Quantum Resources in Heisenberg XX Model Under Noisy Environment
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Quantum Resources in Heisenberg XX Model Under Noisy Environment Zhu Liu1
· Wen-Yang Sun2 · Xiao-Gang Fan1 · Dong Wang1 · Liu Ye1
Received: 19 June 2020 / Accepted: 18 August 2020 / © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract In this paper, we investigate Einstein-Podolsky-Rosen steering, Bell non-locality, first-order coherence and concurrence in the spin- 12 Heisenberg XX model. We first quantify these quantum resources in Heisenberg spin chain model. In fact, the spin chain model will be inevitably affected by environmental noise. Then, we find the dynamical behavior, which is a interaction of two qubits and an open environment, can test the properties of quantum resources. And the influences of these parameters are investigated on quantum resources, including the coupling coefficient, temperature, magnetic field strength and the parameters of channel. Furthermore, we will get dynamical behavior of the stable state under the circumstance of BF channel. And the role of spin chains in quantum information processing can be realized. Finally, we explore the stability of coherence, steering and Bell non-locality in AD channel. These explain how to obtain the ideal quantum state by achieving the control through quantum steering and other operations under noisy environment. Keywords Heisenberg model · Decoherence channel · Bell non-locality · Quantum steering
1 Introduction In the past decades, considerable attention has been paid to quantum information and computation which are contained in quantum mechanics as an important area. However, we can not do a better job of controlling quantum states in some fields. Quantum entanglement stems from the phenomenon of Einstein-Podolsky-Rosen (EPR) paradox [1–3]. The concept of EPR steering was first recommended by Schrodinger in 1935 [4] to analyze the EPR paradox. What is more, it has been playing an significant role in the field of quantum information processing and quantum communication. Quantum steering has been theorized as a special quantum correlation in quantum information, and it is a vital method to quantify Liu Ye
[email protected] 1
School of Physics & Material Science, Anhui University, Hefei 230601, China
2
School of electrical & Electronic Engineering, Science and Technology University, Bengbu 233030, China
International Journal of Theoretical Physics
ideal quantum state [5]. In general, once the steering measures satisfy the constraints, such as the entropic uncertainty relation of steering, we will think there are two systems: one is closed quantum system and the other is open quantum system. Closed systems do not take the environmental impact into consideration, however, the quantum states actually contained in the open environment are inevitably influenced by the surroundings [6–12]. Generally speaking, the degradation of coherence is caused by external noise environment. Hence,we investigate the different cases of quantum steering etc in the above systems. The concept of entangled states was initially proposed b
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