Fig. 1. Photoluminescence properties of GaAs QDs in a p-i-n diode structure at a temperature of 20 K, excited by resonant TPE. (a) p-i-n diode structure with a tunnel barrier between the n-doped and the intrinsic regions. The inset shows the principle of TPE, with $E_{\mathrm{P}}$ the laser energy, $E_{\mathrm{B}}$ the biexciton (XX) binding energy, and $S$ the exciton (X) FSS. (b) Emission spectra at TPE conditions when sweeping the diode voltage $V_{\mathrm{P}}$ in forward bias. The inset shows the diode current $I$ over $V_{\mathrm{P}}$. The white-dashed line indicates $V_{\mathrm{P},0}=0.3\mathrm{V}$, at which the diode is operated during the QKD experiment. (c) Emission at $V_{\mathrm{P}}=V_{\mathrm{P},0}$. (d) Second-order correlation function $g^{(2)}$ of the X signal with a time-bin of $1\mu \mathrm{s}$ at $V_{\mathrm{P}}=V_{\mathrm{P},0}$. The $g^{(2)}$ is shown for the QD in the diode structure (red), indicating an on-time fraction of $\beta =1.00(2)$ and a QD without diode (black, dashed) with a typical value of $\beta \approx 0.3$. (e) Wavelength shift and $\beta$ for different deviations $\delta V_{\mathrm{P}}=V_{\mathrm{P}}-V_{\mathrm{P},0}$. The blue-dashed line indicates a value of $\beta$ corresponding to no blinking.

Fig. 2. Emission properties relevant for the polarization entanglement, measured at a temperature of 20 K. (a) Spectra of the individually filtered XX and X emission lines combined at a 50:50 fiber beam splitter. (b) Single-photon emission characteristics of the XX and X signals observed by detecting coincidences in a Hanbury–Brown–Twiss arrangement. The histogram for the X emission is shifted horizontally and vertically to facilitate reading. (c) Decay dynamics of the XX and X signals. The X signal exhibits a slow secondary decay channel, which is not present at temperatures lower than 10 K. (d) Examples among the 36 recorded coincidence histograms between the XX and X detections, corresponding to a measurement in the HV basis. The red-dashed lines indicate the time-bin of 2 ns, in which the coincidences are summed up to calculate the peak areas. (e) Unpolarized coincidence measurement between the XX and X photons. The excess coincidences at zero time delay stem from a nonunity photon-pair generation probability. (f) Density matrix of the two-photon polarization entangled state of the XX and X photons, recorded by full state tomography.

Fig. 3. Key generation in the BBM92 protocol over a time span of about 8 h and entanglement-based QKD. (a) QKD arrangement. Alice and the photon source are situated on an optical table, and Bob is placed in a movable box on a table in another building and connected with the source via a 350-m long single mode fiber. (b) QBER during the key generation with an average of 8.42%. The red-dashed line marks the maximum allowed QBER for BBM92 in the infinite key regime. (c) Raw key rate (after key sifting) with an average of $54.8\mathrm{bits}/\mathrm{s}$. (d) Encryption of a bitmap with the dimensions of $67\times 70\text{pixels}$ and a color-depth of 4 bits, resulting in a total size of about 2.4 kilobytes. The encryption with Alice’s key yields a scrambled message ready to be sent over a public channel. (e) Decryption at Bob’s site when using an uncorrected key (left) and a corrected key (right).

Table 1. Summarized emitter performance for two representative QDs in a diode structure excited by TPE, measured at temperatures of 5 K and 20 K, respectively.