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Quantum cryptography with local Bell tests

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Quantum cryptography with local Bell tests
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Abstract
In this work, we propose the concept of self-testing QKD which is based on a novel local self-testing method. In particular, devices are tested locally independent of the quantum channel, that is, Alice and Bob perform Clauser-Horne-Shimony-Holt (CHSH) tests, an application of Bell's theorem on their own devices, independent of each other and the quantum channel. Note that because the quantum channel is not included in CHSH test, the channel loss cannot be used to open the detection loophole. The security assessment of the quantum channel follows the channel estimation technique of BB84 QKD protocol, i.e., checking for errors in the bases X and Z. Therefore, by deriving the relation between CHSH test and a recent security proof technique (the smooth version of entropic uncertainty relation), the finite-key security proof is obtained under minimal assumptions. Also, our result – a lower bound on the secret key rate – is intuitively related to the almost tight finite-key analysis of BB84 QKD protocol and it differs only by a term that is dependent on the CHSH value. Most importantly, we obtained secret key rates that are comparable to ones of BB84 QKD protocol.