Decoherence-assisted quantum key distribution

Abstract

We put forward and demonstrate a controllable decoherence-assisted quantum key distribution scheme. The protocol is based on the possibility of introducing controllable decoherence to polarization qubits using the spatial degree of freedom of light. We show that our method reduces the amount of information that an eavesdropper can obtain in the BB84 protocol under the entangling probe attack. We demonstrate experimentally that Alice and Bob can agree on a scheme that gives low values of the quantum bit error rate, despite the presence of a large amount of decoherence in the transmission channel of the BB84 protocol.

Fig. 1

(a) Ideal BB84 protocol: Alice uses a light source that can be randomly prepared in a specific polarization state. Afterwards, Alice sends the light to Bob. On Bob’s side, he randomly chooses a basis to measure the state that Alice has sent. (b) BB84 protocol under the controllable decoherence-assisted scheme. and are parameters that tune the decoherence induced in Alice’s and Bob’s sides, respectively. (c) Entangling probe attack under the controllable decoherence-assisted scheme.

Fig. 2

(a) Rényi information as a function of when Eve uses the entangling probe attack with the controllable decoherence-assisted scheme. Setting , . The inset shows the same function for a wider range of values of . (b) Total Rényi information as a function of the total when Eve uses the entangling probe attack with the controllable decoherence-assisted scheme. For values of , the total Rényi information available to Eve is lower due to the effect of the controllable decoherence-assisted scheme. Since the maximum attainable Rényi information occurs at higher QBER values for lower values of , not only is Eve able to retrieve fewer information, but also obtains its maximal amount of information when introducing a higher amount of errors.

Fig. 3

Secure key rate as a function of distance, using Eq. (23). We assume that the QBER in each basis increases linearly with distance: and . The parameters chosen were (free space transmission), ( is the base QBER at zero distance), and ( is the coefficient that accounts for a linear increase in the QBER).

Fig. 4

Experimental setup. A 407 nm laser pump is used to create photon pairs in a collinear 4 mm BBO type II crystal. The pump’s polarization state is adjusted using a half-wave plate (HWP) and the pump is focused into the crystal using a lens (, with focal length ). After the crystal, the pump is removed using two long pass (LP) filters with cut-off wavelengths of 750 nm and an interference filter (IF) of 810 nm. The idler photon is transmitted in the BS and it is used to herald the presence of its pair taking into account polarization using . The signal photon is reflected in the PBS and then collected into the SMF to obtain a Gaussian mode. The polarization controller (PC) is used to correct the polarization state of the idler photon. After the PC, the spatial mode has a beam waist of  mm that ensures that the light is collimated throughout its whole optical path during the experiment. A rotating half-wave plate () constitutes the preparation stage. Subsequently, decoherence is induced and reversed by inserting P-TBD-A and P-TBD-B, respectively. On Bob’s side, and constitute the measurement stage. All the detections are recorded by a time stamping device.

Fig. 5

in the controllable decoherence-assisted scheme. In (a-d) the is plotted, for different values of , as a function of . Each data point in every figure was made by averaging the QBER of 1000 bits. From the different fits in (a)-(d), was estimated to be 6.87 ± 0.08 mm. In (e), the position of the value of that minimizes the QBER is plotted against . The minimum values of the QBER for every value of are shown in the inset table. The horizontal and vertical error bars correspond to the resolution attained by the PTBD, i.e., .