Calculation Of Quantum Fluctuations For Bipartite Continuous-Variable Entangled State

Quantum optics, the union of quantum field theory and physical optics, is a very important branch in modern physics. It is a subject in studying the coherence and the quantum statistical properties of radiation field, as well as the quantum characters of light interacting with matter. There are some non-classical features which differ from classical theory for quantum field, for example, photon anti-bunching effect, squeezing effects of optical field and sub-poissonian statistics distribution, etc. When the quantum fluctuation of one quadrature in a squeezed state is less than that in a coherent state, the noise in one of the field quadratures is suppressed below the coherent-state noise level, the field is so called squeezed field. Quantum noise will ruin the stability and the precision of signals in optical communication and other fields, therefore, research on squeezed properties has realistic significance in quantum detection and quantum communication.In 1935, quantum entanglement, noted by Einstein and Schr(o|¨)dinger, has also become more and more important and fascinating in understanding some fundamental problems in quantum mechanics and quantum optics. Entanglement is one of the most characteristic and inconceivable properties that makes quantum theory distinct from classical theory. It plays an essential role in quantum information processing such as quantum teleportation, quantum computation, and quantum cryptography. In addition, entanglement in continuous variable systems, which can offer an advantage in some situations in quantum-information processing, has been attracted great interest both theoretically and experimentally. Here, We concentrate our attention on the continuous-variable entangled state continuously.In this dissertation, we study the quantum squeezed properties of bipartite continuous-variable entangled states in Fock space. By virtue of the general linear quantum transformation theory (LQTT) as an effective tool, we obtain a general formula, which calculate the quantum fluctuations for bipartite entangled state of continuous variables in Fock space. Moreover, the squeezed properties of the entangled state are discussed. The relations between the state parameters are depicted by means of the linear fit, when the degree of the fluctuation and entanglement entropy reach the extremum. When the entangled state is maximally entangled, the results show that the squeezed degree is also maximal. In addition, the changing relationship between the quantum fluctuations and the quantum entanglement is acquired. The derived formula are used to calculate the fluctuation of the common two-mode squeezed vacuum state and the two-mode one-sided squeezed vacuum state as examples.