### Abstract

The central question in quantum multi-prover interactive proof systems is whether or not entanglement shared among provers affects the verification power of the proof system. We study for the first time positive aspects of prior entanglement and show how it can be used to parallelize any multi-prover quantum interactive proof system to a one-round system with perfect completeness, soundness bounded away from one by an inverse-polynomial in the input size, and one extra prover. Alternatively, we can also parallelize to a three-turn system with the same number of provers, where the verifier only broadcasts the outcome of a coin flip. This "public-coin" property is somewhat surprising, since in the classical case public-coin multi-prover interactive proofs are equivalent to single-prover ones.

Original language | English (US) |
---|---|

Pages (from-to) | 273-307 |

Number of pages | 35 |

Journal | Computational Complexity |

Volume | 18 |

Issue number | 2 |

DOIs | |

State | Published - Jun 1 2009 |

### Fingerprint

### Keywords

- Entanglement
- Interactive proof systems
- Multi-prover interactive proof systems
- Quantum computing

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computational Theory and Mathematics
- Mathematics(all)
- Computational Mathematics

### Cite this

*Computational Complexity*,

*18*(2), 273-307. https://doi.org/10.1007/s00037-009-0275-3

**Using entanglement in quantum multi-prover interactive proofs.** / Kempe, Julia; Kobayashi, Hirotada; Matsumoto, Keiji; Vidick, Thomas.

Research output: Contribution to journal › Article

*Computational Complexity*, vol. 18, no. 2, pp. 273-307. https://doi.org/10.1007/s00037-009-0275-3

}

TY - JOUR

T1 - Using entanglement in quantum multi-prover interactive proofs

AU - Kempe, Julia

AU - Kobayashi, Hirotada

AU - Matsumoto, Keiji

AU - Vidick, Thomas

PY - 2009/6/1

Y1 - 2009/6/1

N2 - The central question in quantum multi-prover interactive proof systems is whether or not entanglement shared among provers affects the verification power of the proof system. We study for the first time positive aspects of prior entanglement and show how it can be used to parallelize any multi-prover quantum interactive proof system to a one-round system with perfect completeness, soundness bounded away from one by an inverse-polynomial in the input size, and one extra prover. Alternatively, we can also parallelize to a three-turn system with the same number of provers, where the verifier only broadcasts the outcome of a coin flip. This "public-coin" property is somewhat surprising, since in the classical case public-coin multi-prover interactive proofs are equivalent to single-prover ones.

AB - The central question in quantum multi-prover interactive proof systems is whether or not entanglement shared among provers affects the verification power of the proof system. We study for the first time positive aspects of prior entanglement and show how it can be used to parallelize any multi-prover quantum interactive proof system to a one-round system with perfect completeness, soundness bounded away from one by an inverse-polynomial in the input size, and one extra prover. Alternatively, we can also parallelize to a three-turn system with the same number of provers, where the verifier only broadcasts the outcome of a coin flip. This "public-coin" property is somewhat surprising, since in the classical case public-coin multi-prover interactive proofs are equivalent to single-prover ones.

KW - Entanglement

KW - Interactive proof systems

KW - Multi-prover interactive proof systems

KW - Quantum computing

UR - http://www.scopus.com/inward/record.url?scp=68149178814&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=68149178814&partnerID=8YFLogxK

U2 - 10.1007/s00037-009-0275-3

DO - 10.1007/s00037-009-0275-3

M3 - Article

VL - 18

SP - 273

EP - 307

JO - Computational Complexity

JF - Computational Complexity

SN - 1016-3328

IS - 2

ER -