# Limitations of quantum advice and one-way communication

@article{Aaronson2004LimitationsOQ, title={Limitations of quantum advice and one-way communication}, author={Scott Aaronson}, journal={Proceedings. 19th IEEE Annual Conference on Computational Complexity, 2004.}, year={2004}, pages={320-332} }

Although a quantum state requires exponentially many classical bits to describe, the laws of quantum mechanics impose severe restrictions on how that state can be accessed. This paper shows in three settings that quantum messages have only limited advantages over classical ones. First, we show that BQP/qpoly /spl sube/ PP/poly, where BQP/qpoly is the class of problems solvable in quantum polynomial time, given a polynomial-size "quantum advice state " that depends only on the input length. This…

## 112 Citations

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- Computer ScienceSTOC '04
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The main result is that the membership x∈SAT can be proved by a logarithmic-size quantum state, together with a polynomial-size classical proof consisting of blocks of length polylog(n) bits each, such that after measuring the state |Ψ〉 the verifier only needs to read one block of the classical proof.

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- Mathematics21st Annual IEEE Conference on Computational Complexity (CCC'06)
- 2006

This paper introduces a new technique for removing existential quantifiers over quantum states. Using this technique, we show that there is no way to pack an exponential number of bits into a…

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The results imply that quantum-classical protocols need to send ( p n/logn) bits/qubits to compute Equality on n-bit strings, and hence are not significantly better than classical- classical protocols (and are much worse than quantum-quantum protocols such as quantum fingerprinting).

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The complexity of approximate counting, the problem of multiplicatively estimating the size of a nonempty set S ⊆ [N], is resolved in two natural generalizations of quantum query complexity.

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