In this paper, with the weak cross-Kerr nonlinearity, we first present a special experimental scheme called controlled-path gate with which the realization of all possible bipartite positiveoperator-value measurements of two-photon polarization states may be nearly deterministic. Following the same technique, the realization of quantum control gates, including the controlled-NOT gate, Fredkin gate, Toffoli gate, arbitrary controlled-U gate, and even arbitrary multi-controlled-U gate, are proposed. The corresponding probabilities are 1/2, 1/8, 2/23, etc. respectively. Only the coherent states are required but not any ancilla photons, and no coincidence measurement are required which results in these gates are scalable. The structures of these gates are very simple, and then we think they are feasible with the current experimental technology in optics.
We present a simple architecture for deterministic quantum circuits operating on single photon qubits. Few resources are necessary to implement two elementary gates and can be recycled for computing with large numbers of qubits. The deterministic realization of some key multi-qubit gates, such as the Fredkin and Toffoli gate, is greatly simplified in this approach.Comment: 6 pages, 5 figures, to be published in Phys. Rev.
Weak cross-Kerr nonlinearities between single photons and coherent states are the basis for many applications in quantum-information processing. These nonlinearities have so far mainly been discussed in terms of highly idealized single-mode models. We develop a general theory of the interaction between continuous-mode photonic pulses and apply it to the case of a single photon interacting with a coherent state. We quantitatively study the validity of the usual single-mode approximation using the concepts of fidelity and conditional phase. We show that high fidelities, nonzero conditional phases, and high photon numbers are compatible, under conditions where the pulses fully pass through each other and where unwanted transverse-mode effects are suppressed.
Multi-photon states are widely applied in quantum information technology. By the methods presented in this paper, the structure of a multi-photon state in the form of multiple single photon qubit product can be mapped to a single photon qudit, which could also be in separable product with other photons. This makes the possible manipulation of such multi-photon states in the way of processing single photon states. The optical realization of unknown qubit discrimination [B. He, J. A. Bergou, and Y.-H. Ren, Phys. Rev. A 76, 032301 (2007)] is simplified with the transformation methods. Another application is the construction of quantum logic gates, where the inverse transformations back to the input state spaces are also necessary. We especially show that the modified setups to implement the transformations can realize the deterministic multi-control gates (including Toffoli gate) operating directly on the products of single photon qubits.
One of the most fundamental problems in optomechanical cooling is how small the thermal phonon number of a mechanical oscillator can be achieved under the radiation pressure of a proper cavity field. Different from previous theoretical predictions, which were based on an optomechanical system's time-independent steady states, we treat such cooling as a dynamical process of driving the mechanical oscillator from its initial thermal state, due to its thermal equilibrium with the environment, to a stabilized quantum state of higher purity. We find that the stabilized thermal phonon number left in the end actually depends on how fast the cooling process could be. The cooling speed is decided by an effective optomechanical coupling intensity, which constitutes an essential parameter for cooling, in addition to the sideband resolution parameter that has been considered in other theoretical studies. The limiting thermal phonon number that any cooling process cannot surpass exhibits a discontinuous jump across a certain value of the parameter.Preparing the approximate pure quantum states of a sizable mechanical oscillator is a feasible way toward macroscopic quantumness. Practically starting from its thermal equilibrium with the environment, such process is implemented by coupling the oscillator to a cavity field generated by a red-detuned external drive, to reduce the associated thermal phonon number to a low level, similar to cooling the oscillator to a lower temperature. An important feature we will illustrate is that the cooling result depends on how fast the optomechanical system (OMS) evolves to the finally stable quantum state.So far numerous experiments have realized the cooling to a few and even less than one mechanical quanta [1][2][3][4][5][6][7][8][9][10][11][12][13]. Following the earlier study of quantum fluctuations under radiation pressure [14,15], the theoretical description of such optomechanical cooling (see, e.g. [16][17][18][19][20][21][22][23]) was based on a linearization procedure as that described in [24]; that is to decompose the cavity field mode into the sum of the classical mean value α and its quantum fluctuation δâ. The linearized Hamiltonian gives the cooling action as a beamsplitter (BS) type coupling between the mechanical modeb and the fluctuation δâ with their coupling intensity g magnified by α, which was generally treated as a constant of steady-state value. In an actual cooling process, however, the cavity mean field â(t) = α(t) is built up from zero (when the mechanical oscillator is in thermal equilibrium with its environment) and takes time to evolve to stable value. Then the effective coupling strength g|α| used in the previous studies should be more appropriately taken as a variable, since α(t) keeps changing during a cooling process. Due to the impossibility of finding the time-dependent α(t) analytically, it is difficult to study the cooling as a dynamical process if adopting the above-mentioned linearization.In the present work we put forward a quantum dynamical theory for ...
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