Quantum Steganography via Coherent and Fock State Encoding in an Optical Medium

TL;DR

This work develops schemes for steganographic communication using Fock and coherent states in optical channels based on disguising the communications as thermal noise based on bounds on their efficiency in the case of an all-powerful eavesdropper, and explicit methods of encoding and error correction for the noiseless channel case.

Abstract

Steganography is an alternative to cryptography, where information is protected by secrecy -- being disguised as innocent communication or noise -- rather than being scrambled. In this work we develop schemes for steganographic communication using Fock and coherent states in optical channels based on disguising the communications as thermal noise. We derive bounds on their efficiency in the case of an all-powerful eavesdropper, and provide explicit methods of encoding and error correction for the noiseless channel case.

Figures (7)

• Figure 1: A plot of the lower bound on the communication rate for the vertical angle (key) encoding scheme compared to the "Distribution" (no key) scheme.
• Figure 2: in this setup, a beam splitter combines the coherent states denoted by $\ket{r}$ and $\ket{\beta}$, with $n_c$ and $n_d$ denoting detectors that measure the incidence of photons. The value of the homodyne measurement is given by $m=n_c-n_d$.
• Figure 3: Two views of the plot of $p_{err}$ as a function of $r_c=- \frac{m_c}{2\beta\sqrt{\Bar{n}}}$ and $\Bar{n}$. The optimal value of $r_c$ is between .4 and .5.
• Figure 4: The division of the thermal state in terms of $r$ (adapted from phdthesis) (a) and the associated communication rates for various values of $\Bar{n}$ and $f$. In descending order, the plots display the optimized value of the communication rate per bit of secret key (b), and both the communication rate (c) and rate per bit of key (d) when the quantity to be optimized is simply the communication rate.
• Figure 5: The communication rate $R$, key rate $K$, and quotient $\frac{R}{K}$ for encoded transmission using homodyne-type (orange) and Helstrom-type (blue) measurements at a variety of $f$ and $\Bar{n}$ values.