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## Abstract

We show that any classical two-way communication protocol with shared randomness that can approximately simulate the result of applying an arbitrary measurement (held by one party) to a quantum state of n qubits (held by another), up to constant accuracy, must transmit at least Ω(2n) bits. This lower bound is optimal and matches the complexity of a simple protocol based on discretisation using an -net. The proof is based on a lower bound on the classical communication complexity of a distributed variant of the Fourier sampling problem. We obtain two optimal quantum-classical separations as easy corollaries. First, a sampling problem which can be solved with one quantum query to the input, but which requires Ω(N) classical queries for an input of size N. Second, a nonlocal task which can be solved using n Bell pairs, but for which any approximate classical solution must communicate Ω(2n) bits.

Original language | English |
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Pages (from-to) | 154-177 |

Number of pages | 24 |

Journal | Quantum |

Volume | 3 |

DOIs | |

Publication status | Published - 28 Jun 2019 |

## Structured keywords

- Bristol Quantum Information Institute
- QITG