Research On Quantum Statistical Complexity And Quantum Coherence

Statistical complexity and quantum coherence based on quantum information theory have been attracting much attention.Complexity has diversity,which is a context-dependent concept.At present,there is no consensus in the scientific community and various quantities have been proposed to measure complexity.Recently,quantum statistical complexity was proposed to signal quantum phase transition.On the other hand,quantum coherence comes from the quantum superposition principle,which is one of the basic features of quantum mechanics.Recently,people gradually realize the importance of quantum coherence.As a resource,quantum coherence plays an important role in quantum information and quantum computing.Firstly,the driven single qubit system has rich dynamic behaviors.With the Lindblad equation and the Born-Markov approximation,the time evolution of the system can be obtained.Under multiple intermediated measurements,the system has complex dynamic behaviors.Quantum statistical complexity C at the last moment ? is studied in detail.The results show that on the whole,C first increases from zero to a maximal value as ? increases,then decreases,and finally it approaches zero.At first,the system is in a pure state and C=0.Finally,the system is in a maximally mixed state due to the interaction with the environment and C=0 again.When the number of measurement N is relatively small,C fluctuates with ?,but when N is relatively large,the fluctuations disappear.As N is larger,the variation of C with ? is similar to that for the case of no intermediated measurement.Secondly,statistical complexity C and the quantum Fisher information F and other quantities are studied under the phase-damping channel,depolarizing channel and amplitude-damping channel.The results show that under the phase-damping channel and the depolarizing channel,the disequilibrium degree D and F monotonically decreases with yt,the von Neumann entropy S monotonically increases with yt,C first increases and then decreases with yt,where y is the dissipation rate and t is the time.In the generalized amplitude damping channel,D and F first decreases and then increases with ?t,S and C first increases and then decreases.In addition,in the generalized amplitude damping channel,another factor is the average exciton number (?).The larger (?) is,the larger S is,and the smaller D is,the smaller F is.When At is large,C decreases with (?).Finally,the relative entropy of coherence is used to study the evolution of quantum coherence of two qubit systems under the joint channel represented by two Kraus operators.The numerical results show that for a single qubit passes through the phase-damping channel and amplitude-damping channel,the relative entropy CREC decreases monotonously with noise intensity p when the quantum state is not rotated by K2.When p is larger,CREC is close to 0.Meanwhile,as the times n of quantum system passing through the channel increases,CREC decreases.When p=0,CREC remains unchanged in the whole range of ?.As p increases from 0 to 1,CREC first increases and then decreases with ?.For two qubits passes through decoherence channels,the variations of CREC with p and ? are similar as that for a single qubit passing through decoherence channels.