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Quantum Key Distribution: Difference between revisions
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(Created page with "==Functionality== Quantum key distribution is a task that enables two parties, Alice and Bob, to establish a classical secret key by using quantum systems. A classical secret...") |
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*'''Secrecy''' A QKD protocol is <math>\epsilon_{\rm sec}</math>-secret if for every input state it holds that | *'''Secrecy''' A QKD protocol is <math>\epsilon_{\rm sec}</math>-secret if for every input state it holds that | ||
<math> \frac{1}{2}{\|{\rho_{K_AE}}-{\tau_{K_A}\otimes \rho_E}\|}_1\leq \epsilon_{\rm sec},</math> | <math> \frac{1}{2}{\|{\rho_{K_AE}}-{\tau_{K_A}\otimes \rho_E}\|}_1\leq \epsilon_{\rm sec},</math> | ||
where <math>\tau_{K_A}=\frac{1}{|K_A|}\sum_{k} | where <math>\tau_{K_A}=\frac{1}{|K_A|}\sum_{k}|{k}\rangle\langle{k}|_A</math> is the maximally mixed state in the space of strings <math>K_A</math>, and <math>{\|\cdot \|}_1</math> is the trace norm. | ||
*A protocol implements a <math>(n,\epsilon_{\rm corr},\epsilon_{\rm sec},\ell)</math>-QKD if with <math>n</math> rounds it generates an <math>\epsilon_{\rm corr}</math>-correct and <math>\epsilon_{\rm sec}</math>-secret key of size <math>\ell</math> bits. | *A protocol implements a <math>(n,\epsilon_{\rm corr},\epsilon_{\rm sec},\ell)</math>-QKD if with <math>n</math> rounds it generates an <math>\epsilon_{\rm corr}</math>-correct and <math>\epsilon_{\rm sec}</math>-secret key of size <math>\ell</math> bits. | ||