Research On The Key Issues Of Quantum Network Coding Based On Quantum Repeater

With the rapid development of quantum communication technology,global quantum networks are regarded as the next-generation information processing platform for unconditional secure communication.Quantum network coding,as a key technology in quantum communication networks,allows linear operations on data at nodes,effectively alleviating the common bottleneck problems in networks and significantly improving the transmission efficiency of quantum communication networks.Given the increasing demands for enhancing the efficacy of quantum communication networks,quantum network coding has become an indispensable research direction in the field of quantum communication.During the research on quantum network coding,there are four key issues that need to be addressed.Firstly,inappropriate selection of resource states leads to suboptimal coding performance,resulting in high communication overhead and inefficient communication.Secondly,the single dimensional encoding operation restricts the dimensional space of transmitted states,impeding the development of multidimensional quantum communication and leading to a singularity of information dimensions.Thirdly,the lack of scalable quantum networks topology hinders the dynamic construction of multipartite entangled networks and poses limitations on network topology.Fourthly,due to limitations in resources,technology,and costs,existing coding schemes fail to meet the diverse requirements of networks,making it difficult to adapt to different communication tasks and resulting in a monotonicity of communication functions.Among these issues,the high communication overhead and inefficiency caused by the inappropriate selection of resource states are the primary contradictions,which have a chain effect on other key problems.Fortunately,the emergence of quantum repeater technology can largely address the aforementioned issues.The basic principle of quantum repeater technology is to combine segmented entanglement distribution and entanglement swapping,replacing point-to-point transmission with segmented cascading to extend the communication distance.Based on the quantum repeater technology,driven by the key issues in quantum network coding(high communication costs and low efficiency,single information dimensionality,limited network topology,and monotonous network functionality),this thesis focuses on providing construction schemes for multipartite entangled states in quantum repeater networks that aim to reduce costs and increase efficiency.Based on this,different-dimensional quantum multicast schemes and quantum multicast schemes in hybrid topologies are proposed.Finally,by integrating the encoding methods of multicast and unicast,a multi-functional and adaptive quantum network coding scheme is presented.The main research achievements of this thesis are as follows.(1)To address the issue of high communication costs and low efficiency,this thesis refines the key functionalities of the quantum repeater network,quantifies the communication costs of the repeater network,and constructs a new type of high-efficiency,low-cost multipartite entangled states which is suitable for quantum repeater networks.Firstly,based on the principles of quantum repeater,we clarify the four key network functionalities,namely adding,deleting,merging,and splitting.Meanwhile,we quantify the communication cost as the number of Einstein-Podolsky-Rosen(EPR)pairs consumed to achieve the key functionalities by using resource states.Secondly,using quantum graph states as templates,we replace the Controlled-X and Controlled-Z gate operations to generate multipartite entangled states,called C3 state.Thirdly,we verify that using C3 state as network encoding resources requires minimum cost(only 1 EPR pair)for each key functionality.Moreover,C3 state satisfies the characteristics of quantum distributed computing,perfectly demonstrating its high efficiency and low cost.(2)To address the issue of single information dimensionality,this thesis designs multi-dimensional key encoding operations based on the four key network functionalities and presents a quantum repeater multicast network encoding scheme for multi-dimensional state.Firstly,in a generalized butterfly network,different dimensional EPR pairs are distributed between various types of nodes according to the dimensionality requirements of the transmitted states and the node types.Secondly,with the key network functionalities as the objective,utilizing Quantum Fourier Theory,multi-dimensional encoding operations applicable to states of different dimensions are constructed.These operations include multi-dimensional adding,multi-dimensional deleting,multi-dimensional merging,and multi-dimensional splitting.Finally,by employing the corresponding multi-dimensional encoding operations based on the node types,the single-shot transmission of different dimensional quantum states is achieved in multicast communication.(3)To address the limitation of network topology,a hybrid quantum repeater network is iteratively constructed using ring and star topologies.And by referencing the distributed computing characteristics in C3 state,an information aggregation encoding operation is designed to propose a quantum repeater multicast network encoding scheme in the hybrid topology.Firstly,inspired by quantum cooperative multicast,the repeater network is divided into a central aggregation network and peripheral multicast networks.Secondly,it is determined that the central network adopts a ring topology while the peripheral subnets adopt a star topology,ensuring that this type of multicast repeater network can be iteratively expanded.Finally,referencing the C3 state computation characteristics,aggregation operations around Rotation gates Ry(θ)are designed to achieve scalable quantum cooperative multicast on the hybrid topology.(4)To address the issue of limited communication functionality,the concept of adaptive quantum network coding is defined.Building upon the simplified algorithm for two-dimensional multicast(i.e.,quantum state crosscommunication,XQQ),the multicast algorithm is updated to be compatible with it,leading to a multi-functional adaptive network coding scheme.Firstly,adaptive network coding is defined as the utilization of quantum repeater techniques to dynamically adapt to various communication requirements based on fixed network resources.Secondly,leveraging the network resources of XQQ,a quantum cooperative multicast protocol compatible with XQQ is designed by referring to the aggregation operations.Finally,it is demonstrated that this protocol satisfies the conditions of adaptive quantum network coding,which meets the requirements of both quantum state cross-communication and quantum multicast communication,making it suitable for dynamic quantum communication networks.