Private coins versus public coins in interactive proof systems
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Private vs. common random bits in communication complexity
Information Processing Letters
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
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
Quantum multi-prover interactive proof systems with limited prior entanglement
Journal of Computer and System Sciences
Exponential separation of quantum and classical one-way communication complexity
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Consequences and Limits of Nonlocal Strategies
CCC '04 Proceedings of the 19th IEEE Annual Conference on Computational Complexity
Limitations of Quantum Advice and One-Way Communication
CCC '04 Proceedings of the 19th IEEE Annual Conference on Computational Complexity
Quantum and Classical Strong Direct Product Theorems and Optimal Time-Space Tradeoffs
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Tensor norms and the classical communication complexity of nonlocal quantum measurement
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Prior Entanglement, Message Compression and Privacy in Quantum Communication
CCC '05 Proceedings of the 20th Annual IEEE Conference on Computational Complexity
Bounded-error quantum state identification and exponential separations in communication complexity
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Nondeterministic exponential time has two-prover interactive protocols
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
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Despite the apparent similarity between shared randomness and shared entanglement in the context of Communication Complexity, our understanding of the latter is not as good as of the former. In particular, there is no known "entanglement analogue" for the famous theorem by Newman, saying that the number of shared random bits required for solving any communication problem can be at most logarithmic in the input length (i.e., using more than O(log n) shared random bits would not reduce the complexity of an optimal solution). In this paper we prove that the same is not true for entanglement. We establish a wide range of tight (up to a polylogarithmic factor) entanglement vs. communication trade-offs for relational problems. The low end is: for any t 2, reducing shared entanglement from logtn to o(logt-2n) qubits can increase the communication required for solving a problem almost exponentially, from O(logtn) to Ω(√n). The high end is: for any ε 0, reducing shared entanglement from n1-ε log n to Ω(n1-ε/log n) can increase the required communication from O(n1-ε log n) to Ω(n1-ε/2/ log n). The upper bounds are demonstrated via protocols which are exact and work in the simultaneous message passing model, while the lower bounds hold for bounded-error protocols, even in the more powerful model of 1-way communication. Our protocols use shared EPR pairs while the lower bounds apply to any sort of prior entanglement. We base the lower bounds on a strong direct product theorem for communication complexity of a certain class of relational problems. We believe that the theorem might have applications outside the scope of this work.