Single-photon quantum key distribution in the presence of loss

Journal Article · Tue May 15 04:00:00 EDT 2007 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.75.052336· OSTI ID:20982505

Curty, Marcos ^[1]; Moroder, Tobias ^[2]

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1. Center for Quantum Information and Quantum Control, Department of Physics and Department of Electrical and Computer Engineering, University of Toronto, Toronto, Ontario, Canada M5S 3G4 (Canada)
2. Institute for Quantum Computing, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, Canada N2L 3G1 (Canada)

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.

• OSTI ID: 20982505
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 5 Vol. 75; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DISTRIBUTION
EVALUATION
EXPECTATION VALUE
INFORMATION THEORY
LOSSES
MATHEMATICAL SOLUTIONS
OPTIMIZATION
PHOTONS
QUANTUM CRYPTOGRAPHY
QUANTUM MECHANICS
SECURITY
VERIFICATION