automata and Random Access Codes
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Information Theory Methods in Communication Complexity
CCC '02 Proceedings of the 17th IEEE Annual Conference on Computational Complexity
Exponential separation of quantum and classical one-way communication complexity
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
A semidefinite programming approach to optimal unambiguous discrimination of quantum states
IEEE Transactions on Information Theory
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
A property of quantum relative entropy with an application to privacy in quantum communication
Journal of the ACM (JACM)
Unbounded-error classical and quantum communication complexity
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
On quantum-classical equivalence for composed communication problems
Quantum Information & Computation
On the role of shared entanglement
Quantum Information & Computation
Quantum communication complexity of block-composed functions
Quantum Information & Computation
Quantum predictive learning and communication complexity with single input
Quantum Information & Computation
Hi-index | 0.00 |
We consider the problem of bounded-error quantum state identification: given either state α0 or state α1, we are required to output '0', '1' or 'DONO' ("don't know"), such that conditioned on outputting '0' or '1', our guess is correct with high probability. The goal is to maximize the probability of not outputting 'DONO'. We prove a direct product theorem: if we're given two such problems, with optimal probabilities a and b, respectively, and the states in the first problem are pure, then the optimal probability for the joint bounded-error state identification problem is O(ab). Our proof is based on semidefinite programming duality and may be of wider interest.Using this result, we present two exponential separations in the simultaneous message passing model of communication complexity. First, we describe a relation that can be computed with O(log n) classical bits of communication in the presence of shared randomness, but needs Ω(n1/3) communication if the parties don't share randomness, even if communication is quantum. This shows the optimality of Yao's recent exponential simulation of shared-randomness protocols by quantum protocols without shared randomness. Second, we describe a relation that can be computed with O(log n) classical bits of communication in the presence of shared entanglement, but needs Ω((n/log n)1/3) communication if the parties share randomness but no entanglement, even if communication is quantum. This is the first example in communication complexity where entanglement buys you much more than quantum communication does.