A two-sphere ("Bloch" or "Poincare") is familiar for describing the dynamics of a spin-1/2 particle or light polarization. Analogous objects are derived for unitary groups larger than SU(2) through an iterative procedure that constructs evolution operators for higher-dimensional SU in terms of lowerdimensional ones. We focus, in particular, on the SU(4) of two qubits which describes all possible logic gates in quantum computation. For a general Hamiltonian of SU(4) with 15 parameters, and for Hamiltonians of its various sub-groups so that fewer parameters suffice, we derive Bloch-like rotation of unit vectors analogous to the one familiar for a single spin in a magnetic field. The unitary evolution of a quantal spin pair is thereby expressed as rotations of real vectors. Correspondingly, the manifolds involved are Bloch two-spheres along with higher dimensional manifolds such as a foursphere for the SO(5) sub-group and an eight-dimensional Grassmannian manifold for the general SU(4). This latter may also be viewed as two, mutually orthogonal, real six-dimensional unit vectors moving on a five-sphere with an additional phase constraint.

New experimental data on double-ionization cross sections of neutral atoms, positive and negative ions by electron impact are reported. These and other relevant data are compared with recent multiple-ionization semiempirical formulae extended for the case of two-electron ionization. Theory gives analytical dependence of the double-ionization cross sections on the main parameters of the collision system in a wide energy range. For the He atom, He-like ions and H − ion high-energy asymptotic behaviour of the double-ionization cross sections are considered on the basis of a quantum mechanical treatment. Suggested cross section scaling for fast collisions, employing a target-effective nuclear charge, is in good agreement with experimental data.

One of the major efforts in the quantum biological program is to subject biological systems to standard tests or measures of quantumness. These tests and measures should elucidate if non-trivial quantum effects may be present in biological systems. Two such measures of quantum correlations are the quantum discord and the relative entropy of entanglement. Here, we show that the relative entropy of entanglement admits a simple analytic form when dynamics and accessible degrees of freedom are restricted to a zero- and single-excitation subspace. We also simulate and calculate the amount of quantum discord that is present in the Fenna-Matthews-Olson protein complex during the transfer of an excitation from a chlorosome antenna to a reaction center. We find that the single-excitation quantum discord and relative entropy of entanglement are equal for all of our numerical simulations, but a proof of their general equality for this setting evades us for now. Also, some of our simulations demonstrate that the relative entropy of entanglement without the single-excitation restriction is much lower than the quantum discord. The first picosecond of dynamics is the relevant timescale for the transfer of the excitation, according to some sources in the literature. Our simulation results indicate that quantum correlations contribute a significant fraction of the total correlation during this first picosecond in many cases, at both cryogenic and physiological temperature.Comment: 15 pages, 7 figures, significant improvements including (1) an analytical formula for the single-excitation relative entropy of entanglement (REE), (2) simulations indicating that the single-excitation REE is equal to the single-excitation discord, and (3) simulations indicating that the full REE can be much lower than the single-excitation RE

Numerical optimization is used to design linear-optical devices that implement a desired quantum gate with perfect fidelity, while maximizing the success rate. For the 2-qubit CS (or CNOT) gate, we provide numerical evidence that the maximum success rate is S = 2/27 using two unentangled ancilla resources; interestingly, additional ancilla resources do not increase the success rate. For the 3-qubit Toffoli gate, we show that perfect fidelity is obtained with only three unentangled ancilla photons -less than in any existing scheme -with a maximum S = 0.00340. This compares well with S = (2/27) 2 /2 ≈ 0.00274, obtainable by combining two CNOT gates and a passive quantum filter [1]. The general optimization approach can easily be applied to other areas of interest, such as quantum error correction, cryptography, and metrology [2,3].PACS numbers: 03.67.Lx, 42.50.Dv Linear optics is considered as a viable method for scalable quantum information processing, due in large part to the seminal work of Knill, Laflamme, and Milburn (KLM) [4]. These authors showed that an elementary quantum logic gate on qubits, encoded in photonic states, can be constructed using a combination of linearoptical elements and quantum measurement. The tradeoff in this measurement-assisted scheme is that the gate is properly implemented only when the measurement yields a positive outcome, i.e., the gate is non-deterministic. Soon after the KLM scheme became a paradigm for linear optical quantum computation (LOQC), it became clear that there is a general unresolved theoretical problem of finding the optimal implementation for a desired quantum transformation [5].For the nonlinear sign (NS) gate, which acts on photons in a single optical mode, α 0 |0 + α 1 |1 + α 2 |2 → α 0 |0 + α 1 |1 − α 2 |2 , the maximum success probability without feed-forward has been theoretically proved to be 1/4 [6]. Here we focus on more complicated gates, taking as examples the two-qubit controlled sign (CS) gate (equivalently, the CNOT gate), and the three-qubit Toffoli gate. For these physically important gates, existing theoretical results are limited to upper or lower bounds on the success probability [1,7,8].A linear-optical quantum gate, or state generator (LO-QSG) [5], can be viewed formally as a device implementing a contraction transformation (for ideal detectors) that converts pure input states into desired pure output states. The goal of the optimization problem is to find a proper linear optical network (see Fig. 1), characterized by a unitary matrix U, that performs the desired transformation [9,10]. The problem is naturally partitioned into two tasks: i) finding a subspace of perfect fidelity within the space of all unitary matrices U, and ii) maximizing the success probability within this subspace. While in this paper we address transformations implemented by linear optics, the method is universal and with minor modifications can be successfully applied to any quantum-information problem involving unitary operations combined with measurements. Origina...

We optimize two-mode, entangled, number states of light in the presence of loss in order to maximize the extraction of the available phase information in an interferometer. Our approach optimizes over the entire available input Hilbert space with no constraints, other than fixed total initial photon number. We optimize to maximize the Fisher information, which is equivalent to minimizing the phase uncertainty. We find that in the limit of zero loss the optimal state is the so-called N00N state, for small loss, the optimal state gradually deviates from the N00N state, and in the limit of large loss the optimal state converges to a generalized two-mode coherent state, with a finite total number of photons. The results provide a general protocol for optimizing the performance of a quantum optical interferometer in the presence of photon loss, with applications to quantum imaging, metrology, sensing, and information processing. PACS numbers: 42.50.St, 42.50.Ar, 42.50.Dv, Quantum states of light play an important role in applications including metrology, imaging, sensing, and quantum information processing [1]. In quantum interferometry, entangled states of light, such as the maximally path-entangled N00N states, replace conventional laser light to achieve a sensitivity below the shot-noise limit, even reaching the Heisenberg limit, and a resolution well below the Rayleigh diffraction limit [2]. For an overview of quantum metrology applications see, for example, Ref.[1]. However, for real-world applications, diffraction, scattering, and absorption of quantum states of light need to be taken into account. Recently it has been shown that many quantum-enhanced metrology schemes using N00N states perform poorly when a considerable amount of loss is present [3,4,5]. However, our team has also discovered a new class of entangled number states, which are more resilient to loss [6]. These so-called M &M ′ states still outperform classical light sources under a moderate 3 dB of loss.In this work, we systematize the numerical search for optimal quantum states in a two-mode interferometer in the presence of loss. We employ the Fisher information to obtain the phase sensitivity of the interferometer. An exhaustive review and application of the Fisher information concept to the sensitivity of a March-Zehnder interferometer, particularly in the zero loss case, has been presented in the recent work by Durkin and Dowling [7]. The chief utility of the Fisher information approach is that it provides a bound on the phase sensitivity, even in the absence of a fully specified detection scheme, and is now widely adopted in studies of interferometer sensitivity. Such numerical optimization has been previously carried out in the absence of loss, and with loss over a restricted class of input states [8,9]. Here, we provide a completely general optimization scheme that is applied to the two-mode interferometer, but also has application to the optimization of linear optical systems for quantum linear optical information processing [10,11].Using...