Quantitative Studies On Wave-particle Duality

With the development and application of quantum theory,the quantumness of quantum states plays an important role in the fields of quantum optics,quantum biology and quantum informatics.The research on quantumness can enrich quantum theory and explain quantum phenomena more deeply.Wave-particle duality is related to complementary property of a quantum system.Therefore,it is of great significance to explore the quantum properties of different quantum systems for promoting the practical application of quantum theory.In this paper,the particle-like and wave-like of quantum states in non-uniform lattice systems,one-dimensional quantum random walk model and quantum noise channels are studied.Numerical results explain the corresponding phenomena and relevant conclusions.Firstly,the quantum coherence C and site distinguishability D_Q,which related to wave-like and particle-like respectively,are measured.Quantum coherence C and site distinguishability D_Q are studied for an electron in several typical nonuniform lattice systems.Numerical results show that both C and D_Q can reflect electron localization properties.At Anderson transition,an electron exhibiting relatively more wavelike behavior changes to relatively more particlelike behaviorSecondly,two types of one-dimensional quantum random walk models are studied.The effects of coin operator,system initial state and phase defect on the quantumness of the quantum state are discussed.The numerical simulation results show that the predictability P and the visibility V reflect wavelike behavior and particlelike behavior of the walker.At the same time,it can reflect the localization phenomenon.Finally,the influence of quantum noise on the quantumness of quantum states is studied.A single qubit in different decoherence channels are discussed.The analytical expressions of predictability P and visibility V are derived from the Bloch sphere representation of the channel.The results show that the P of the quantum state in the phase-damped channel is only related to the input state,and V is related to the channel parameters and the input state.In the depolarized channel,both P and V are related to the channel parameters.In the generalized amplitude damping channel,P and V are related to channel parameters and input quantum states.