SARG04 (named after Valerio Scarani, Antonio Acín, Gregoire Ribordy, and Nicolas Gisin) is a 2004 quantum cryptography protocol derived from the first protocol of that kind, BB84.
Origin Researchers built SARG04 when they noticed that by using the four states of BB84 with a different information encoding they could develop a new protocol which would be more robust, especially against the photon-number-splitting attack, when attenuated laser pulses are used instead of single-photon sources. SARG04 was defined by Scarani et al. in 2004 in Physical Review Letters as a prepare and measure version (in which it is equivalent to BB84 when viewed at the level of quantum processing). An entanglement-based version has been defined as well.
Description In the SARG04 scheme, Alice wishes to send a private key to Bob. She begins with two strings of bits, a {\displaystyle a} and b {\displaystyle b} , each n {\displaystyle n} bits long. She then encodes these two strings as a string of n {\displaystyle n} qubits,
| ψ ⟩ = ⨂ i = 1 n | ψ a i b i ⟩ . {\displaystyle |\psi \rangle =\bigotimes _{i=1}^{n}|\psi _{a_{i}b_{i}}\rangle .}
a i {\displaystyle a_{i}} and b i {\displaystyle b_{i}} are the i t h {\displaystyle i^{\mathrm {th} }} bits of a {\displaystyle a} and b {\displaystyle b} , respectively. Together, a i b i {\displaystyle a_{i}b_{i}} give us an index into the following four qubit states:
| ψ 00 ⟩ = | 0 ⟩ {\displaystyle |\psi _{00}\rangle =|0\rangle }
| ψ 10 ⟩ = | 1 ⟩ {\displaystyle |\psi _{10}\rangle =|1\rangle }
| ψ 01 ⟩ = | + ⟩ = 1 2 | 0 ⟩ + 1 2 | 1 ⟩ {\displaystyle |\psi _{01}\rangle =|+\rangle ={\frac {1}{\sqrt {2}}}|0\rangle +{\frac {1}{\sqrt {2}}}|1\rangle }
| ψ 11 ⟩ = | − ⟩ = 1 2 | 0 ⟩ − 1 2 | 1 ⟩ . {\displaystyle |\psi _{11}\rangle =|-\rangle ={\frac {1}{\sqrt {2}}}|0\rangle -{\frac {1}{\sqrt {2}}}|1\rangle .}
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