Quantum Metrology And The Experimental Realization Of Quantum Channels

Quantum information is an interdisciplinary subject of quantum mechanics and information science.Since the birth,quantum information has received extensive attention form scientists from both quantum physics and information science.In recent years,quantum information has made great progress both theoretically and experimentally,and it has broad prospects.The main work of this master's thesis includes the following two parts:Firstly,we introduce quantum metrology and simulate amplitude-damping channel with linearoptical elements.In the classical case,the accuracy of the parameter estimation is bounded by the standard quantum limit.Quantum metrology,i.e.,quantum parameter estimation,refers to use quantum methods such as quantum entanglement,quantum interference,and quantum measurement to estimate unknown parameters.The precision of the estimation of a parameter is limited by the Heisenberg limit,which beats the standard quantum limit to achieve high-precision estimation.A quantum parameter estimation is composed of three stages: the preparation stage,the sampling stage,and the measurement stage.We demonstrate quantum metrology for noisy channels,where entanglement with an ancillary qubit reduces the effect of noise.Entanglement-assisted quantum metrology refers to the scenario in which the probes are entangled with an ancilla that does not participate in the sampling stage.This thesis describes in detail how to simulate amplitude-damping channel in experiments using linear-optical elements and introduces quantum process tomography.We can use quantum process tomography to analyze the performance of the experiment.Our photonic experiment proposed in this thesis,we can achieve high-fidelity amplitude damping channels with arbitrary parameters.Our results demonstrate that entanglement with an ancilla is a valuable approach for quantum-enhanced metrology in noise channels.Secondly,the manipulation of quantum state lies in the heart of realizing quantum metrology,as an example,we explore the topological properties of a chiral one-dimensional split-step discrete-time quantum walk.Discrete-time quantum walk,first introduced in 1993,exhibits distinct features compared to classical random walk.We know that the probability distribution of classical random walk is a Gaussian distribution,and the probability of quantum walk tends to be ballistically distributed.The standard deviation of the probability distribution of classical walk is N^1/N,while for quantum walk it is proportional to .Thus,quantum walk has a larger diffusion rate than classic walk.Quantum walk has a wide range of applications,one of which is to simulate and study topological phase transitions.In the field of quantum simulation of topological phenomena,quantum walks are emerging as a versatile tool.Here we propose a method to detect topological properties of one dimensional split-step discrete-time quantum walk by introducing two controlled parameters in coin flipping operators.And we validate experimentally these properties in a photonic 7-step splitstep quantum walk.Topological invariants can be observed by measuring the mean chiral displacement.We find that the probability distribution moments of the walker position after many steps can be used as direct indicators of the topological quantum transition: while varying a control parameter that defines the phase of the system,these moments exhibit a slope discontinuity at the transition point.Furthermore,we create an inhomogeous quantum walk to probe the existence of edge states via peaked probability distribution at the boundary for photons in the quantum walk dynamics.We find that the edge states of the one-dimensional discrete-time quantum walk are robust against static disorder.