Nondeterministic gates for photonic single-rail quantum logic

We discuss techniques for producing, manipulating, and measuring qubits encoded optically as vacuum- and single-photon states. We show that a universal set of nondeterministic gates can be constructed using linear optics and photon counting. We investigate the efficacy of a test gate given realistic detector efficiencies.

Practical scheme for quantum computation with any two-qubit entangling gate

Which gates are universal for quantum computation? Although it is well known that certain gates on two-level quantum systems (qubits), such as the controlled-NOT, are universal when assisted by arbitrary one-qubit gates, it has only recently become clear precisely what class of two-qubit gates is universal in this sense. We present an elementary proof that any entangling two-qubit gate is universal for quantum computation, when assisted by one-qubit gates. A proof of this result for systems of arbitrary finite dimension has been provided by Brylinski and Brylinski; however, their proof relies on a long argument using advanced mathematics. In contrast, our proof provides a simple constructive procedure which is close to optimal and experimentally practical.

Preparing encoded states in an oscillator

Recently a scheme has been proposed for constructing quantum error-correcting codes that embed a finite-dimensional code space in the infinite-dimensional Hilbert space of a system described by continuous quantum variables. One of the difficult steps in this scheme is the preparation of the encoded states. We show how these states can be generated by coupling a continuous quantum variable to a single qubit. An ion trap quantum computer provides a natural setting for a continuous system coupled to a qubit. We discuss how encoded states may be generated in an ion trap.

QCD thermal phase transition in the presence of a small chemical potential

We propose a new method to investigate the thermal properties of QCD with a small quark chemical potential mu. Derivatives of quark and gluonic observables with respect to mu are computed at mu=0 for two flavors of p4 improved staggered fermions with ma=0.1,0.2 on a 16(3)x4 lattice, and used to calculate the leading order Taylor expansion in mu of the location of the pseudocritical point about mu=0. This expansion should be well behaved for the small values of mu(q)/T(c)similar to0.1 relevant for BNL RHIC phenomenology, and predicts a critical curve T-c(mu) in reasonable agreement with estimates obtained using exact reweighting. In addition, we contrast the case of isoscalar and isovector chemical potentials, quantify the effect of munot equal0 on the equation of state, and comment on the complex phase of the fermion determinant in QCD with munot equal0.

Application of the maximum entropy method to the (2 + 1)D four-fermion model

We investigate spectral functions extracted using the maximum entropy method from correlators measured in lattice simulations of the (2+1)-dimensional four-fermion model. This model is particularly interesting because it has both a chirally broken phase with a rich spectrum of mesonic bound states and a symmetric phase where there are only resonances. In the broken phase we study the elementary fermion, pion, sigma, and massive pseudoscalar meson; our results confirm the Goldstone nature of the π and permit an estimate of the meson binding energy. We have, however, seen no signal of σ→ππ decay as the chiral limit is approached. In the symmetric phase we observe a resonance of nonzero width in qualitative agreement with analytic expectations; in addition the ultraviolet behavior of the spectral functions is consistent with the large nonperturbative anomalous dimension for fermion composite operators expected in this model.

One-dimensional quantum walk with unitary noise

The effect of unitary noise on the discrete one-dimensional quantum walk is studied using computer simulations. For the noiseless quantum walk, starting at the origin (n=0) at time t=0, the position distribution P-t(n) at time t is very different from the Gaussian distribution obtained for the classical random walk. Furthermore, its standard deviation, sigma(t) scales as sigma(t)similar tot, unlike the classical random walk for which sigma(t)similar toroott. It is shown that when the quantum walk is exposed to unitary noise, it exhibits a crossover from quantum behavior for short times to classical-like behavior for long times. The crossover time is found to be Tsimilar toalpha(-2), where alpha is the standard deviation of the noise.

Electron exchange coupling for single-donor solid-state spin qubits

Intervalley interference between degenerate conduction band minima has been shown to lead to oscillations in the exchange energy between neighboring phosphorus donor electron states in silicon [B. Koiller, X. Hu, and S. Das Sarma, Phys. Rev. Lett. 88, 027903 (2002); Phys. Rev. B 66, 115201 (2002)]. These same effects lead to an extreme sensitivity of the exchange energy on the relative orientation of the donor atoms, an issue of crucial importance in the construction of silicon-based spin quantum computers. In this article we calculate the donor electron exchange coupling as a function of donor position incorporating the full Bloch structure of the Kohn-Luttinger electron wave functions. It is found that due to the rapidly oscillating nature of the terms they produce, the periodic part of the Bloch functions can be safely ignored in the Heitler-London integrals as was done by Koiller, Hu, and Das Sarma, significantly reducing the complexity of calculations. We address issues of fabrication and calculate the expected exchange coupling between neighboring donors that have been implanted into the silicon substrate using an 15 keV ion beam in the so-called top down fabrication scheme for a Kane solid-state quantum computer. In addition, we calculate the exchange coupling as a function of the voltage bias on control gates used to manipulate the electron wave functions and implement quantum logic operations in the Kane proposal, and find that these gate biases can be used to both increase and decrease the magnitude of the exchange coupling between neighboring donor electrons. The zero-bias results reconfirm those previously obtained by Koiller, Hu, and Das Sarma.

Numerical study of hydrogenic effective mass theory for an impurity P donor in Si in the presence of an electric field and interfaces

In this paper we examine the effects of varying several experimental parameters in the Kane quantum computer architecture: A-gate voltage, the qubit depth below the silicon oxide barrier, and the back gate depth to explore how these variables affect the electron density of the donor electron. In particular, we calculate the resonance frequency of the donor nuclei as a function of these parameters. To do this we calculated the donor electron wave function variationally using an effective-mass Hamiltonian approach, using a basis of deformed hydrogenic orbitals. This approach was then extended to include the electric-field Hamiltonian and the silicon host geometry. We found that the phosphorous donor electron wave function was very sensitive to all the experimental variables studied in our work, and thus to optimize the operation of these devices it is necessary to control all parameters varied in this paper.

Photon-added detection

The production of conditional quantum states and quantum operations based on the result of measurement is now seen as a key tool in quantum information and metrology. We propose a different type of photon number detector. It functions nondeterministically, but when successful, it has high fidelity. The detector, which makes use of an n-photon auxiliary Fock state and high efficiency homodyne detection, allows a tunable trade-off between fidelity and probability. By sacrificing probability of operation, an excellent approximation to a photon-number detector is achieved.

Stokes-operator-squeezed continuous-variable polarization states

We investigate nonclassical Stokes-operator variances in continuous-wave polarization-squeezed laser light generated from one and two optical parametric amplifiers. A general expression of how Stokes-operator variances decompose into two-mode quadrature operator variances is given. Stokes parameter variance spectra for four different polarization-squeezed states have been measured and compared with a coherent state. Our measurement results are visualized by three-dimensional Stokes-operator noise volumes mapped on the quantum Poincare sphere. We quantitatively compare the channel capacity of the different continuous-variable polarization states for communication protocols. It is shown that squeezed polarization states provide 33% higher channel capacities than the optimum coherent beam protocol.

Experimental investigation of criteria for continuous variable entanglement

We generate a pair of entangled beams from the interference of two amplitude squeezed beams. The entanglement is quantified in terms of EPR paradox and inseparability criteria, with both results clearly beating the standard quantum limit. We experimentally analyze the effect of decoherence on each criterion and demonstrate qualitative differences. We also characterize the number of required and excess photons present in the entangled beams and provide contour plots of the efficacy of quantum information protocols in terms of these variables.

Experimental investigation of continuous-variable quantum teleportation

We report the experimental demonstration of quantum teleportation of the quadrature amplitudes of a light field. Our experiment was stably locked for long periods, and was analyzed in terms of fidelity F and with signal transfer T-q=T++T- and noise correlation V-q=Vinparallel to out+Vinparallel to out-. We observed an optimum fidelity of 0.64+/-0.02, T-q=1.06+/-0.02, and V-q=0.96+/-0.10. We discuss the significance of both T-q>1 and V-q

Quantum theory of the far-off-resonance continuous-wave Raman laser: Heisenberg-Langevin approach

We present the quantum theory of the far-off-resonance continuous-wave Raman laser using the Heisenberg-Langevin approach. We show that the simplified quantum Langevin equations for this system are mathematically identical to those of the nondegenerate optical parametric oscillator in the time domain with the following associations: pump pump, Stokes signal, and Raman coherence idler. We derive analytical results for both the steady-state behavior and the time-dependent noise spectra, using standard linearization procedures. In the semiclassical limit, these results match with previous purely semiclassical treatments, which yield excellent agreement with experimental observations. The analytical time-dependent results predict perfect photon statistics conversion from the pump to the Stokes and nonclassical behavior under certain operational conditions.

Tailoring teleportation to the quantum alphabet

We introduce a refinement of the standard continuous variable teleportation measurement and displacement strategies. This refinement makes use of prior knowledge about the target state and the partial information carried by the classical channel when entanglement is nonmaximal. This gives an improvement in the output quality of the protocol. The strategies we introduce could be used in current continuous variable teleportation experiments.