Finite-size security of continuous-variable quantum key distribution with digital signal processing

Abstract

In comparison to conventional discrete-variable (DV) quantum key distribution (QKD), continuous-variable (CV) QKD with homodyne/heterodyne measurements has distinct advantages of lower-cost implementation and affinity to wavelength division multiplexing. On the other hand, its continuous nature makes it harder to accommodate to practical signal processing, which is always discretized, leading to lack of complete security proofs so far. Here we propose a tight and robust method of estimating fidelity of an optical pulse to a coherent state via heterodyne measurements. We then construct a binary phase modulated CV-QKD protocol and prove its security in the finite-key-size regime against general coherent attacks, based on proof techniques of DV QKD. Such a complete security proof is indispensable for exploiting the benefits of CV QKD.

Explicit asymptotic secret key rate of continuous-variable quantum key distribution with an arbitrary modulation

“…At the other end of the spectrum, it is tempting to drastically reduce the number of coherent states in the constellation to simplify as much as possible the hardware requirements of the protocols as well as the reconciliation procedure (where Alice and Bob extract a common raw key from their correlated data). Protocols with 2, 3 or 4 coherent states have been considered in the literature and are part of the general class of M -PSK (phaseshift keying) protocols where Alice sends coherent states of the form |α k = |αe 2πik/M for some α > 0 [2,16,17,25,28,30,33,39,47]. While M = 2 or 3 appear to be too small to yield good performance, the 4-PSK (also known as quadrature phase-shift keying, QPSK) modulation scheme has attracted some interest since it performs reasonably well, although quite far from a Gaussian modulation.…”

Discrete-modulation continuous-variable quantum key distribution with high key rate

“…The future works include the optimization of the key rate of the discrete-modulation protocol in the short distance transmission by extending current state constellation or other new constellation design schemes [52], and finding better data postselection strategies [53,54]. Extending our security analysis to include the impact of finite-size is also an important future task [55][56][57]. In Fig.…”

Discrete-variable quantum key distribution with homodyne detection

“…Indeed, in the case of the first assumption, one would need an infinite amount of randomness to simulate the required Gaussian distribution, which is clearly not possible in practice. To overcome this gap, one solution is to consider the discrete approximation of Gaussian modulation [11], or alternatively, discrete-modulated CV-QKD protocols based on constellations of coherent states (or displaced thermal states) [12][13][14][15][16][17][18][19][20][21][22]. Moreover, working with discrete modulation protocols has another advantage, in that could significantly reduce the implementation complexity and computational resources required by the classical post-processing layer [5, 14-16, 23, 24].…”

“…An example of Gaussian-modulated CV-QKD is the aforementioned GG02 protocol [10], while some examples of discrete-modulated CV-QKD can be found in Refs. [11][12][13][14][15][16][17][18][19][20][21][22]. Finally, DV-QKD with homodyne detection includes Ref.…”