Continuous-variable quantum key distribution (CV-QKD) protocols with discrete modulation are interesting due to their experimental simplicity, but their security analysis is less advanced than that of Gaussian modulation schemes. We analyze the security of two variants of CV-QKD protocol with quaternary modulation against collective attacks in the asymptotic limit. Our security analysis is based on the numerical optimization of the asymptotic key rate formula with a photon number cutoff assumption that truncates the dimension of the system. When the cutoff photon number is chosen to be sufficiently large, our results do not depend on the specific choice of cutoff. Our analysis shows that this protocol can achieve much higher key rates over long distances compared with binary and ternary modulation schemes and yield key rates comparable to Gaussian modulation schemes. Furthermore, our security analysis method allows us to evaluate variations of the discretemodulated protocols, including direct and reverse reconciliation, and also postselection strategies. We also demonstrate that postselection in combination with reverse reconciliation can improve the key rates.

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.

We present an analysis of the entangling quantum kicked top focusing on the few qubit case and the initial condition dependence of the time-averaged entanglement SQ for spin-coherent states. We show a very strong connection between the classical phase space and the initial condition dependence of SQ even for the extreme case of two spin-1/2 qubits. This correlation is not related directly to chaos in the classical dynamics. We introduce a measure of the behavior of a classical trajectory which correlates far better with the entanglement and show that the maps of classical and quantum initial-condition dependence are both organized around the symmetry points of the Hamiltonian. We also show clear (quasi-)periodicity in entanglement as a function of number of kicks and of kick strength.

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