Research On Coherence Measure And Coherence Monotone Of Quantum States

Quantum coherence arising from the superposition of quantum states occupies an important position in the field of physics and has a wide range of applications in quantum information and quantum computing.Its measurement is an important subject.The robustness of multilevel coherence is an important coherence measure,but for general mixed states,this measure cannot be accurately calculated.First,this paper aims at the problem that the robustness of multilevel coherence is difficult to accurately calculate for the mixed state,using the theoretical method of semi-definite programming,through optimizing the coherence witnesses,a lower bound of the robustness of multilevel coherence is obtained.This paper gives the numerical expression of this lower bound,avoiding the difficulty of calculating the maximum eigenvalue of the k-order principal submatrix.In addition,a numerical example is used to verify the effectiveness of the lower bound.At the same time,this paper proposes a new coherence monotone that satisfies the non-negativity,monotonicity and convexity of the coherence measures.Although this coherence monotone does not strictly meet the four requirements of the coherence measurement in the coherent resource theory,to a certain extent,the coherence monotone quantifies quantum coherence,and plays a quantitative role in quantifying the cost of consumption in some algorithms of quantum computing.The first part of the thesis mainly introduces the research background of coherence measures,research status and progress at home and abroad.The second part of the thesis introduces the basic knowledge of quantum information and the resource theory of coherence needed in this article.The third part of the thesis uses the semi-definite programming method to construct the corresponding witness operators of coherence by restricting and optimizing a class of Hermite operators,and then obtains the lower bound of the robustness of multilevel coherence.At the same time,a numerical example is used to verify the effectiveness of the obtained lower bounds.The fourth part of the thesis gives a kind of coherence monotone,which satisfies the non-negativity,monotonicity and convexity of the coherence measures.In the variational algorithm of quantum computing,the coherence monotone quantifies the coherence and estimates the cost consumed in the algorithm,which is significant in optimizing the variational algorithms.