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We study electron and positron exchange without a spin flip in a single collision between two polarized orthopositronium beams. We use angular-momentum coupling and density-matrix techniques to calculate the probabilities of obtaining only parapositronium, both para- and orthopositronium or only orthopositronium, after the collision. The probabilities are functions of the angle between the polarization vectors of the beams and scattering amplitudes labeled with total electron spin and total positron spin. The real parts of the scattering amplitudes and products of the polarization tensors for the beams are given in terms of the probabilities for certain angles and initial spin orientations. We show that quenching probabilities for different transitions and the spin-exchange quenching cross section depend on the angle, but the ratio of the total quenching probability to the total probability for positronium scattering does not.

We present three protocols for directly measuring the concurrence of two-photon polarization-entangled states, including pure states and mixed states. Two signal photon pairs in the same polarization-entangled states are needed in each detection round, and the signal photons will pass through polarization-independent beam splitters simultaneously. The concurrence of the photon pairs will be encoded in the total probability of picking up the balanced states in the two output modes of the beam splitter, which can be directly measured by single-photon detectors. The photon detection efficiency can be further enhanced with the help of the weak cross-Kerr nonlinearity, and the signal photons will not be absorbed. The third scheme using the bilateral nondemolition measurements can measure the concurrence of both pure and mixed states with high efficiency and high fidelity and is robust against the copy error of the state to be measured. The sophisticated controlled-not operation of the previous schemes is not required here, so our protocols are more feasible within the current experimental technology.

Auger decay including direct double processes of Ar $2{p}^{\ensuremath{-}1}$ hole levels is investigated in the framework of perturbation theory implemented by distorted wave approximation with balanced large-scale configuration interaction among the successive ions being taken into account. The complex transition amplitude obtained from the second perturbation theory for the direct double Auger decay (DAD) is decomposed into approximate formulas according to two generally agreed mechanisms of shake-off and knock-out. Practical computations showed that the knock-out condition is fulfilled and thus justified such a decomposition treatment of knock-out mechanism. The contribution to the DAD probability from knock-out mechanism is larger than shake-off by an order of magnitude and therefore the former is dominant. The interference effect between the knock-out and shake-off mechanisms should be trivial and neglecting it we obtained a branching ratio of 12.0$%$ for the direct DAD into triply charged states of Ar${}^{3+}$. By including cascade double decay, a total branching ratio of 14.9$%$ is obtained. Our result explained recent experimental results on the branching ratio into triply charged ion, and should be useful for further detailed experimental investigations.

Probability rates of electron-positron pair creation in collisions of a relativistic nucleus with a two-color laser field are calculated using the $S$-matrix approach. The case when both components of the laser field have commensurate frequencies and comparable strengths is considered. Pronounced interference effects are observed in angular distributions of created particles as well as in the total probability rates of pair production. These interference effects show a significant phase dependence of the pair-creation process.

Quantum cellular automata (QCA) have been introduced [G. Gr\"ossing and A. Zeilinger, Complex Syst. 2, 197 (1988); 2, 611 (1988)] as n-dimensional arrays of discrete sites characterized by a complex number whose absolute square lies between 0 and 1 such that each site represents a quantum-mechanical probability amplitude. The evolutions of one-dimensional QCA with a local (i.e., nearest-neighbor) interaction and with periodic boundary conditions have been studied in some detail. In this paper we present a thorough mathematical analysis of one-dimensional QCA, and we particularly emphasize the effects of what we term nonlocal computation: because of the conservation of the total probability for each time step, information of the global array spread out over generally nonlocal distances must be conveyed for each time step to each local site via the normalization procedure. With the aid of a mathematical description of QCA evolution the following, previously observed phenomena can be explained: (i) the asymptotic appearance of plane-wave patterns after a characteristic transient phase, (ii) the dependence of the period of the patterns on the input parameters for both small and large values of the couplings between the sites, and (iii) the role of the initial values of the cells. Finally, the effects of nonlocal computation are made visible with the simulation of a ``double-slit-like'' experiment on a QCA grid.

Triply differential probability rates for electron-positron pair creation in laser-nucleus collisions, calculated within the S-matrix approach, are investigated as functions of the nuclear recoil. Pronounced enhancements of differential probability rates of multiphoton pair production are found for a nonzero momentum transfer from the colliding nucleus. The corresponding rates show a very dramatic dependence on the polarization of the laser field impinging on the nucleus; only for a linearly polarized light are the multiphoton rates for electron-positron pair production considerably large. We focus therefore on this case. Our numerical results for different geometries of the reaction particles demonstrate that, for the linearly polarized laser field of an infinite extent (which is a good approximation for femtosecond laser pulses), the pair creation is far more efficient if the nucleus is detected in the direction of the laser-field propagation. The corresponding angular distributions of the created particles show that the high-energy pairs are predominantly produced in the plane spanned by the polarization vector and the laser-field propagation direction, while the low-energy pairs are rather spread around the latter of the two directions. The enhancement of differential probability rates at each energy sector, defined by the four-momentum conservation relation, is observed with varying themore » energy of the produced particles. The total probability rates of pair production are also evaluated and compared with the corresponding results for the case when one disregards the recoil effect. A tremendous enhancement of the total probability rates of the electron-positron pair creation is observed if one takes into account the nuclear recoil.« less

A scheme for fault-tolerant quantum computation (FTQC) with probabilistic two-qubit gates is proposed. The error thresholds for FTQC are estimated by numerical simulations, where the conditional error probability (the error probability under the condition of 'success') is taken into account in addition to the failure probability. As a result, it turns out that FTQC is possible even if the failure probability is as high as 10% (5%) under the condition that the conditional error probability is lower than about 0.03% (0.3%). These results mean that the present scheme has a great advantage in using probabilistic two-qubit gates.

Inspired by the idea of conditional probabilities, we introduce a variant of conditional density operators. But unlike the conditional probabilities which are bounded by 1, the conditional density operators may have eigenvalues exceeding 1 for entangled states. This has the consequence that although any bivariate classical probability distribution has a natural separable decomposition in terms of conditional probabilities, we do not have a quantum analogue of this separable decomposition in general. The ``nonclassical'' eigenvalues of conditional density operators are indications of entanglement. The resulting separability criterion turns out to be equivalent to the reduction criterion introduced by Horodecki [Phys. Rev. A 59, 4206 (1999)] and Cerf et al. [Phys. Rev. A 60, 898 (1999)]. This supplies an intuitive probabilistic interpretation for the reduction criterion. The conditional density operators are also used to define a form of quantum conditional entropy which provides an alternative mechanism to reveal quantum discord.

transitions are calculated numerically and the arising equations for probability amplitudes to find a molecule at ground-state vibrational levels are solved ~a! in stationary and ~b! in the initial-value-problem formulations. In the stationary formulation, complex quasienergies and quasienergy zones are found. Specific values of the light frequency v are found at which some quasienergy zones narrow with growing light intensity. Such an effect indicates a possibility of stabilization, which is confirmed to occur by a direct solution of the initial-value problem. The calculated total probability of photodissociation per pulse in the dependence on the light peak intensity is shown to decrease its growth with growing light intensity. Dynamics of photodissociation in the stabilization regime and structure of the arising vibrational wave packets are investigated and discussed. The method of description, in which Raman-type vibrational-vibrational transitions are taken into account is compared with that based on the ideas of the field-induced avoided crossing.

The atmospheric turbulence is the main factor that influences quantum properties of propagating optical signals and may sufficiently degrade the performance of quantum communication protocols. The probability distribution of transmittance (PDT) for free-space channels is the main characteristics of the atmospheric links. Applying the law of total probability, we derive the PDT by separating the contributions from turbulence-induced beam wandering and beam-spot distortions. As a result, the obtained PDT varies from log-negative Weibull to truncated log-normal distributions depending on the channel characteristics. Moreover, we show that the method allows one to consistently describe beam tracking, a procedure which is typically used in practical long-distance free-space quantum communication. We analyze the security of decoy-state quantum key exchange through the turbulent atmosphere and show that beam tracking does not always improves quantum communication., Comment: 15 pages, 6 figures