Theoretical And Experimental Research On Quantum Coherence And Uncertainty Relations

Quantum information science is a new interdisciplinary research field produced by the combination of quantum mechanics and information science.From its birth to now,it has made many important achievements in theory and experiment,with rich and fascinating application prospects.It is a research hotspot of the frontier science and a benchmark to measure the development level of national science and technology.Quantum coherence and quantum uncertainty relation are the essential characteristics of the quantum world different from the classical world.They are also the basic theories in the field of quantum information science,which are widely concerned by researchers.Quantum coherence is the cause of quantum interference,nonlocality and entanglement.Its physical essence is from the fluctuation of micro particles,and it is often regarded as a useful physical resource.The research on quantum coherence mainly includes the theory of coherent resources,the quantification of coherence,the coherence of open systems,and the experimental research on coherence.Quantum coherence is widely used in quantum information processing and some cross fields,such as quantum algorithms,quantum thermodynamics,quantum metrology,quantum biology,etc.On the other hand,quantum uncertainty relation is one of the most basic rules that the quantum world abides by,which represents and measures the uncertainty of quantum measurement.There are many forms of uncertainty,such as standard-deviation-based uncertainty relations,Shannon-entropy-based uncertainty relations and linear-entropy-based uncertainty relations,etc.Uncertainty relations have many practical applications in the field of quantum information,such as quantum random number generation,quantum key distribution,quantum entanglement witness and quantum cryptography.In this paper,we focus on quantum coherence and quantum uncertainty.In theory,we study the maximum quantum coherence in noisy channels.In the experiment,we use the linear optical system to investigate the nonlocal advantage of quantum coherence,linear-entropy-based uncertainty relations,entropic uncertainty relations and coherence uncertainty relations.We have achieved some research results,mainly including the following aspects:1.Maximum coherence under noisy channelsThe quantification of the coherence of quantum states depends on the choice of reference basis.From the point of view of quantum resource theory,if the coherence of quantum state is regarded as a useful resource in quantum information processing,it is very important to choose the optimal reference base to obtain the maximum coherence of quantum state.For the relative entropy of coherence,the optimal bases are mutually unbiased bases to the eigenvectors of the given state.Based on the Bloch sphere,we explain the geometric significance of the optimal basis of the single qubit system,and give the basic conditions that must be satisfied to obtain the maximum relative entropy coherence in the noisy channel.Furthermore,we study the evolution of the maximum relative entropy coherence in the depolarizing channel.Then,we extend the research object from the single qubit system to the qudit system.For the maximally coherent state and the maximally mixed marginal state,we give the analytical form of the evolution of the maximum relative entropy coherence in the depolarizing channel,which lays the foundation for the coherence resource theory.2.Experimental investigation of the nonlocal advantage of quantum coherenceThe nonlocal advantage of quantum coherence is a stronger nonclassical correlation than Bell nonlocality,which can be used as entanglement witness or a kind of quantum resource.In order to verify the nonlocal advantage of quantum coherence,we use the linear optical experimental system to prepare the Bell diagonal state with high fidelity and adjustable parameters as the initial state,and then perform the local projective measurement of the subsystem.Finally,we reconstruct the density matrix of the initial state and the measured quantum state,and calculate the corresponding measurement probability by use of quantum state tomography.We use the₁l norm of coherence,the relative entropy of coherence and the skew information of coherence to study the relationship between the nonlocal advantage of quantum coherence,Bell nonlocality and quantum entanglement.The experimental results coincide with the theoretical predictions very well,which not only verifies the theory,but also deepens the understanding of nonclassical correlation,and accumulates some experience for application.3.Experimental investigation of linear-entropy-based uncertainty relationsThe linear-entropy-based uncertainty relations are one of the concrete forms of quantum uncertainty relation.It behaves as a uncertainty equality for local measurements over a complete set of mutually unbiased bases?MUBs?,or an uncertainty inequality for local measurements over incomplete set of MUBs.Here we design an all-optical experiment to investigate the uncertainty relations.We prepare two kinds of bi-photon states initially,i.e.,Bell-like states and Werner states.Three groups of Pauli measurements are selected for the subsystem.Together with the initial state and the states of the post-measurement system available by quantum state tomography,linear-entropy-based uncertainty relations can be fully verified.We also compare the uncertainty relation with quantum entanglement,and obtain the reverse correlation property between them.4.Experimental investigation of entropic uncertainty relations and coherence uncertainty relations in the mutually unbiased basesIn the theory,based on the entropy uncertainty relation of multiple measurements,we generalize entropic uncertainty relations and coherence uncertainty relations in the mutually unbiased bases.In the experiment,we use the linear optical experimental system to design the verification scheme.The initial state is Bell-like state and Bell-like diagonal state.Three groups of Pauli measurements are selected for the measurement of unbiased basis.The density matrix of the initial state and the post-measurement state is obtained by quantum state tomography.The experimental results show that the fidelity of quantum state is high.The entropic uncertainty relations and coherence uncertainty relations are verified.It is also proved that the coherence uncertainty relations can be effectively optimized by Holevo quantity.