# Quantum Image Steganography Schemes for Data Hiding: A Survey
## 2 Background  
Today, quantum computers provide a new paradigm for solving problems that are computationally intensive using traditional programming methods. However, before real quantum computers become mainstream, classical emulation with high-performance computing is an acceptable approach for the efficient simulation and simplification of quantum algorithms. For practical scenarios, quantum processing units (or QPUs) are expected to be added as accelerators at the hardware level for improved performance. For instance, QPUs can work together with graphics processing units (GPUs) in classic supercomputers. For this matter, a few hybrid algorithms have been proposed such as variational quantum eigensolver, variational factoring, etc. [20; 21]. The concept of steganography has gone through a long history, as the first documented implementation was around 440 BC [22]. After that, steganography has been expressed through different mediums. From hiding messages using traditional communication methods and letters to using computers by hiding messages through classical bits and the employment of quantum information and protocols to implement steganography. Figure 1: Recently implemented quantum image steganography schemes. In steganography, attackers can detect and gain access to hidden data through a steganographic source if the scheme is not secure enough. For instance, if the embedding scheme is too simple to detect, it becomes easy for attackers to access the embedded information. Moreover, the hidden data must not be detectable when embedded in an image, making it important to increase the imperceptibility of a steganographic picture [23]. There are several attributes that a steganography scheme must include to succeed in achieving high security. The authors in [6; 24] described a few main categories for calculating an image steganography's performance, which include:  
* Hiding capacity--Evaluates the size of data that the scheme is capable to embed into the carrier image. The sizes can vary from hiding text segments to images equal to the size of the cover image. * Imperceptibility--demonstrates the opaqueness of the hidden image and assesses whether the human eye can depict a steganographic image. * Security--determines the difficulty for unauthorized parties to access and manipulate the hidden data. * Robustness--exhibits how robust the hidden data is against received attacks and its ability to maintain its state. * Unambiguity--the ability to identify the copyright owner of the secret data. To implement quantum image steganography, researchers experimented with hiding images and messages with different quantum image representations [25]. With the presence of different models of quantum images, finding the appropriate image model for implementing a steganography scheme is essential, as each image representation comprises unique characteristics that distinguish it from other models [26]. For this reason, deciding on the appropriate type of image representation to be used in steganography is a crucial step to ensure the success of data hiding. The most popular image representations, namely, flexible representation of quantum images, novel enhanced quantum representation, new quantum representation of color digital images, and quantum multi-wavelength image representation are presented below [27]:  
Flexible representation of quantum images (FRQI) is a model that produces information regarding an image's color as well as its position in a quantum state directly from a classical image representation, producing a grayscale image. The FRQI model can be represented using the following formula, as mentioned in [23]:  
\[|I\rangle=\ \frac{1}{2^{n}}\sum_{i=0}^{2^{2n}-1}|\ c_{i}\rangle\otimes|\ i\rangle, \tag{1}\]  
In the previous formula, \(\otimes\) defines the tensor product notation, while \(|\ c_{i}\rangle\) portrays the two-dimensional quantum states, as well as the image's color information, which corresponds to the angle vector represented by \(\theta\).