The security of quantum key distribution protocols can be proven in an information-theoretic manner. While principal security may be proven for one protocol or a family of protocols, proving security under realistic conditions, such as with finite data sets and noise, requires the adaptation of existing proofs to account for these effects.

A common distinction is made between discrete- and continuous-variable protocols (DV and CV protocols). DV protocols have a finite set of measurement outcomes, which experimentally correspond to single-photon detectors detecting a click or not. CV protocols have an infinite amount of possible measurement outcomes and experimentally correspond to homodyne detection. Mathematically, DV security proofs work with low-dimensional Hilbert spaces, while CV proofs have to deal with infinite dimensional ones, which makes their security proofs more challenging.

The tables below are meant to serve as a state-of-the art reference of open problems in security proofs and the associated publications that solved the issues.

DV Security Proofs

ProtocolIndividual AttacksCollective AttacksCoherent AttacksFinite-sizeDetector noise
Decoy BB84
Differential phase-shift (DPS)

CV Security Proofs

Attack Strategy
General coherent)
Finite-size effects
Detector noise
Gaussian modulation of coherent states (GMCS)
---- GG02 [arXiv][PRL]
Binary phase-shift keying (BPSK)
---- Leverrier2010-02 [arXiv]
Quadrature phase-shift keying (QPSK)
---- Leverrier2010-02 [arXiv]
---- Leverrier2010-05 [arXiv][PRA]
m-ary phase-shift keying (mPSK)
---- Becir2010 [arXiv][IJQI]
Quadrature Amplitude Modulation (QAM)