Research On The Quantum Coherence Manipulations

In the framework of quantum resource theory,quantum coherence is a kind of important and available physical resource,and it can be used to realize quantum communication and quantum computation which are difficult to realize in classical information processing.Relative to the mature field of quantum entanglement,the study of quantum coherence has just emerged,and it has become a hot topic in the basic research of quantum theory in recent years.The research field of quantum coherence includes coherence quantification,the dynamic evolution and protection of coherence,the relationship between coherence and non-classical correlations,the application of coherence and so on.Quantum coherence manipulation is one of the main research topics in the framework of quantum resource theory,and it mainly deals with the conversion between two coherent states via incoherent operations.Coherent states can be viewed as a kind of physical resource,and we need specific coherent states for quantum information processing in practical applications,so studying coherence manipulation and transformation will help us to get the target coherent states we need,and it is of great significance to study coherence manipulation in quantum information processing.The study of non-classical correlations such as quantum entanglement can help people to understand the relationship between non-classical correlations and their physical significance.In addition,studying the enhancement of quantum superposition will help us to understand the quantum superposition from a more general point of view.In this dissertation,based on the existing coherence theory,studies including quantum coherence manipulation(quantum coherence transformation),quantum coherence distillation,the relationship between quantum coherence and non-classical correlations,and the enhancement of quantum superposition have been given carried out.The main new results are presented as follows:1.The conditions for coherence manipulation of mixed coherent states under incoherent operations are proposed.The sufficient and necessary conditions for coherence transformation from a pure coherent state to a mixed coherent state are given,based on which,the optimal distillation scheme from a coherent pure state to the maximally coherent state is studied,and the largest amount of distilled coherence and the corresponding optimal probability can be obtained.On the basis of this optimal distillation protocol,another optimal distillation protocol which is only involving a single incoherent operation has been constructed.Besides,the sufficient and necessary conditions for coherence transformation of arbitrary two pure states and two general mixed states are obtained.2.The coherence-assisted transformation of pure coherent states and mixed coherent states is studied.For pure coherent states,the amount of coherence loss can be reduced by appropriately designing the coherence-assisted transformation,thus the waste of resources is avoided.The catalytic coherence transformation of pure states and the supercatalytic coherence transformation of pure states are studied,and the results show that the coherence transformation between two arbitrary finite dimensional pure coherent states can be realized via only low-dimensional auxillary states.For mixed coherent states,starting from the coherence transformation and distillation for a class of special mixed coherent states,the protocol of the catalytic coherence transformation of higher-rank mixed coherent states has been proposed.The corresponding strictly incoherent operations are proposed,and thus the coherence distillation can be realized.The conditions for catalytic coherence transformation for arbitrary two general mixed coherent states is obtained.3.The relationship between coherence and non-classical correlations is studied.In the framework of coherence resources theory,studying the relationship between coherence and non-classical correlations can reveal their intrinsic relations and the profound physical meaning of different non-classical correlations.Firstly,for the simple case of two particle coherent pure states,the strict mathematical relationship between coherence and entanglement can be obtained.The results show that the coherence and entanglement are equivalent in some respects,although the range of coherence is larger than that of entanglement.Secondly,the result of pure states can be extended to mixed states by the methods of spectral decomposition and convex expansion,and in general the strict mathematical relationship between coherence and entanglement is obtained.4.The problem of enhancing superposition of a quantum state under superposition-free operations is studied.We study the issue of enhancing the superposition of a quantum state in the framework of superposition resource theory,that is,the superposition of quantum states can be enhanced under the stochastic diagonal superposition-free Kraus operators.Then,according to the matrix analysis theory,the maximal value of superposition that can be achieved for a general mixed state under the stochastic diagonal superposition-free Kraus operators is given,and the corresponding optimal probability can be obtained too.The study of quantum superposition in a general sense can help us to understand quantum correlations and resource theory from a more general perspective.