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== Quantum image representations ==
There are various approaches for quantum image representation, that are usually based on the encoding of color information. A common representation is FRQI (''Flexible Representation for Quantum Images''), that captures the color and position at every pixel of the image, and defined as:<ref name=":0">{{Citation |last1=Yan |first1=Fei |title=Quantum Image Representations |date=2020 |work=Quantum Image Processing |pages=19–48 |url=http://link.springer.com/10.1007/978-981-32-9331-1_2 |access-date=2024-10-31 |place=Singapore |publisher=Springer Singapore |language=en |doi=10.1007/978-981-32-9331-1_2 |isbn=978-981-329-330-4 |last2=Venegas-Andraca |first2=Salvador E.|url-access=subscription }}</ref><math display="block">\vert I \rangle = \frac{1}{2^{n}} \sum^{2^{2n-1}}_{i=0} \vert c_{i} \rangle \otimes \vert i \rangle</math>where <math display="inline">| i \rangle </math> is the position and <math display="inline">\vert c_{i} \rangle = cos \theta_{i} \vert 0 \rangle + sin \theta_{i} \vert 1 \rangle</math> the color with a vector of angles <math display="inline">\theta_{i} \in \left[0, \pi/2 \right]</math>. As it can be seen, <math display="inline">\vert c_{i} \rangle </math> is a regular [[Qubit#Qubit states|qubit state]] of the form <math>\vert \psi\rangle = \alpha \vert 0 \rangle + \beta \vert 1 \rangle</math>, with basis states <math display="inline">\vert 0 \rangle = \begin{pmatrix} 1 \\ 0 \end{pmatrix}</math> and <math display="inline">\vert 1 \rangle = \begin{pmatrix} 0 \\ 1 \end{pmatrix} </math>, as well as amplitudes <math display="inline">\alpha </math> and <math display="inline">\beta </math> that satisfy <math display="inline">\left|\alpha\right|^{2} + \left|\beta\right|^{2} = 1</math>.<ref>{{Citation |last1=Yan |first1=Fei |title=Introduction and Overview |date=2020 |work=Quantum Image Processing |pages=1–17 |url=http://link.springer.com/10.1007/978-981-32-9331-1_1 |access-date=2024-10-31 |place=Singapore |publisher=Springer Singapore |language=en |doi=10.1007/978-981-32-9331-1_1 |isbn=978-981-329-330-4 |last2=Venegas-Andraca |first2=Salvador E.|url-access=subscription }}</ref>
Another common representation is MCQI (''Multi-Channel Representation for Quantum Images''), that uses the [[RGB color model|RGB]] channels with quantum states and following FRQI definition:<ref name=":0" /><math display="block">\vert I\rangle = \frac{1}{2^{n+1}} \sum^{2^{2n-1}}_{i=0} \vert C^{i}_{RGB}\rangle \otimes \vert i\rangle</math><math display="block">\begin{aligned}
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