Quantum key distribution with any two independent and identically distributed states

To prove the security of quantum key distribution (QKD) protocols, several assumptions have to be imposed on users' devices. From an experimental point of view, it is preferable that such theoretical requirements are feasible and the number of them is small. In this paper, we provide a security proof of a QKD protocol where the usage of any light source is allowed as long as it emits two independent and identically distributed (i.i.d.) states. Our QKD protocol is composed of two parts: the first part is characterization of the photon-number statistics of the emitted signals up to three-photons based on the method [M. Kumazawa, T. Sasaki, and M. Koashi, Opt. Express 27, 5297 (2019)], followed by running our differential-phase-shift protocol [A. Mizutani, T. Sasaki, Y. Takeuchi, K. Tamaki, and M. Koashi, npj Quantum Inf. 5, 87 (2019)]. It is remarkable that as long as the light source emits two i.i.d. states, even if we have no prior knowledge of the light source, we can securely employ it in the QKD protocol. As this result substantially simplifies the requirements on light sources, it constitutes a significant contribution to realizing truly secure quantum communication.

Figure 1

Our model of a light source with which we prove the security. The upper (lower) figure shows that, when Alice chooses $b_i^A=0$ ($b_i^A=1$), the light source emits state ${\widehat{\rho }}_0$ (${\widehat{\rho }}_1$). As long as the light source emits these i.i.d states, no other characterizations of the light source are required.

Figure 2

The characterization method [19] using a Hanbury-Brown-Twiss setup with $D=4$ threshold detectors. By monitoring the $r$-fold coincidence probabilities for $r\in \{1,...,D\}$, Alice obtains all the parameters in $P_{\mathrm{char}}$. Specifically, state ${\widehat{\rho }}_0$ (${\widehat{\rho }}_1$) is measured for obtaining $p_0^L$ and $p_0^U$ ($p_1^L$ and $p_1^U$), and ${\left\{{\widehat{\rho }}_S^{{\vec{b}}_A}\right\}}_{{\vec{b}}_A\in {\{0,1\}}^3}$ is measured for obtaining ${\left\{q_n\right\}}_{n=1}^3$.

Figure 3

Secret key rate $R$ per pulse as a function of the overall channel transmission $\eta$. From top to bottom, we plot the key rates for the cases of 0, 1, 3, and 5% intensity fluctuations under $e_{\mathrm{bit}}=1\%$. Note that the top line with no-intensity fluctuations corresponds to the case of Ref. [20].

Figure 4

Secret key rate $R$ per pulse as a function of the overall channel transmission $\eta$. From top to bottom, we plot the key rates for the cases of 0, 1, 3, and $5\%$ intensity fluctuations. Unlike the calculations in Fig. 3, $e_{\mathrm{bit}}$ is not constant, and the degradation of $e_{\mathrm{bit}}$ over distance is reflected.