Research On The Transformation Of Quantum States Under The Theory Of Quantum Resources

As a rapidly developing field in quantum information science,quantum coherence is a basic feature of quantum mechanics and plays a very important role in quantum physics.After the theoretical framework of standard coherent resource was proposed,quantum coherence has attracted the attention of many scholars,and other theoretical frameworks of coherent resources have been proposed one after another.It is of great significance for quantum informatics to study the transformation of quantum states and the measure of quantum coherence within the framework of quantum coherence resource theory.The main content of this paper is to study the transformation of quantum states and coherence measurement in block-coherent resource theory and POVM coherent resource theory.This paper is organized as follows.In chapter 1,we mainly review some basic knowledge and basic concepts in quantum information science,including the density matrix of quantum states,quantum measurement,the theoretical framework of standard coherent resources,entropy and the coherence measure of quantitative quantum state transformation under the framework of standard coherent resource theory.In chapter 2,we first review the theoretical framework of block-coherent resources.Then we introduce a block-coherent monotone C_max(?,P)based on the maximally relative entropy under the maximally block-incoherent operation and another block-coherent monotone C₀(?,P)under the block-incoherent operation.Then we give the expression of the maximally block-coherent state in the framework of block-coherent resource theory,calculate the value of the block-coherent monotonic C_max(?,P)when the state is the maximally block-coherent state,and draw the conclusion that the value of block-coherent monotone C_max(?_N,P)is related to the number of projection operators N in the space.At the same time,the upper bound of the block-coherent monotone C_max(?,P)with specific states is calculated.In addition,we dis-cuss the deterministic block-coherent dilution process in the block-coherent resource theory by constructing block-incoherent operations,and give a set of specific block-incoherent operation Kraus operators by an example.Finally,we define one-shot block-coherent cost,quantify the value of block-coherent dilution in one-shot scenario,and give the bounds of one-shot block-coherent cost under the maximally block-incoherent operation and block-incoherent operation,respectively.In chapter 3,we review several well-defined block-coherence metrics under the block-coherent resource theory,and define another block-coherence metric C_min(?,P)based on min-imum relative entropy.Then we specifically calculate the upper bound of the block-coherent metric C_min(?,P)and the block-coherent monotone C_max(?,P)of two special quantum states,and calculate the value of the block-coherence metric C_rel(?,P),and all of them are shown in the graph.In chapter 4,we first review the theoretical framework of POVM coherent resources,and we introduce the POVM coherent monotone C_max(?,E)based on the maximally relative en-tropy.Then we give the definition of one-shot coherent cost in the POVM coherent resource theoretical framework,and prove the bound of one-shot coherent dilution under the maximally POVM incoherent operation.