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We study inelastic resonant scattering of a Gaussian wave packet with the parameters close to a zero of the complex scattering coefficient. We demonstrate, both theoretically and experimentally, that such near-zero scattering can result in anomalously-large time delays and frequency shifts of the scattered wave packet. Furthermore, we reveal a close analogy of these anomalous shifts with the spatial and angular Goos-H\"anchen optical beam shifts, which are amplified via quantum weak measurements. However, in contrast to other beam-shift and weak-measurement systems, we deal with a one-dimensional scalar wave without any intrinsic degrees of freedom. It is the non-Hermitian nature of the system that produces its rich and non-trivial behaviour. Our results are generic for any scattering problem, either quantum or classical. As an example, we consider the transmission of an optical pulse through a nano-fiber with a side-coupled toroidal micro-resonator. The zero of the transmission coefficient corresponds to the critical coupling conditions. Experimental measurements of the time delays near the critical-coupling parameters verify our weak-measurement theory and demonstrate amplification of the time delay from the typical inverse resonator linewidth scale to the pulse duration scale., Comment: 14 pages, 5 figures

We introduce three compact graph states that can be used to perform a measurement-based Toffoli gate. Given a weighted graph of six, seven or eight qubits, we show that success probabilities of 1/4, 1/2 and 1 respectively can be achieved. Our study puts a measurement-based version of this important quantum logic gate within the reach of current experiments. As the graphs are setup-independent, they could be realized in a variety of systems, including linear optics and ion-traps., Comment: 4 pages, 3 figures, RevTeX4; Accepted version

Generation and control of quantum entanglement are studied in an equivalent-neighbor system of spatially-separated semiconductor quantum dots coupled by a single-mode cavity field. Generation of genuinely multipartite entanglement of qubit states realized by conduction-band electron-spin states in quantum dots is discussed. A protocol for quantum teleportation of electron-spin states via cavity decay is briefly described., Comment: 9 pages, 7 figures, to appear in e-J. Surf. Sci. Nanotech

Coherent oscillations between any two levels from four nuclear spin states of I=3/2 have been demonstrated in a nanometre-scale NMR semiconductor device, where nuclear spins are all-electrically controlled. Using this device, we discuss quantum logic operations on two fictitious qubits of the I=3/2 system, and propose a quantum state tomography scheme based on the measurement of longitudinal magnetization, $M_z$., Comment: 5 pages, 4 figures

We have developed semiconductor point contact devices in which nuclear spins in a nanoscale region are coherently controlled by all-electrical methods. Different from the standard nuclear-magnetic resonance technique, the longitudinal magnetization of nuclear spins is directly detected by measuring resistance, resulting in ultra-sensitive detection of the microscopic quantity of nuclear spins. All possible coherent oscillations have been successfully demonstrated between two levels from four nuclear spin states of I = 3/2 nuclei. Quantum information processing is discussed based on two fictitious qubits of an I = 3/2 system and methods are described for performing arbitrary logical gates both on one and two qubits. A scheme for quantum state tomography based on Mz-detection is also proposed. As the starting point of quantum manipulations, we have experimentally prepared the effective pure states for the I = 3/2 nuclear spin system., Comment: 16 pages, 5 figures

Using the tensor product representation in the density matrix renormalization group, we show that a quantum circuit of Grover's algorithm, which has one-qubit unitary gates, generalized Toffoli gates, and projective measurements, can be efficiently simulated by a classical computer. It is possible to simulate quantum circuits with several ten qubits., Comment: 4 pages, 5 figures

We propose a distribution scheme of polarization states of a single photon over collective-noise channel. By adding one extra photon with a fixed polarization, we can protect the state against collective noise via a parity-check measurement and post-selection. While the scheme succeeds only probabilistically, it is simpler and more flexible than the schemes utilizing decoherence-free subspace. An application to BB84 protocol through collective noise channel, which is robust to the Trojan horse attack, is also given., Comment: 4 pages, 3 figures; published version in Phys. Rev. Lett

The non-resonant interaction between the high-density excitons in a quantum well and a single mode cavity field is investigated. An analytical expression for the physical spectrum of the excitons is obtained. The spectral properties of the excitons, which are initially prepared in the number states or the superposed states of the two different number states by the resonant femtosecond pulse pumping experiment, are studied. Numerical study of the physical spectrum is carried out and a discussion of the detuning effect is presented., Comment: 7 pages, 8 figures

Equivalent-neighbor interactions of the conduction-band electron spins of quantum dots in the model of Imamoglu et al. [Phys. Rev. Lett. 83, 4204 (1999)] are analyzed. Analytical solution and its Schmidt decomposition are found and applied to evaluate how much the initially excited dots can be entangled to the remaining dots if all of them are initially disentangled. It is demonstrated that the perfect maximally entangled states (MES) can only be generated in the systems of up to 6 dots with a single dot initially excited. It is also shown that highly entangled states, approximating the MES with a good accuracy, can still be generated in systems of odd number of dots with almost half of them being excited. A sudden decrease of entanglement is observed by increasing the total number of dots in a system with a fixed number of excitations., Comment: 6 pages, 7 figures, to appear in Phys. Rev. A

Time evolution of entanglement of N quantum dots is analyzed within the spin-1/2 van der Waals (or Lipkin-Meshkov-Glick) XY model. It is shown that, for a single dot initially excited and disentangled from the remaining unexcited dots, the maximum bipartite entanglement can be obtained in the systems of N=2,...,6 dots only., Comment: 2 pages, 3 figures

The Wehrl information entropy and its phase density, the so-called Wehrl phase distribution, are applied to describe Schr\"odinger cat and cat-like (kitten) states. The advantages of the Wehrl phase distribution over the Wehrl entropy in a description of the superposition principle are presented. The entropic measures are compared with a conventional phase distribution from the Husimi Q-function. Compact-form formulae for the entropic measures are found for superpositions of well-separated states. Examples of Schr\"odinger cats (including even, odd and Yurke-Stoler coherent states), as well as the cat-like states generated in Kerr medium are analyzed in detail. It is shown that, in contrast to the Wehrl entropy, the Wehrl phase distribution properly distinguishes between different superpositions of unequally-weighted states in respect to their number and phase-space configuration., Comment: 10 pages, 4 figures

The safety of a quantum key distribution system relies on the fact that any eavesdropping attempt on the quantum channel creates errors in the transmission. For a given error rate, the amount of information that may have leaked to the eavesdropper depends on both the particular system and the eavesdropping strategy. In this work, we discuss quantum cryptographic protocols based on the transmission of weak coherent states and present a new system, based on a symbiosis of two existing ones, and for which the information available to the eavesdropper is significantly reduced. This system is therefore safer than the two previous ones. We also suggest a possible experimental implementation., Comment: 20 pp. Revtex, Figures available from the authors upon request, To be published in PRA (March 95)