Some conservative estimates in quantum cryptography

Abstract

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.