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


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 by naturally extending the model of quantum single-prover interactive proof systems defined by Watrous. They then proved that the class of languages that have quantum multi-prover interactive proof systems is equal to NEXP, implying that the quantum analogue has no gain to the classical counterpart in the setting 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 showed that, in case the prover does not have his private qubits, the class of languages that have single-prover quantum interactive proof systems is also equal to NE XP. This gives the first exact characterization of classical time complexity class in quantum computational words.
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 provides insights into the power of quantum computation in the setting of multi-prover interactive proof systems. It suggests that quantum computation may not always offer a significant advantage over classical computation, even in scenarios where quantum computation has demonstrated superior performance. This could have implications for the development of quantum algorithms and the understanding of the limits 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/0102013v2
Link to Article: https://arxiv.org/abs/0102013v5
Authors:  
Authors:  
arXiv ID: 0102013v2
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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