Uncertainty Relation Of Quantum Coherence

The quantum uncertainty relation reveals the intrinsic difference that distinguishes the quantum world from the classical world.For the same particle,two noncommutative quantities（such as position and momentum）cannot be measured accurately at the same time.The quantum uncertainty relation based on entropy is of great significance in the field of quantum information theory,such as the quantum key distribution,quantum teleportation,generation of quantum random number and so on.On the other hand,the coherence of quantum state is the embodiment of superposition principle of quantum state,and it is one of the most basic characteristics of quantum mechanics.Quantum uncertainty relation usually includes classical part and quantum part.The quantum uncertainty relation of coherence is regarded as quantum part（or real quantum uncertainty relation）.Based on the definition of quantum relative entropies of coherence,this paper mainly makes the following work:1.The analytical expression of Sandwiched Renyi relative entropy of coherence in the mixed states has not been solved.In this paper,the analytic expression of Sandwiched Renyi relative entropy of coherence in mixed state is obtained by convex-roof construction.The unified（α,β）-relative entropy is taken as the distance function,it is shown that the unified（α,β）-relative entropy of coherence is a qualified quantum coherence measure.And the analytical formula of the unified（α,β）-relative entropy of coherence is presented.2.The quantum uncertainty relations of Sandwiched Renyi relative entropy of coherence,unified（α,β）-relative entropy of coherence and a affinity coherence for single-qubit states are considered by analytic expression.3.Considering the limitation of the method in single qubit system,it can not be extended to general qubits,therefore,this paper uses the optimization method to improve this defect.The uncertainty relation of the Renyi relative entropy of coherence,the unified（α,β）-relative entropy of coherence and the α affinity coherence are presented in a d-dimensional quantum system;in addition,our results cover the quantum uncertainty relations of the other three coherence measures（the logarithmic robustness of coherence,Renyi relative entropy of coherence and Tsallis relative entropy of coherence）.4.In the last part of this paper,the dynamics of quantum uncertainty based on coherence in quantum channel which mainly includes amplitude damped channel,phase flip channels,depolarization channel and phase damped channel are studied.The influence of the initial state of the quantum state on the uncertainty relation of the coherence is also discussed.