Phase noise model for continuous-variable quantum key distribution using a local local oscillator

Polarization Attack on Continuous-Variable Quantum Key Distribution with a Local Local Oscillator

“…Based on the scheme described above, the phase noise for the quantum signal can be estimated by [ 21 , 30 , 35 ] where the phase noise is dominated by the phase reference measurement noise . Here, is the amplitude of the phase reference on Bob’s side, is the total added noise imposed on the phase reference given by [ 30 , 31 , 35 ] where is the excess noise of the phase reference with typical value [ 36 ].…”

“…Based on the scheme described above, the phase noise for the quantum signal can be estimated by [ 21 , 30 , 35 ] where the phase noise is dominated by the phase reference measurement noise . Here, is the amplitude of the phase reference on Bob’s side, is the total added noise imposed on the phase reference given by [ 30 , 31 , 35 ] where is the excess noise of the phase reference with typical value [ 36 ]. In the trusted phase noise model [ 30 ], part of the phase reference measurement noise associated with the detector efficiency and the electronic noise of Bob’s detector as well as the phase reference intensity on the receiver side that can be locally calibrated by Bob is considered to be trusted in order to get a higher secret key rate and longer transmission distance.…”

“…In this regard, the added noises for the quantum signal can be modeled as follows [ 30 ]: In Equation (6), represents the total channel added noise referred to the channel input, in which stands for the total excess noise obtained from the parameters estimation procedure, and mainly consists of the following parts [ 30 ]: Here, is the system excess noise stemming from the unidentified or unprotected sources [ 28 ]. is the modulation noise that can be expressed as [ 35 ] , where quantifies the maximal amplitude of the quantum signal.…”

“…Despite the outstanding superiority of the LLO CVQKD in simplifying the hardware required and circumventing the LO attacks, its performance improvement is still severely retarded by the relatively high phase noise [ 28 , 29 ]. As a realistic option, one can use the trusted phase noise model to significantly improve the phase noise tolerance of the LLO CVQKD, in which part of the phase noise that can be locally calibrated by Bob is moved from the channel-added noise to the detector-added noise to get a better QKD performance [ 30 ]. For example, with some typical parameters, the transmission distance of the LLO CVQKD based on Gaussian modulation is limited to 40-km.…”

“…For example, with some typical parameters, the transmission distance of the LLO CVQKD based on Gaussian modulation is limited to 40-km. Then, using the trusted phase noise model one can increase the corresponding maximum transmission distance by more than 65% and the secret key rate at the transmission distance of 25-km by more than 60% with the same simulation parameters [ 30 ]. Nevertheless, in a practical LLO CVQKD system, a relatively weak classical phase reference is generated from the signal laser and propagates along with the quantum signal from Alice to Bob to establish a reliable phase relationship between the quantum signal and the LO.…”