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Paper 1
Parallel repetition with a threshold in quantum interactive proofs
Abel Molina
- Year
- 2020
- Journal
- arXiv preprint
- DOI
- arXiv:2008.07445
- arXiv
- 2008.07445
In this note, we show that $O(\log (1/ε))$ rounds of parallel repetition with a threshold suffice to reduce completeness and soundness error to $ε$ for single-prover quantum interactive proof systems. This improves on a previous $O(\log (1/ε) \log \log (1/ε))$ bound from Hornby (2018), while also simplifying its proof. A key element in our proof is a concentration bound from Impagliazzo and Kabanets (2010).
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Security bound of cheat sensitive quantum bit commitment
Guang Ping He
- Year
- 2014
- Journal
- arXiv preprint
- DOI
- arXiv:1407.7517
- arXiv
- 1407.7517
Cheat sensitive quantum bit commitment (CSQBC) loosens the security requirement of quantum bit commitment (QBC), so that the existing impossibility proofs of unconditionally secure QBC can be evaded. But here we analyze the common features in all existing CSQBC protocols, and show that in any CSQBC having these features, the receiver can always learn a non-trivial amount of information on the sender's committed bit before it is unveiled, while his cheating can pass the security check with a probability not less than 50%. The sender's cheating is also studied. The optimal CSQBC protocols that can minimize the sum of the cheating probabilities of both parties are found to be trivial, as they are practically useless. We also discuss the possibility of building a fair protocol in which both parties can cheat with equal probabilities.
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