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
Protocol | Individual Attacks | Collective Attacks | Coherent Attacks | Finite-size | Detector noise |
---|---|---|---|---|---|
BB84 | |||||
Decoy BB84 | |||||
Differential phase-shift (DPS) | |||||
CV Security Proofs
Protocol | (Individual, Collective, General coherent) | Finite-size effects | |
---|---|---|---|
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) | |||
Post-selection | |||