Some conservative estimates in quantum cryptography
S. N. Molotkov · Journal of Experimental and Theoretical Physics · 2006
Relationship is established between the security of the BB84 quantum key distribution protocol and the forward and converse coding theorems for quantum communication channels. The upper bound Q c ≈ 11% on the bit error rate compatible with secure key distribution is determined by solving the transcendental equation % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfKttLearuqr1ngBPrgarmWu51MyVXgatC% vAUfeBSjuyZL2yd9gzLbvyNv2CaeHbd9wDYLwzYbItLDharyavP1wz% ZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbb% L8F4rqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yqaqpe% pae9pg0FirpepeKkFr0xfr-xfr-xb9adbaqaaeGaciGaaiaabeqaam% aaeaqbaaGcbaaceiGaa8hsaGabaiaa+HcacaWFrbWaaSbaaSqaaiaa% -ngaaeqaaOGaa4xkaiaa+1daceWFdbGbaebacaGFOaaccaGae0xWdi% Naa4xkaiaa+9cacaGFYaaaaa!44F9! $$H(Q_c ) = \bar C(\rho )/2$$ , where ρ is the density matrix of the input ensemble, % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfKttLearuqr1ngBPrgarmWu51MyVXgatC% vAUfeBSjuyZL2yd9gzLbvyNv2CaeHbd9wDYLwzYbItLDharyavP1wz% ZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbb% L8F4rqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yqaqpe% pae9pg0FirpepeKkFr0xfr-xfr-xb9adbaqaaeGaciGaaiaabeqaam% aaeaqbaaGcbaaceiGab83qayaaraaceaGaa4hkaGGaaiab9f8aYjaa% +Lcaaaa!3ED5! $$\bar C(\rho )$$ is the classical capacity of a noiseless quantum channel, and H(Q) is the capacity of a classical binary symmetric channel with error rate Q.