Study On Two-dimensional Discrete Quantum Walk And Quantum Entropy

In recent years,quantum walk and quantum entropy are popular research fields in quantum computation and quantum information.In this paper,the two-dimensional discrete quantum walk in closed and open systems and quantum entropy in open systems are considered.The discussion is arranged as followsFirst of all,the two-dimensional discrete quantum walk in closed and open sys-tems are studied.Unitary evolution is the main characteristic of two-dimensional discrete quantum walk in closed systems.When the unitary operator takes the Hadamard operator,the probability measure estimation of quantum walk can be ob-tained by Fourier transformation of evolution matrix and stationary phase method The main feature of two-dimensional discrete quantum walk in open systems is that the unitary operator is replaced by the density matrix.Two examples are given to illustrate that the quantum walk distribution under this density matrix is approxi-mately GaussianThen,the quantum entropy based on two-dimensional discrete quantum walk and local quantum Bernoulli noise in open systems is discussed respectively,and the related properties of the two kinds of quantum entropy are discussed.By calculating the quantum entropy of the two examples in the two-dimensional discrete quantum walk,the uncertainty of the two walkers at the same position and at the same time can be compared.For the quantum entropy of local quantum Bernoulli noise,the key point is to define the appropriate density operator ?k=2-klko=2-klk*lk by using the local creation operator lk*and the local annihilation operator lk,so that it is a positive definite operator with trace 1.After careful operation,some basic properties of quantum entropy of local quantum Bernoulli noise can be obtained,such as subadditivity,nonnegative property,concavity,tensor property,etc.