Quantum key distribution (QKD) is a cryptographic task in which two honest parties, Alice and Bob, wish to establish a common secret key that is unknown to any potential eavesdropper, Eve.
A security proof in quantum key distribution is a mathematical argument that shows the protocol is secure against any potential eavesdropper, even one with unlimited computing power and access to quantum technology.
The security proof is divided into two conditions. The first condition is correctness, which ensures that the probability that the final key of Alice differs from the final key of Bob is smaller than a specified threshold. Essentially, it ensures that Alice and Bob obtain the same key, and the protocol operates correctly. The second condition is secrecy, which guarantees that Eve learns almost nothing about the key even if she intercepts the quantum signals and uses full-fledged quantum technology to interpret them. The most general attack Eve can perform is called a coherent attack, where Eve can perform an arbitrary operation on her quantum side information, and further, the states distributed to Alice and Bob can have arbitrary correlations.
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