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Cryptographic security of quantum key distribution is currently based on atrace distance criterion. The widespread misinterpretation of the criterion asfailure probability and also its actual scope have been discussed previously.Recently its distinguishability advantage interpretation is re-emphasized as anoperational guarantee, and the failure probability misinterpretation ismaintained with a further failure probability per bit interpretation. In thispaper we explain the basic perpetuating error as a confusion on thecorrespondence between mathematics and reality. We note that the assignment ofequal a priori probability of 1/2 to the real and ideal situations fordistinguishability advantage would not lead to operational guarantee. Weexplain why operational guarantee in terms of Eve's probabilities of gettingvarious key bits is necessary for security, and why the failure probabilityinterpretation misrepresents the security situation. The scope and limits ofthe trace distance guarantee are summarized. It is shown that there would havebeen no security problem to begin with if the failure probability per bitinterpretation validity.

What The Trace Distance Security Criterion in Quantum Key Distribution Does And Does Not Guarantee