A novel enhanced quantum image representation based on bit-planes for log-polar coordinates

Quantum image representation has a significant impact in quantum image processing. In this paper, a bit-plane representation for log-polar quantum images (BRLQI) is proposed, which utilizes $(n+4)$ or $(n+6)$ qubits to store and process a grayscale or RGB color image of $2^n$ pixels. Compared to a quantum log-polar image (QUALPI), the storage capacity of BRLQI improves 16 times. Moreover, several quantum operations based on BRLQI are proposed, including color information complement operation, bit-planes reversing operation, bit-planes translation operation and conditional exchange operations between bit-planes. Combining the above operations, we designed an image scrambling circuit suitable for the BRLQI model. Furthermore, comparison results of the scrambling circuits indicate that those operations based on BRLQI have a lower quantum cost than QUALPI. In addition, simulation experiments illustrate that the proposed scrambling algorithm is effective and efficient.

Quantum imaging of a polarisation sensitive phase pattern with hyper-entangled photons

A transparent polarisation sensitive phase pattern makes a polarisation dependent transformation of quantum state of photons without absorbing them. Such an invisible pattern can be imaged with quantum entangled photons by making joint quantum measurements on photons. This paper shows a long path experiment to quantum image a transparent polarisation sensitive phase pattern with hyper-entangled photon pairs involving momentum and polarisation degrees of freedom. In the imaging configuration, a single photon interacts with the pattern while the other photon, which has never interacted with the pattern, is measured jointly in a chosen polarisation basis and in a quantum superposition basis of its position which is equivalent to measure its momentum. Individual photons of each hyper-entangled pair cannot provide a complete image information. The image is constructed by measuring the polarisation state and position of the interacting photon corresponding to a measurement outcome of the non-interacting photon. This paper presents a detailed concept, theory and free space long path experiments on quantum imaging of polarisation sensitive phase patterns.