Quantum Multi-Prover Interactive Proof Systems: Difference between revisions

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Title: Quantum Multi-Prover Interactive Proof Systems
Title: Quantum Multi-Prover Interactive Proof Systems


Main Research Question: Can quantum computation provide a significant advantage over classical computation in the setting of multi-prover interactive proof systems?
Main Research Question: How strong is a quantum analogue of multi-prover interactive proof systems?


Methodology: The researchers introduced a model of quantum multi-prover interactive proof systems, which is a natural extension of the single-prover quantum interactive proof systems. They aimed to determine if the quantum analogue has any gain over the classical counterpart in this setting.
Methodology: The researchers used the formal treatment of quantum computation to construct a quantum multi-prover interactive protocol. They assumed that provers could share at most polynomially many prior-entangled qubits.


Results: The researchers proved that the class of languages having quantum multi-prover interactive proof systems is equal to NEXP, implying that the quantum analogue has no gain over the classical counterpart. They also showed that, in case the prover does not have his private qubits, the class of languages having single-prover quantum interactive proof systems is also equal to NEXP.
Results: The researchers proved that the class of languages having quantum multi-prover interactive proof systems is necessarily contained in non-deterministic exponential time (NEXP). This implies that, under the assumption of limited prior entanglement, the class of languages having quantum multi-prover interactive proof systems is equal to NEXP. They also showed that, in the case a prover does not have his private qubits, the class of languages having quantum single-prover interactive proof systems is also equal to NEXP.


Implications: These results provide the first exact characterizations of a classical time complexity class in quantum computational terms. They suggest that the power of quantum computation in the setting of multi-prover interactive proof systems is not significantly greater than that of classical computation. This could have implications for the development of quantum computing algorithms and the understanding of the power of quantum computation.
Implications: This research suggests that quantum multi-prover interactive proof systems might be weaker than classical ones, especially when provers are allowed to share prior-entangled qubits. It also provides a basis for further exploration into the power and limitations of quantum interactive proof systems.


Link to Article: https://arxiv.org/abs/0102013v3
Link to Article: https://arxiv.org/abs/0102013v5
Authors:  
Authors:  
arXiv ID: 0102013v3
arXiv ID: 0102013v5


[[Category:Computer Science]]
[[Category:Computer Science]]

Latest revision as of 02:03, 24 December 2023

Title: Quantum Multi-Prover Interactive Proof Systems

Main Research Question: How strong is a quantum analogue of multi-prover interactive proof systems?

Methodology: The researchers used the formal treatment of quantum computation to construct a quantum multi-prover interactive protocol. They assumed that provers could share at most polynomially many prior-entangled qubits.

Results: The researchers proved that the class of languages having quantum multi-prover interactive proof systems is necessarily contained in non-deterministic exponential time (NEXP). This implies that, under the assumption of limited prior entanglement, the class of languages having quantum multi-prover interactive proof systems is equal to NEXP. They also showed that, in the case a prover does not have his private qubits, the class of languages having quantum single-prover interactive proof systems is also equal to NEXP.

Implications: This research suggests that quantum multi-prover interactive proof systems might be weaker than classical ones, especially when provers are allowed to share prior-entangled qubits. It also provides a basis for further exploration into the power and limitations of quantum interactive proof systems.

Link to Article: https://arxiv.org/abs/0102013v5 Authors: arXiv ID: 0102013v5

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