Application Of Cross-Kerr Medium In Quantum Information

Since the nineties of the 20th century, quantum information science has evolved as a new object. It mainly includes quantum computation and quantum communication. Quantum communication is in the quantum approach for transmission and processing of quantum information. And quantum communication includes quantum dense coding, quantum teleportation, quantum cloning and quantum key distribution, etc. It provides a new direction for the secure transmission of information. In recent years the subject has been gradually shifted from theory to experiment.Entangled states, due to its unique quantum properties, have become an important information resource in quantum information processing. Quantum communication based on quantum entanglement as the information unit to achieve the effective delivery of information. There are some common multipartite entangled states, such as GHZ state, W state, Dicke state, Cluster state, etc.In principle quantum communication can be implemented in nuclear magnetic resonance (NMR), in cavity quantum electrodynamics (QED), in optical system, in ion trap, or in quantum Dot system, in practice the implementation of choice for long-distance quantum communication will almost certainly be optical system. However, photonic qubits have the disadvantage that it is difficult to realize the direct interaction between photons. This problem has been overcome by cross-phase modulation (XPM), which refers to the nonlinear phenomenon that the phase of an optical field is modulated by another field. Such nonlinear interaction, i.e. cross-Kerr nonlinearity, between photons offers an ideal playground for quantum state engineering, and a number of applications have been studied, such as photon number quantum non-demolition (QND) measurements, quantum state preparation and detection, quantum teleportation and the implementation of quantum logic gates and so on., Nonlinear optical processes between traveling pulses with a low number of photons will become feasible when in the multi-level atomic system the ultraslow group velocity, which is obtained as a consequence of electromagnetically induced transparency (EIT), is the dominant feature.Based on the cross-Kerr nonlinearity, we present some simple experimental schemes for preparing multipartite entangled states via linear optical elements such as beam splitter (BS) or polarization beam splitter (PBS), and half wave plate (HWP) in this paper. Mutli-photon entangled states could be prepared by utilizing the nonlinear interaction between the signal mode and probe mode in the cross-Kerr medium and by using homodyne measurement on the probe mode.Firstly, we study how to prepare the entangled photon number states among four modes, e.g., W state and Dicke state, by using the nonlinear interaction between signal beams and by controlling the interaction time and probe coherent field followed by homodyne measurement which can be made much more efficient than the single-photon detection. The preparation scheme has the higher success probability and near perfect fidelity. In addition, the scheme can be generalized to produce maximally 2k-qubit entangled states.Secondly, an experimental scheme is proposed for preparing four-photon Cluster states based on cross-Kerr nonlinearity combined with P-quadrature (P:momentum) homodyne measurement on the probe mode. The scheme uses P-quadrature homodyne measurement, which requires considerably smaller strength of the coherent state in the probe mode than the X-quadrature (Ⅹ:position) homodyne measurement in other schemes. Contrary to other previous schemes for generating Cluster states, the present scheme has the higher success probability. It is also not necessary to have an ancilla photon and to remove a relative phase factor in the present scheme.Finally, another scheme is presented for preparing the polarization-entangled states among four modes, e.g., W state and Dicke state, through weak cross-Kerr nonlinearity combined with the P-quadrature homodyne measurement on the probe mode. The distinct advantage of this scheme is that the success probability of the preparation is high and fidelity is near perfect. It is also not necessary to to remove a relative phase factor in the preparation scheme. In addition, the scheme can also be generalized to produce maximally 2k-qubit polarization-entangled states.Our proposed schemes use only the basic tools, such as PBS and HWP, in quantum optical laboratories and can be implemented in the regime of the cross-Kerr nonlinearity. It is not necessary that the cross-Kerr nonlinearity is very large, as long as the coherent light is bright enough in order to amplify the effect of the cross-Kerr nonlinearities. The needed cross-Kerr nonlinearity in the paper can be obtained if both light pulses are subject to EIT and propagate with slow but equal group velocities. We employ homodyne measurement, which can be made much more efficient than the single-photon detection, on the probe beam. These facts make us more confident on the feasibility of the proposed schemes.