Controlling Of The Entropic Uncertainty In Qubits System Under Noisy Environment By Local Quantum Operations

As one of the fundamental ideas of quantum theory, the uncertainty principle reveals the characteristics of quantum mechanics distinctively di?ering from the classical world. The principle constrains the uncertainty about the outcomes of two incompatible measurements performed on a particle. Quantum-memoryassisted entropic uncertainty relation is improved entropic uncertainty relation depending on the amount of entanglement, which is not only a generalization and extension of the original uncertainty relations, but also more convenient for application in developing quantum technologies, such as quantum measures, quantum cryptography, and witnessing entanglement. Since its fundamental role, quantummemory-assisted entropic uncertainty relation has attracted wide attention and has been studied from various viewpoints.Any realistic physical system will su?er from unwanted interactions with the outside environments. One of the natural consequences of the interaction between the system and its environment is decoherence and destroying entanglement, which can be viewed as the loss of information of the system and thus increases system’s entropic uncertainty. How to eliminate the in?uence of noises on the coherence of quantum systems, break through the restriction of the quantum entropic uncertainty of measurements and realize quantum physics experiments with ultra low noise or noiseless is one of central concerns in quantum physics researches. Using the technologies of weak measurements and PT-symmetric operation, two schemes of local quantum operations have been brought out to control the entropic uncertainty in entangled qubits system under quantum noises, and a series of innovative results are obtained.The main contents are as follows:In Chapter 1, a research background of uncertainty relations is introduced.In Chapter 2, the study progress of uncertainty relations is introduced in brief. The theory of the quantum-memory assisted entropic uncertainty relation is expatiated chie?y.In Chapter 3, the basic theory of quantum computation and quantum measurements, and two types of quantum operations are introduced.In Chapter 4, the dynamics of quantum-memory assisted entropic uncertainty relation in two-qubit system under quantum noisy environment and classical noisy environment respectively has been studied. Under the local quantum noisy environment, the mathematical expression of quantum-memory assisted entropic uncertainty relation for a class Bell-diagonal states is given. Based on that, the dynamics of quantum-memory assisted entropic uncertainty relation under types of typical local quantum noisy channel has been examined. It is shown that the entropic uncertainty of measurements increases signi?cantly by the in?uence of noises. On the other hand, we also con?rm the e?ciency of quantum memory on reducing the entropic uncertainty in qubits system. For the situation that the local noise environments are modeled as classical noises, we focus on two classes of classical noise: the random phase noise and the random telegraph noise with a Lorentzian spectrum. It is shown that the quantum entropic uncertainty increases monotonously in the Markovin regime, while display risen oscillations in the non-Markovian regime. The increasing ratio of quantum entropic uncertainty is related to the coe?cients of the environmental noises. Thus, we can suppress the quantum-memory assisted entropic uncertainty in qubits system by controlling the noisy coe?cients.In Chapter 5, a scheme of local weak measurement and weak measurement reversal using to control the entropic uncertainty in entangled two-qubit system under local generalized amplitude damping channel has been presented. The optimum strength of weak measurements in this scheme is obtained through numericalanalysis. We ?nd that, by choosing suitable operation strength, the scheme of weak measurements works well for suppressing the entropic uncertainty in qubits system even in the long-time limit or under strong noises. The di?erent in?uence of weak measurement and weak measurement reversal on entropic uncertainty reduction has also been discussed respectively.In Chapter 6, a scheme of local PT-symmetric operation using to reduce the entropic uncertainty in entangled two-qubit system under local amplitude damping channel has been presented. It is found that local PT-symmetric operation can e?ectively reduce the entropic uncertainty in qubits system for comparatively strong operation strength. When the PT-symmetric operation is strongly nonHermitian, the quantum-memory-assisted entropic uncertainty can be reduced to its lower bound. Based on the property of entanglement and the Non-Hermiticity ofPT-symmetric Hamiltonian, possible physical explanations for the behavior of entropic uncertainty under local PT-symmetric operation has been given respectively.In Chapter 7, a summary and outlook is presented.