Intermode-interaction-induced dynamics of continuous-variable quantum-key-distribution observables

We theoretically study the dynamical regimes of the observables that govern the operating conditions of continuous-variable (CV) quantum-key-distribution (QKD) systems, depending on quantum-channel-induced intermode interactions. In contrast to the widely used approach in which losses and thermal broadening are introduced through a beam-splitter transformation, our analysis uses the exactly solvable quantum channel model describing the Lindblad dynamics of multimode bosonic systems interacting with a heat bath and additionally takes into account imperfections of the homodyne-detection scheme. The analytical results for the photon-count difference and the quadrature probability distributions are used to derive the expression for the mutual information between legitimate parties, which explicitly links the information properties of CV QKD and the parameters of the channel. For the important special case of a two-mode photonic system propagating in a fiber channel, the latter can be conveniently parameterized using the frequency and the relaxation-rate vectors that characterize the coherent (dynamical) intermode couplings and the incoherent (environment mediated) interaction between the bosonic modes, respectively. It turns out that these vectors determine four qualitatively different dynamical regimes of the mutual information and the phase difference between the signal and the local oscillator that may significantly affect the operation of CV QKD.