Entangled Two-photon Quantum Positioning

Since the 1920's has formed the basic theory of quantum mechanics, quantum entanglement has drawn wide attention, because quantum entanglement is one of the most significant characteristics in quantum theory which is different from the classical theory. It is the foundation of the entire quantum information transmission process and quantum computation, and moreover, it reflects a non-classical correlation (indistinguishable) characteristic among each sub-system of many quantum systems. Quantum spatial positioning, clock synchronization and fiber optic communications become possible through researching the quantum entanglement characteristic between the simple two particles system. However, with the development of science and technology nowadays, the existing two-photon entanglement theory fell far short of the demands of application as the increased demand of the precision in the time and the space position in the area of military, navigation, communications and so on. Therefore, it is necessary for us to strive as much as possible in the practice of quantum spatial positioning by means of further studying the correlated properties of entangled biphoton.Another remarkable characteristic of entangled biphoton is non-locality, which closely relates with quantum entanglement. Two distant particles have subtle correlation characteristics in space, that is, when one of the particles changes in time and space coordinates, the other changes in them as well. This correlation is called non-locality in the quantum mechanics. Non-locality plays a key role in schemes such as quantum positioning, optical fiber communication, quantum teleportation, entanglement swapping, and quantum key distribution. However, there are still some theoretical issues in practice, which can be resolved by studying the influence of the pulse bandwidth and dispersion on the entangled biphoton time of arrival. In the experiment, the polarization entangled two-photon with good control often is selected as the coherent light. Two-photon polarization entangled state can be produced by spontaneous type-Ⅱparametric down conversion.The article is based on nonlinear optics and the principle of quantum coherence, and analyzes in detail the spectrum character and the correlated properties of the entanglement photons with non-degenerate and degenerate spontaneous type-Ⅱparametric down-conversion pumped by a broadband frequency pulse laser. Then the quantum coherent properties of entangled biphoton are researched deeply and compared it with the entangled biphoton pumped by a continuous laser. Evolution regularity of the second-order correlation function and average coincidence counting rate are obtained by numerical simulation calculation. At the same time, the experimental scheme of the quantum spatial positioning is designed based on the principle of quantum spatial positioning. The impact of. the quantum spatial positioning is discussed under the entanglement photons with non-degenerate spontaneous type-II parametric down-conversion pumped by a broadband frequency pulse laser. It is shown that as the pump band-width increases, the asymmetry of the phase-matching function also increases, but the coherence (distinguishability) of entangled biphoton and quantum interference visibility diminish, and the measuring accuracy of the quantum spatial positioning reduces as well. However, symmetric still is the phase-matching function of the frequency-coincident biphoton state with degenerate spontaneous type-II parametric down-conversion pumped by no matter continuous or pulse laser, and the coherence (distinguishability) of entangled biphoton maximizes.