Secure Communication Using Mesoscopic Coherent States

We demonstrate theoretically and experimentally that secure communication using intermediate-energy (mesoscopic) coherent states is possible. Our scheme is different from previous quantum cryptographic schemes in that a short secret key is explicitly used and in which quantum noise hides both the bit and the key. This encryption scheme allows optical amplification. New avenues are open to secure communications at high speeds in fiber-optic or free-space channels.

Figure 1

$P_e^E$ as a function of $M$ for $|\alpha {|}^2=1,10,100,1000$.

Figure 2

Left side: Basic ciphering scheme with qumodes of polarization. Right side: Two neighboring bases in an $M$ry manifold on a great circle of Poincaré’s sphere. Bits $0$ and $1$ are antipodals for each basis. Closest states (similar polarization ellipses) represent opposite bit values.

Figure 3

Schematic of the experimental setup. SPCM, single photon counting module; PBS, polarization beam splitter; L, lens; P, polarizer; NDF, neutral density filter. Two (optional) telescopes are shown for field work.

Figure 4

Difference of $V$ and $H$ counts ($V-H$) from Bob’s receiver operating at 200 kHz, with the average number of received photons $⟨n⟩=|\alpha {|}^2=27$ and $M=50$. The right inset shows the corresponding histogram indicating clear separation between the 0 and 1 bit values.

Figure 5

$V-H$ counts from Eve’s receiver in an opaque attack in which she takes all the power from the channel that would have gone to Bob. All operating parameters are the same as in Fig. 4, except for Eve lacking the key ${\mathbf{K}}^{\prime }$. The corresponding histogram on the right shows that distinct bits are not distinguishable by her.

Figure 6

(a) Measurement of the polarization angle through two-mode direct detection with use of a PBS. A $\lambda /2$ wave plate is rotated to produce different polarization angles $\varphi$. (b) Uncertainties in $\varphi$, $\Delta \varphi$, arise owing to photon-number fluctuations around $⟨n_H⟩$ and $⟨n_V⟩$, where $n_H$ and $n_V$ are the photon numbers sampled by the two detectors ($⟨n_H{n}_V⟩=⟨n_H⟩⟨n_V⟩$). (c) Variance in the angle $\varphi$ obtained via the two-mode measurement versus the angle set by the $\lambda /2$ plate. The solid line is the theoretical prediction, not a fit, without considering the detector noises (mainly “dark” and Johnson noises), which will set the ultimate precision limit in these measurements.

Figure 7

Number of bases $N_{\sigma }$ covered by the quantum noise as a function of the number of photons $⟨n⟩=|\alpha {|}^2$. For a given $⟨n⟩$, Alice repeatedly sets every basis, separated by $\pi /M$ ($M=500$), one by one, by applying a voltage to the EOM. By measuring $n_H$ and $n_V$, Eve performs an angle reconstruction in an attempt to identify the basis used. Eve’s standard deviation around the basis sent by Alice gives $N_{\sigma }$. The line is the theory.