Quantum image representations based on density matrices in open quantum systems

Abstract

So far, research on quantum image representation has gone through more than 20 years. During this time, the quantum image representation models used have almost all been based on state vectors. However, in practical problems, the environment and the principal quantum system cannot be separated, and isolated quantum systems do not exist in principle. This case is often referred to as an open quantum system. In open quantum systems, many problems involve density matrices, such as the calculation of Von Neumann entropy, the quantization of coherence, and the operator-sum representations of quantum operations. Therefore, the existing quantum image representation models are only suitable for closed quantum systems. To this end, the paper proposes three models that can not only represent quantum images in an open quantum system but also decompose the evolution process of quantum images utilizing operator-sum decomposition. These three models are the representation model of quantum gray-scale images, the tensor product representation model of quantum color images, and the representation model of quantum color images based on mixed states in the Bloch sphere, respectively. All these image representation models have strong correlations among them and are very different from their classical analogues. Between them, the biggest difference is that the paper employs density matrices, inspired by incoherent-coherent states, to represent quantum images rather than classical state vectors. By means of one of the representation models proposed in the paper, we finally demonstrate the evolution process of the quantum image going through the amplitude damping channel.