# Quantum Image Steganography Schemes for Data Hiding: A Survey
## 3 Quantum Image Steganography Schemes
### Entanglement as a Degree of Freedom  
Briefly, the concept suggested by [PERSON] et al. introduces a novel approach to quantum steganography which manipulates the characteristics of the communication channel of an entangled pair of photons [13]. The entangled duo's channel combines two domains, entanglement, and polarization. The intended exploiting of the medium occurs when the entanglement domain is used as a secondary method to represent the concealed message. Conversely, the cover data used as a disguise is encoded within the polarization domain.  
First, for this quantum steganography scheme to be employed, it must distinguish between an entangled pair and an independent single photon. To detect entanglement an interferometer is used, with respect to a Mach-Zehnder interferometer in Figure 3, which is applied for analysis.  
Figure 3 illustrates the regular composition of a Mach-Zehnder interferometer. The beam splitter BS is normally considered a semi-reflecting mirror, built using a transparent material with one side reflecting. The mentioned interferometer comprises two base vectors named lower arm and upper arm, which depict a photon's state spanning the interferometer either through its lower or upper arm, respectively.  
\[\mid L\rangle=\ \binom{1}{0},\ \mid U\rangle-\ \binom{0}{1}. \tag{11}\]  
Due to the beam splitter being reflective on one side, the first beam splitter (BS1) will allow the reversing to the upper arm \(U\) only for half of the incident beam, while the second half of the beam will go across the lower arm \(L\). By quantum mechanics, the photon issimultaneously mirrored through \(U\) and crosses into \(L\). The below matrix expresses the behavior as a model of the quantum operator:  
\[BS1=\frac{1}{\sqrt{2}}\begin{pmatrix}e^{2i\theta}&e^{i\theta}\\ e^{\theta}&-1\end{pmatrix} \tag{12}\]  
Secondly, after birthing the photon, the information can be encoded within the entanglement domain. Codes, for instance, 0's and 1's bits are determined by the physical process that generated that photon. Values of induced bits are known by the triggering of a certain photon detector in the interferometer. Specifically, when a photon is transferred via a Mach-Zehnder interferometer, it can provoke a 1 or 0 reading by correspondingly exiting the apparatus vertically or horizontally. A vertical exit results in a registered click by D2. However, a horizontal exit issues a click by D1. Often, entangled photons' way out are performed horizontally.  
Finally, the scheme implements quantum steganography by concealing secret data with the host data. Both can hold any format (image, video, audio, text, etc.). The results of this scheme have shown an outstanding performance in all areas, such as embedding capacity, as it can hide an image equal to the size of the cover image, along with its ability to cause no degradation to the stego image's quality, and its simplicity and adaptability. Since the two states of photons are independent, both secret and host data are separate, such that any modifications made to the carrier image will not affect the hidden image.