Xun-Li Feng

Scheme for unconventional geometric quantum computation in cavity QED

In this paper, we present a scheme for implementing the unconventional geometric two-qubit phase gate with nonzero dynamical phase based on two-channel Raman interaction of two atoms in a cavity. We show that the dynamical phase and the total phase for a cyclic evolution are proportional to the geometric phase in the same cyclic evolution; hence they possess the same geometric features as does the geometric phase. In our scheme, the atomic excited state is adiabatically eliminated, and the operation of the proposed logic gate involves only the metastable states of the atoms; thus the effect of the atomic spontaneous emission can be neglected. The influence of the cavity decay on our scheme is examined. It is found that the relations regarding the dynamical phase, the total phase, and the geometric phase in the ideal situation are still valid in the case of weak cavity decay. Feasibility and the effect of the phase fluctuations of the driving laser fields are also discussed.

Quantum entanglement distribution with hybrid parity gate

We propose a scheme for entanglement distribution among different single atoms trapped in separated cavities. In our scheme, by reflecting an input coherent optical pulse from a cavity with a single trapped atom, a controlled phase-shift gate between the atom and the coherent optical pulse is achieved. Based on this gate and homodyne detection, we construct an n-qubit parity gate and show its use for the distribution of a large class of entangled states in one shot, including the GHZ state |GHZ{sub n}>, W state |W{sub n}>, Dicke state |D{sub n,k}>, and certain sums of Dicke states |G{sub n,k}>. We also show that such a distribution could be performed with high success probability and high fidelity even in the presence of channel loss.

Remote preparation of a three-particle state via positive operator-valued measurement

We present a scheme to remotely prepare an arbitrary three-particle pure state in real Hilbert space by using three bipartite partially entangled pairs as a quantum channel, and then generalize it to the tripartite equatorial-like case. Our results show that remote preparation of the three-particle state both in real space and in imaginary space can be probabilistically achieved with unity fidelity by performing an appropriate three-particle projective measurement at the senders side and an optimal positive operator-valued measurement at the receivers side. Moreover, the probability of success of our scheme is determined by the smaller parameters of the three initial entangled pairs.

Optical quantum computation with cavities in the intermediate coupling region

Large-scale quantum computation is currently a hot area of research. The scalable quantum computation scheme with cavities originally proposed by Duan and Kimble (Phys. Rev. Lett., 92 (2004) 127902) is further developed here to operate in the intermediate coupling region, which not only greatly relaxes experimental demands on the Purcell factor, but also eliminates the need to consider internal trade-off between cavity quality and efficiency. In our scheme, by controlling the reflectivity of the input single-photon pulse in the cavity, we can realize local atom-photon and nonlocal atom-atom controlled phase-flip (CPF) gates. We also introduce a theoretical model to analyze the performance of our scheme under practical noise. Furthermore, we show that the nonlocal CPF gate can be used to realize a quantum repeater.

Time-delay effects and simplified control fields in quantum Lyapunov control

Lyapunov-based quantum control has the advantage that it is free from the measurement-induced decoherence and it includes the instantaneous information of the system in the control. The Lyapunov control is often confronted with time delay in the control fields and difficulty in practical implementations of the control. In this paper, we study the effect of time delay on the Lyapunov control and explore the possibility of replacing the control field with a pulse train or a bang–bang signal. The efficiency of the Lyapunov control is also presented through examining the convergence time of the system. These results suggest that the Lyapunov control is robust against time delay, easy to realize and effective for high-dimensional quantum systems.As a hybrid of techniques from open-loop and feedback control, Lyapunov control has the advantage that it is free from the measurement-induced decoherence but it includes the system’s instantaneous message in the control loop. Often, the Lyapunov control is confronted with time delay in the control fields and difficulty in practical implementations of the control. In this paper, we study the effect of time-delay on the Lyapunov control, and explore the possibility of replacing the control field with a pulse train or a bang-bang signal. The efficiency of the Lyapunov control is also presented through examining the convergence time of the controlled system. These results suggest that the Lyapunov control is robust gainst time delay, easy to realize and effective for high-dimensional quantum systems.

Generation of a genuine four-particle entangled state of trap ions

We present a scheme for the generation of a genuine four-qubit entangled state in an ion trap. This state has many interesting entanglement properties and possible applications in quantum information processing and fundamental tests of quantum physics. In our scheme, the ion is driven by a standing-wave field, whose frequency is resonant with the ion carrier transition. By adjusting the phase of the field, both the vibration mode population and the ionic carrier excitation can be avoided. So our scheme is insensitive to the vibration states, which is important in view of decoherence.

Entanglement purification via controlled–controlled-NOT operations

Abstract We present an entanglement purification protocol based on controlled–controlled-NOT operations and Bell state measurements. We show that the protocol is more efficient than the standard protocol of Bennett et al. [Phys. Rev. Lett. 76 (1996) 722].

Deterministic remote two-qubit state preparation in dissipative environments

We propose a new scheme for efficient remote preparation of an arbitrary two-qubit state, introducing two auxiliary qubits and using two Einstein–Podolsky–Rosen (EPR) states as the quantum channel in a non-recursive way. At variance with all existing schemes, our scheme accomplishes deterministic remote state preparation (RSP) with only one sender and the simplest entangled resource (say, EPR pairs). We construct the corresponding quantum logic circuit using a unitary matrix decomposition procedure and analytically obtain the average fidelity of the deterministic RSP process for dissipative environments. Our studies show that, while the average fidelity gradually decreases to a stable value without any revival in the Markovian regime, it decreases to the same stable value with a dampened revival amplitude in the non-Markovian regime. We also find that the average fidelity’s approximate maximal value can be preserved for a long time if the non-Markovian and the detuning conditions are satisfied simultaneously.

Strongly interacting photons in asymmetric quantum well via resonant tunneling.

We propose an asymmetric quantum well structure to realize strong interaction between two slow optical pulses. The essential idea is the combination of the advantages of inverted-Y type scheme and resonant tunneling. We analytically demonstrate that giant cross-Kerr nonlinearity can be achieved with vanishing absorptions. Owing to resonant tunneling, the contributions of the probe and signal cross-Kerr nonlinearities to total nonlinear phase shift vary from destructive to constrictive, leading to nonlinear phase shift on order of π at low light level. In this structure, the scheme is inherent symmetric for the probe and signal pulses. Consequently, the condition of group velocity matching can be fulfilled with appropriate initial electron distribution.

Effective Hamiltonian Approach to Open Systems and Its Applications

By using the effective Hamiltonian approach, we present a self-consistent framework for the analysis of geometric phases and dynamically stable decoherence-free subspaces in open systems. Comparisons to the earlier works are made. This effective Hamiltonian approach is then extended to a non-Markovian case with the generalized Lindblad master equation. Based on this extended effective Hamiltonian approach, the non-Markovian master equation describing a dissipative two-level system is solved, an adiabatic evolution is defined and the corresponding adiabatic condition is given.