A Family of Finite Geometry LDPC Codes for Quantum Key Expansion

• A quantum key distribution (QKD) protocol allows two parties Alice and Bob to establish secret key through one-way quantum communications and classical public communications. With the aid of an entanglement-assisted (EA) quantum error correcting (QEC) code, QKD can be made to expand a secret key, and the process is known as quantum key expansion (QKE). • Luo and Devetak[1] derived a QKE protocol by modifying the EA entanglement-distillation (EAED) protocol with the use of EA Calderbank-Shor-Steane (CSS) QEC codes. • Our initial goal is to search for QEC codes that guarantee high net key rates for QKE. The Original QKE Protocol • Let C1 and C2 be two classical [n, k1] and [n, k2] codes with parity-check matrices H1 and H2. and c = rank(M), ∃ nonsingu-• Let M = H1H T 2 lar matrices T1 and T2 s.t. • For i = 1, 2, le