Private vs. common random bits in communication complexity
Information Processing Letters
Communication complexity
Quantum vs. classical communication and computation
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
On the power of quantum fingerprinting
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Some complexity questions related to distributive computing(Preliminary Report)
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
Convex Optimization
Strengths and Weaknesses of Quantum Fingerprinting
CCC '06 Proceedings of the 21st Annual IEEE Conference on Computational Complexity
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
A Direct Product Theorem for Discrepancy
CCC '08 Proceedings of the 2008 IEEE 23rd Annual Conference on Computational Complexity
Disjointness Is Hard in the Multi-party Number-on-the-Forehead Model
CCC '08 Proceedings of the 2008 IEEE 23rd Annual Conference on Computational Complexity
The Quantum Moment Problem and Bounds on Entangled Multi-prover Games
CCC '08 Proceedings of the 2008 IEEE 23rd Annual Conference on Computational Complexity
Complexity measures of sign matrices
Combinatorica
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
Tensor Norms and the Classical Communication Complexity of Nonlocal Quantum Measurement
SIAM Journal on Computing
Lower bounds in communication complexity based on factorization norms
Random Structures & Algorithms
Simulating Quantum Correlations with Finite Communication
SIAM Journal on Computing
Bell violations through independent bases games
Quantum Information & Computation
Classical and quantum partition bound and detector inefficiency
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Hi-index | 0.00 |
We study a model of communication complexity that encompasses many well-studied problems, including classical and quantum communication complexity, the complexity of simulating distributions arising from bipartite measurements of shared quantum states, and XOR games. In this model, Alice gets an input x, Bob gets an input y, and their goal is to each produce an output a, b distributed according to some pre-specified joint distribution p(a, b|x, y). Our results apply to any non-signaling distribution, that is, those where Alice's marginal distribution does not depend on Bob's input, and vice versa. By taking a geometric view of the non-signaling distributions, we introduce a simple new technique based on affine combinations of lower-complexity distributions, and we give the first general technique to apply to all these settings, with elementary proofs and very intuitive interpretations. Specifically, we introduce two complexity measures, one which gives lower bounds on classical communication, and one for quantum communication. These measures can be expressed as convex optimization problems. We show that the dual formulations have a striking interpretation, since they coincide with maximum violations of Bell and Tsirelson inequalities. The dual expressions are closely related to the winning probability of XOR games. Despite their apparent simplicity, these lower bounds subsume many known communication complexity lower bound methods, most notably the recent lower bounds of Linial and Shraibman for the special case of Boolean functions. We show that as in the case of Boolean functions, the gap between the quantum and classical lower bounds is at most linear in the size of the support of the distribution, and does not depend on the size of the inputs. This translates into a bound on the gap between maximal Bell and Tsirelson inequality violations, which was previously known only for the case of distributions with Boolean outcomes and uniform marginals. It also allows us to show that for some distributions, information theoretic methods are necessary to prove strong lower bounds. Finally, we give an exponential upper bound on quantum and classical communication complexity in the simultaneous messages model, for any non-signaling distribution. One consequence of this is a simple proof that any quantum distribution can be approximated with a constant number of bits of communication.