Research On Quantum Secure Communication Based On Tensor Network

The classical encryption technique of security based on computational complexity is facing a tremendous challenge as a result of the ongoing development of quantum computers and quantum algorithms,posing a serious threat to the current level of information security on the Internet.As a cross-discipline arising from the combination of information science and quantum mechanics,quantum secure communication can guarantee the absolute security of information transmission based on the inherent nonclonability of quantum states and Heisenberg’s uncertainty principle.In the present subject of quantum secure communication,quantum key distribution(QKD)has made significant breakthroughs in theory,experiment,and application.The QKD protocol utilizes the"one-time-pad"encryption method,which theoretically provides unconditional security.However,with the development of the Internet,the exponentially increasing data volume and various forms of communication require the consumption of large amounts of encryption keys,and the key generation rate of existing QKD protocols can hardly meet the demand of exponential growth of data volume.Hence,it becomes increasingly important to improve the secure key rate of QKD.As an important physical resource in the field of quantum information,quantum entanglement,especially the research related to the entanglement of quantum many-body systems,has been a hot issue and plays a crucial role in the development of quantum communication.However,as the size of the quantum many-body system expands,its dimensionality rises exponentially.As a result,the computational complexity also rises exponentially as the quantum many-body system’s size increases.Fortunately,the tensor network state(TNS)and its related tensor network(TN)method,which were developed from quantum many-body physics,can reduce the complexity of quantum many-body systems from the exponential level to the polynomial level while also precisely computing the ground state of the local interaction model in quantum many-body systems.This enables the combination of quantum many-body systems with QKD in order to increase secure key rates and communication distances.Therefore,in this thesis,two studies are conducted on the application of tensor network states and tensor networks in improving the QKD secure key rate and communication distance.The details are as follows:(1)An improved quantum network communication model based on compressed tensor network states is proposed.This thesis first uses partial isometries to compress the matrix product state(MPS)to obtain the compressed MPS(?).Then,a sender,Alice,utilizes the compressed MPS(?)to communicate with a receiver,Bob,via the quantum channel.At the same time,Alice sends the number of compression operations to Bob via a secure classical channel.The measurement of the quantum state between the communicating parties is performed in a similar way to the BB84 protocol.Finally,based on the measurement results and the number of compression operations,Alice and Bob complete the decompression operation of the compressed MPS(?)and share the cryptographic key from the MPS.The improved model using MPS is able to obtain a higher key generation capability and longer communication distance.This thesis also applies the flow network model to obtain the upper bound of dimensionality of the geometric metrics of MPS.(2)A quantum key expansion(QKE)protocol based on number-state-entanglement-preserving tensor network with compression is proposed.A series of singlet states is first operated by number-state-entanglement-preserving compressed tensors for compression.And then,the entanglement between adjacent subsystems is eliminated by a disentangler to obtain a compressed two-body entangled state.After that,Alice and Bob carry out the generation of the subkey using a method resembling that of the BBM92 protocol.The generation of subkeys based on the obtained two-body entangled states is subsequently completed by Alice and Bob using a process resembling that of the BBM92 protocol.Then,based on the generated subkey,the cryptographic key is obtained by utilizing a number-state-entanglement-preserving tensor network.This thesis discusses the advantages of the proposed QKE protocol over the classical key expansion algorithm in terms of the key expansion method,the key length and the security.In addition,due to the structure of the number-state-entanglement-preserving tensor network with compression,the proposed QKE protocol can resistant the intercept-resend attack,the entanglement-and-measurement attack,and the coherent attack.