We develop a multi-valued logic for quantum computing for use in multi-level quantum systems, and discuss the practical advantages of this approach for scaling up a quantum computer. Generalizing the methods of binary quantum logic, we establish that arbitrary unitary operations on any number of d-level systems (d > 2) can be decomposed into logic gates that operate on only two systems at a time. We show that such multi-valued logic gates are experimentally feasible in the context of the linear ion trap scheme for quantum computing. By using d levels in each ion in this scheme, we reduce the number of ions needed for a computation by a factor of log 2 d. 03.67. Lx, 03.65.Bz, 89.80.+h
Two uncoupled two-level atoms cannot be jointly excited by classical light under general circumstances, due to destructive interference of excitation pathways in two-photon absorption. However, with temporally entangled light, two-atom excitation is shown possible. Photons arising from three-level cascade decay are intrinsically ordered in time of emission. This field correlation induces a joint resonance in the two-atom excitation probability via suppression of one of the time-ordered excitation pathways. The relative gain in two-photon absorption increases with the time-frequency entanglement. which gives the joint probability of absorbing two photons at positions r i and r j , and times t 1 and t 2 , respectively. A microscopic model for a detection system that makes a two-photon measurement is the joint excitation of two independent, two-level atoms. In this Letter, we take a closer look at this basic problem from the point of view of understanding the effects of source field entanglement on two-photon absorption. In particular, we are interested in the effects of time-frequency entanglement on the two-atom excitation probability under conditions of two-photon resonance. Nearly 20 years ago, it was demonstrated [3] that the entangled states produced by an optical parametric amplifier (OPA) exhibit, for weak fields, a linear intensity dependence in the coincident absorption probability, rather than the usual quadratic dependence expected for a two-photon process. Theoretical treatments of the problem [3-6] explained the effect as due to the correlated nature of the two-photon state: the absorption of the signal photon within some coherence window automatically implies the absorption of the idler photon, as these ''travel'' together. However, this point of view does not readily distinguish between quantum entanglement, as found in a pure two-photon state, and classical correlation, as exists with temporally copropagating pulses.In this Letter, we report a qualitative distinction between quantum and classical light that arises from the time asymmetry that is intrinsic to the two-photon state vector produced by successive decay of a three-level cascade system [7][8][9], one of Nature's fundamental sources of entangled photons. A similar asymmetry can be introduced into an OPA source by splitting the signal and idler photons produced by a type-II down converter using a polarizing beam splitter and delaying one of the photons with respect to the other before recombining them at an ordinary beam splitter. The time asymmetry in the entangled state is the key ingredient that enables the joint excitation of two noninteracting atoms, an event that is not possible to accomplish with classical light under general circumstances. We believe that the results of our Letter can be realized by utilizing two ions in a trap, as was done previously to demonstrate Young's interference fringes for single-photon scattering [10]. The proposed two-photon experiment can be done with either a cascade or an OPA source.To understand the e...
We show how to achieve subwavelength diffraction and imaging with classical light, previously thought to require quantum fields. By correlating wave vector and frequency in a narrow band, multiphoton detection process that uses Doppleron-type resonances, we show how to achieve arbitrary focal and image plane patterning with classical laser light at submultiples of the Rayleigh limit, with high efficiency, visibility, and spatial coherence. A frequency-selective measurement process thus allows one to simulate, semiclassically, the path-number correlations that distinguish a quantum entangled field.
We consider the exchange of spin and orbital angular momenta between a circularly polarized Laguerre-Gaussian beam of light and a single atom trapped in a two-dimensional harmonic potential. The radiation field is treated classically but the atomic center-of-mass motion is quantized. The spin and orbital angular momenta of the field are individually conserved upon absorption, and this results in the entanglement of the internal and external degrees of freedom of the atom. We suggest applications of this entanglement in quantum information processing.
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