2006/11/14 by Marcos Curty, Tobias Moroder
Computer Science · Mathematics · Physics and Astronomy · #Computer science #Computer security #Key (lock) #Mathematics #Operator (biology) #Photon #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum channel #Quantum information #Quantum key distribution #Quantum mechanics #Quantum state #Set (abstract data type) #quant-ph
paper · pdf · doi:10.1103/physreva.75.052336
published as Phys. Rev. A 75, 052336 (2007) · 14 pages, 6 figures
arxiv created 2006/11/14 · openalex publication_date 2007/05/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We investigate two-way and one-way single-photon quantum key distribution (QKD) protocols in the presence of loss introduced by the quantum channel. Our analysis is based on a simple precondition for secure QKD in each case. In particular, the legitimate users need to prove that there exists no separable state (in the case of two-way QKD), or that there exists no quantum state having a symmetric extension (one-way QKD), that is compatible with the available measurements results. We show that both criteria can be formulated as a convex optimization problem known as a semidefinite program, which can be efficiently solved. Moreover, we prove that the solution to the dual optimization corresponds to the evaluation of an optimal witness operator that belongs to the minimal verification set of them for the given two-way (or one-way) QKD protocol. A positive expectation value of this optimal witness operator states that no secret key can be distilled from the available measurements results. We apply such analysis to several well-known single-photon QKD protocols under losses.