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On problems in security of quantum key distribution raised by Yuen

In 2007, it was found that Known-Plaintext-Attack would reveal whole the string of the distributed key by Quantum Key Distribution (QKD) when the part of the plaintext was known to the eavesdropper, Eve, under the mutual information security criterion between Eve and legitimate users, Alice and Bob. To overcome, the trace distance criterion was introduced in the paper that the distance between the distributed quantum state and the ideal quantum state with Eve’s quantum system decoupled from the quantum systems shared by Alice and Bob. On the other hand, Shor and Preskill proved in 2000 that entanglement-based QKDs are equivalent to prepare-and-measure QKDs, such as the first QKD, BB84. Their proof employed the mutual information criterion, therefore M. Koashi applied Shor-Preskill approach to the trace distance criterion in 2009. However, H. P. Yuen started criticisms on the security of QKDs from 2009, then completed his criticisms in 2016. He warned the security of QKDs are not sufficient. Furthermore, the trace distance would not provide “universal composability”, which is supposed to guarantee Independent and Identically Distributed (IID) keys. He also proposed a new security criterion “Bit-Error-Rate (BER) guarantee,” to evaluate the BER in the decoded message by Eve with her key close to the correct key. In this work, the author explains Yuen’s criticisms and shows an example of the BER guarantee on BB84. Furthermore, the study revisits whether Shor-Preskill security proof approach really worked.