On Quantum-Classical Equivalence for Composed Communication Problems

Details On Quantum-Classical Equivalence for Composed Communication Problems On Quantum-Classical Equivalence for Composed Communication Problems

2009-06-08

arxiv.org/abs/0906.1399v3

Quantum Information & Computation, 10(5-6):435-455, 2010

Computer Science

Computational Complexity

Journal version

Scientific paper

An open problem in communication complexity proposed by several authors is to prove that for every Boolean function f, the task of computing f(x AND y) has polynomially related classical and quantum bounded-error complexities. We solve a variant of this question. For every f, we prove that the task of computing, on input x and y, both of the quantities f(x AND y) and f(x OR y) has polynomially related classical and quantum bounded-error complexities. We further show that the quantum bounded-error complexity is polynomially related to the classical deterministic complexity and the block sensitivity of f. This result holds regardless of prior entanglement.

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