On single-photon quantum key distribution in the presence of loss

Abstract

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 optimisation problem known as a semidefinite program, which can be efficiently solved. Moreover, we prove that the solution to the dual optimisation 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.

14 pages, 6 figures

References in corpus (6)

• A complete family of separability criteria
• Efficient quantum key distribution secure against no-signalling eavesdroppers
• Detecting multipartite entanglement
• Security proof of a three-state quantum key distribution protocol without rotational symmetry
• Spherical Code Key Distribution Protocols for Qubits
• One-way quantum key distribution: Simple upper bound on the secret key rate

Cited by in corpus (2)

• Testing Quantum Devices: Practical Entanglement Verification in Bipartite Optical Systems
• Upper bounds for the secure key rate of decoy state quantum key distribution