Physics

Pathology

Cryptography

Key (lock)

Mathematics

Algorithm

Statistics

Reduction (mathematics)

Square root

Mathematical analysis

Key generation

Matching (statistics)

Alternative medicine

Geometry

Protocol (science)

Computer science

Quantum mechanics

Quantum key distribution

Security analysis

Computer security

Medicine

Upper and lower bounds

Quantum

Scaling

Physical review. A/Physical review, A

Variations of phase-matching measurement-device-independent quantum key distribution (PM-MDI QKD) protocols have been investigated before, but it was recently discovered that this type of protocol (under the name of twin-field QKD) can beat the linear scaling of the repeaterless bound on secret key capacity. We propose a variation of PM-MDI QKD protocol, which reduces the sifting cost and uses non-phase-randomized coherent states as test states. We provide a security proof in the infinite key limit. Our proof is conceptually simple and gives tight key rates. We obtain an analytical key rate formula for the loss-only scenario, confirming the square root scaling and also showing the loss limit. We simulate the key rate for realistic imperfections and show that PM-MDI QKD can overcome the repeaterless bound with currently available technology.

Simple security analysis of phase-matching measurement-device-independent quantum key distribution