Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  presents three results on the por of two-prover one-round interactive proof systems based on oracularization under the existence of prior entanglement beten dishonest provers. It is proved that the two-prover one-round interactive proof system for PSPACE by Cai, Condon, and Lipton [JCSS 48:183-193, 1994] still achieves exponentially small soundness error in the existence of prior entanglement beten dishonest provers (and more strongly, even if dishonest provers are allod to use arbitrary no-signaling strategies). It follows that, unless the polynomial-time hierarchy collapses to the second level, two-prover systems are still advantageous to single-prover systems even when only malicious provers can use quantum information. It is also shown that a "dummy" question may be helpful when constructing an entanglement-resistant multi-prover system via oracularization. This affirmatively settles a question posed by Kempe et al. [FOCS 2008, pp. 447-456] and every language in NEXP is proved to have a two-prover one-round interactive proof system even against entangled provers, albeit with exponentially small gap beten completeness and soundness. In other words, it is NP-hard to approximate within an inverse-polynomial the value of a classical two-prover one-round game against entangled provers. Finally, both for the above proof system for NEXP and for the quantum two-prover one-round proof system for NEXP proposed by Kempe et al., it is proved that exponentially small completeness-soundness gaps are best achievable unless soundness analysis uses the structure of the underlying system with unentangled provers.
['Tsuyoshi Ito', 'Hirotada Kobayashi', 'Keiji Matsumoto']
I am writing a research paper on a idea Oracularization and Two-Prover One-Round Interactive Proofs against Nonlocal Strategies
[{"from": "human", "value": "I am writing a research paper on a idea Oracularization and Two-Prover One-Round Interactive Proofs against Nonlocal Strategies"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  presents three results on the por of two-prover one-round interactive proof systems based on oracularization under the existence of prior entanglement beten dishonest provers. It is proved that the two-prover one-round interactive proof system for PSPACE by Cai, Condon, and Lipton [JCSS 48:183-193, 1994] still achieves exponentially small soundness error in the existence of prior entanglement beten dishonest provers (and more strongly, even if dishonest provers are allod to use arbitrary no-signaling strategies). It follows that, unless the polynomial-time hierarchy collapses to the second level, two-prover systems are still advantageous to single-prover systems even when only malicious provers can use quantum information. It is also shown that a \"dummy\" question may be helpful when constructing an entanglement-resistant multi-prover system via oracularization. This affirmatively settles a question posed by Kempe et al. [FOCS 2008, pp. 447-456] and every language in NEXP is proved to have a two-prover one-round interactive proof system even against entangled provers, albeit with exponentially small gap beten completeness and soundness. In other words, it is NP-hard to approximate within an inverse-polynomial the value of a classical two-prover one-round game against entangled provers. Finally, both for the above proof system for NEXP and for the quantum two-prover one-round proof system for NEXP proposed by Kempe et al., it is proved that exponentially small completeness-soundness gaps are best achievable unless soundness analysis uses the structure of the underlying system with unentangled provers."}]