Data loss in quantum image representation methods

Quantum Image Representation is a well-studied area in quantum informatics. The first proposed algorithm was the qubit lattice method introduced in 2003. This method was not harnessing the full potential of the quantum system - using as many qubits as there were pixels in the image. The most commonly used methods right now are Flexible Representation of Quantum Images (FRQI) proposed in 2011, and Novel Enhanced Quantum Representation (NEQR) proposed in 2013, which uses superposition to encode a monochrome image on a quantum computer using a reduced number of qubits. In this paper, we want to compare these two methods, alongside Local Phase Image Quantum Encoding (LPIQE) method proposed in 2020, to see which method produces images with minimal data loss. Another comparison will be done with image encoded using the LPIQE method with Phase Distortion Unraveling (PDU) error mitigation method, which is done entirely on a classical computer. LPIQE implementation was intended for using the photonic quantum system since the phase-shift is easy to produce, and it will be implemented on real, photonic quantum computers after further development.