Multipartite Entanglement Of Photonic Quantum States And Its Potential Application In Quantum Phase Estimation

In this graduate thesis, we focus on the quantum entanglement of entangled states, including the NOON state and the entangled coherent states(ECS). With the purpose to investigate the generation of NOON state and the Fisher information of N-photon states.Firstly, we review quantum states of a quantized light field and introduce the concept of entanglement and quantum Fisher information. We show the quantum entanglement of Gaussian states such as the product coherent state and the two-mode squeezed vacuum. We also calculate the phase sensitivity of the product state of coherent state and the vacuum and the product state of coherent state and the squeezed vacuum. In addition, we show the quantum Fisher information of NOON state and ECS without photon losses.In chapter3, we further investigate the entanglement properties of entangled coherent state, with and without photon losses. By separating the coherent state into|α)=c0|0)+(?)|a)> we derive exact results of the logarithmic negativity EN, which quantifies the degree of entanglement between the two bosonic modes. Without particle losses, EN=1for the NOON state; while for the ECS, EN increases from0to1as|α2â†'∞. In the presence of photon losses, we find that the ECS with large enough photon number is more robust than that of the NOON state. An optimal ECS is obtained by maximizing EN with respect to|α|2.As main part of this thesis, we study in chapter4the generation of path-entangled NOON state. As an input state of a two-mode Mach-Zehnder interferometer, a product of coherent state|α) and squeezed vacuum state|ξ) was proposed to generate path-entangled NOON states:(|N,0)+exp(iφ|0,N)), with the photon number N=N1+N2post-selected in a photon counting measurement. Under the phase-matching condition cos(θb-2θa)=+1, we show here that the fidelity between the input state and the NOON states depends only on the ratio x≡|α|2/tanh r, where θa/b is the phase of the coherent/squeezed state and r is the squeeze factor. Numerically, we find that by maximizing the generation probability of N-photon state, the fidelity between the input state and the NOON states and the Fisher information of N-photon state,we obtain the different value of ratio. In addition, we prove that classical Fisher information always saturate quantum Fisher information provided all the outcomes {N1, N2} with N1+N2=Nbeing counted.