Study On The Construction Of Mutually Unbiased Bases And Its Application In Quantum Coherence

Quantum information theory is an interdisciplinary subject of quantum mechan-ics and information science.It has been widely studied because quantum mechanics plays an important role in quantum communication and quantum computing.Mutual-ly unbiased bases on optimal measurement is an effective tool in quantum informatics Quantum coherence is one of the most basic properties in quantum mechanics.Quan-tum coherence plays an important role in quantum computing and quantum biology.This shows that it is of great significance to explore the construction of mutually un-biased bases and its applications in quantum coherence.In order to achieve this aims,many scholars are studying the construction of mutually unbiased bases in term of mutually unbiased bases.And the unbiasedness between different bases is also dis-cussed.In terms of quantum coherence,many scholars started to study the nature of quantum coherence from the theoretical framework of quantum coherence proposed by Baumgratz et al.Regarding the application of mutually unbiased bases in quantum coherence,a few scholars have recently discussed the low-dimensional system.This article focuses on the research of mutually unbiased basis and quantum co-herence.Mainly study the two from three aspects.First,study on the construction of mutually unbiased bases.Second,study on the character of quantum coherence.Finally,study on the application of mutually unbiased basis in quantum coherence.The content of the paper is as follows:First,we study the the construction of mutually unbiased bases.We study the construction of mutually unextended maximally entangled bases in Cd(?)Cd+1.And we construct d+1 mutually unbiased bases using orthogonal Latin squares in Cd(?)Cd.Finally,the construction of mutually unbiased bases in multi-system system is studiedThen,we study on quantum coherence.In terms of quantum coherence,we mainly consider two coherence:l2 norm of coherence and Schatten-2 norm of coherence.We calculate two coherence and the two incoherent states closest to these.And we calculate the coherence in some states.Finally,we explore the trade-off relationship between these two coherence and mixednessIn the last part,we combine mutually unbiased bases and quantum coherence.First,the calculation and comparison of quantum coherence in some different states are studied.Then,we examine the study of quantum coherence by mutually unbiased bases in C2 and C4.