**Quantum Error Correcting Codes and The Security of BB84 Part I** - Richard Cannings

BB84 is a quantum key distribution protocol that allows two parties to generate an unbreakable secret key. This is a very important protocol in both quantum information science and cryptography because BB84 has unparalleled security and it appears close to being physically realizable. It took over 12 years to prove the security of BB84, and even then, the proofs were complicated and only understood by few. In 2000, Shor and Preskill published a simplified proof of security for BB84 based on properties of CSS quantum error correcting codes. In this two part tutorial, we follow the Shor-Preskill proof (quant-ph/0003004) and introduce necessary background material.
BB84 is a quantum key distribution protocol that allows two parties to generate an unbreakable secret key. This is a very important protocol in both quantum information science and cryptography because BB84 has unparalleled security and it appears close to being physically realizable. It took over 12 years to prove the security of BB84, and even then, the proofs were complicated and only understood by few. In 2000, Shor and Preskill published a simplified proof of security for BB84 based on properties of CSS quantum error correcting codes. In this two part tutorial, we follow the Shor-Preskill proof (quant-ph/0003004) and introduce necessary background material.
In the first lecture, we discuss
- BB84
- classical error correcting codes,
- the random sample test,
- correlation purification, and
- a practical variant of BB84.