A phase relaxation process of interacting two qubits is studied by means of the quantum master equation, where each qubit is influenced by an independent thermal reservoir. The damping operator of the quantum master equation consists of two parts; one includes the effects of the interaction between the qubits and the other does not. It is shown that the interaction significantly affects the phase relaxation process. The decoherence of entanglement is investigated for the two qubits initially prepared in the $X$ state.

In the framework of Kohn-Sham density-functional theory, systems with ground-state densities that are not pure-state $v$-representable (PSVR) in the noninteracting reference system occur frequently. In the present contribution, an algorithm, which allows the solution of such systems, is proposed. It is shown that the use of densities which do not correspond to a ground state of their noninteracting reference system is forbidden. As a consequence, the proposed algorithm considers only noninteracting ensemble $v$-representable densities. The Fe atom, a well-known non-PSVR system, is used as an illustration. Finally, the problem is analyzed within finite-temperature density-functional theory, where the physical significance of fractional occupations is exposed and the question of why degenerate states can be unequally occupied is resolved.

In this paper we describe in detail and generalize a method for quantum process tomography that was presented by Bendersky et al. [Phys. Rev. Lett. 100, 190403 (2008)]. The method enables the efficient estimation of any element of the $\chi$ matrix of a quantum process. Such elements are estimated as averages over experimental outcomes with a precision that is fixed by the number of repetitions of the experiment. Resources required implementing it scale polynomially with the number of qubits of the system. The estimation of all diagonal elements of the $\chi$ matrix can be efficiently done without any ancillary qubits. In turn, the estimation of all the off-diagonal elements requires an extra clean qubit. The key ideas of the method, which is based on efficient estimation by random sampling over a set of states forming a 2-design, are described in detail. Efficient methods for preparing and detecting such states are explicitly shown.

Using a two-step, two-color laser spectroscopy technique, we have completed a measurement of the hyperfine structure within the $\left(5s^{2}6p\right)$ ${{}^{2}P}_{3/2}$ excited state in ${}^{115}\text{I}\text{n}$ $\left(I=9/2\right)$. A frequency stabilized GaN diode laser at 410 nm is locked to the $5P_{1/2}\to 6S_{1/2}$ ground-state transition and a second 1291 nm diode laser is scanned over the $6S_{1/2}\to 6P_{3/2}$ transition to produce hyperfine spectra for the $6P_{3/2}\left(F=3,4,5,6\right)$ manifold. We find the hyperfine splittings of consecutive sublevels to be as follows: $\Delta {\nu }_{4-3}=275.25\left(42\right)\text{MHz}$, $\Delta {\nu }_{5-4}=384.05\left(71\right)\text{MHz}$, and $\Delta {\nu }_{6-5}=517.48\left(44\right)\text{MHz}$. The magnetic dipole, electric quadrupole, and magnetic octupole hyperfine coupling constants derived from these three splittings are, respectively, $a=79.33\left(7\right)\text{MHz}$, $b=62.5\left(5\right)\text{MHz}$, and $c=-0.04\left(4\right)\text{MHz}$. The measured value of the dipole constant, $a$, agrees to within 2% with a recent theoretical prediction.

The statistical fluctuations in energy loss have been measured for O, Si, and S ions, in varying thicknesses of polyethylene naphthalate [PEN, or $\left({\text{C}}_7{\text{H}}_5{\text{O}}_2\right)$] polymeric foils. The measurements have been performed in the fractional energy-loss limits $\Delta E/E\sim 5–90\%$. These fluctuations have been found to be enhanced with an increase in $\Delta E/E$. Such a behavior has been reproduced by Bethe-Livingston formulation after modifying it suitably.

We calculate analytically both coherent and incoherent parts of the total spectrum of light scattered by a three-level system in either lambda or ladder configurations. The spectrum is restricted to the cases of the incident light pulse weakly depopulating the initial level and of the carrier frequency much lower than the excitation frequency in the system. We give special attention to the spectra under the conditions of different multiphoton resonances in the system and emphasize the effects resulting from the presence of the third level. The analytic theory is shown to explain the numerically calculated spectra as far as the number of frequency components, their positions in the spectrum, relative intensities, and sensitivity to the pulse shape are concerned.

We present an unconventional form of decoy-state technique to make the single-photon Bennett 1992 protocol robust against losses and noise of a communication channel. Two uninformative states are prepared by the transmitter in order to prevent the unambiguous state discrimination attack and improve the phase-error rate estimation. The presented method does not require strong reference pulses, additional electronics, or extra detectors for its implementation.

We consider measurement-based quantum computation using the state of a spin-lattice system in equilibrium with a thermal bath and free to evolve under its own Hamiltonian. Any single qubit measurements disturb the system from equilibrium and, with adaptive measurements performed at a finite rate, the resulting dynamics reduces the fidelity of the computation. We show that it is possible to describe the loss in fidelity by a single quantum operation on the encoded quantum state that is independent of the measurement history. To achieve this simple description, we choose a particular form of spin-boson coupling to describe the interaction with the environment, and perform measurements periodically at a natural rate determined by the energy gap of the system. We found that an optimal cooling exists, which is a trade-off between keeping the system cool enough that the resource state remains close to the ground state, but also isolated enough that the cooling does not strongly interfere with the dynamics of the computation. For a sufficiently low temperature we obtain a fault-tolerant threshold for the couplings to the environment.

We measure the absolute frequency of 12 sub-Doppler lines of the $P\left(6\right)$ and $P\left(7\right)$ transitions in the ${\nu }_3$ band of ${{}^{12}\text{C}\text{H}}_4$ using difference-frequency-generation (DFG) of $1.064\text{−}\mu \text{m}$ Nd:YAG and $1.55\text{−}\mu \text{m}$ DFB lasers and a fiber-based frequency comb referenced to International Atomic Time. The relative uncertainties are typically $9.4\times {10}^{-11}$, and the determined value for the $P\left(7\right)$ $F_2^{\left(2\right)}$ line agrees with the International Committee for Weights and Measures recommendation with a discrepancy of $\left(1.2\pm 8.4\right)\text{kHz}$. The combination of the DFG spectrometer and the frequency comb enables determining energy levels as accurately as microwave spectroscopy.

Reversible, nonlinear (saturable) absorption is useful when deep penetration of light into dye layers, beyond the exponential depth in Beer’s law, is required. Examples are in the photomechanics of nematic elastomers, or in the two-color simultaneous absorption exploited to lithographically write structures in the deeply subwavelength region. We explicitly calculate the intensity distribution and the dynamics of its development from the three nonlinear coupled partial differential absorption equations for strong two-color interactions with dye layers. We show how the nonlinearity produces sharp transverse profiles of one color at the expense of the other.

We study optical wave turbulence using as a particular example recently created ultralong-fiber laser. We show that the sign of the cavity dispersion has a critical impact on the spectral and temporal properties of generated radiation that are directly relevant to the fiber laser performance. For a normal dispersion, we observe an intermediate state with an extremely narrow spectrum (condensate), which experiences an instability and a sharp transition to a strongly fluctuating regime with a wide spectrum and increased probability of spontaneous generation of large-amplitude pulses.

The security of the decoherence-free version of the Bennett-Brassard 1984 (BB84) protocol [A. Cabello, Phys. Rev. A 75, 020301 (2007)] is analyzed and shown to be vulnerable under the intercept-resend attack. We propose two improved versions of this protocol. Both improvements remain the performance of robustness against collective noise and refuse the security flaw. Especially, the second improvement, which is called four-qubit decoherence-free (DF) BB84 protocol, not only remains all characteristics of the original protocol but also has a higher efficiency. We also give a detailed security proof of four-qubit DF BB84 protocol.

We present an analysis of complete positivity constraints on qutrit-qubit and qutrit-qutrit quantum channels that have a form of affine transformations of a generalized Bloch vector. We show that, in general, the complete positivity constraints for qutrit channels’ parameters reveal nonlinearities and cannot be reduced to piecewise linear conditions defining a convex simplex. We discuss qutrit-qubit entanglement breaking channels and show Kraus representation for qutrit-qutrit damping channels.

The statistical distance between pure quantum states is obtained by finding a measurement that is optimal in a sense defined by Wootters. As such, one may expect that the statistical distance will turn out to be different if the set of possible measurements is restricted in some way. It nonetheless turns out that if the restriction is to local operations and classical communication on any multipartite system, then the statistical distance is the same as it is without restriction, being equal to the angle between the states in Hilbert space.

Is the closest product state to a symmetric entangled multiparticle state also symmetric? This question has appeared in the recent literature concerning the geometric measure of entanglement. First, we show that a positive answer can be derived from results concerning symmetric multilinear forms and homogeneous polynomials, implying that the closest product state can be chosen to be symmetric. We then prove the stronger result that the closest product state to any symmetric multiparticle quantum state is necessarily symmetric. Moreover, we discuss generalizations of our result and the case of translationally invariant states, which can occur in spin models.

We explore procedures to detect entanglement of unknown mixed states, which can be experimentally viable. The heart of the method is a hierarchy of simple feasibility problems, which provides sufficient conditions to entanglement. Our numerical investigations indicate that the entanglement is detected with a cost which is much lower than full state tomography. The procedure is applicable to both free and bound entanglements and involves only single copy measurements.

We show that the three-qubit entanglement classes, (0) null, (1) separable $A\text{−}B\text{−}C$, (2a) biseparable $A\text{−}BC$, (2b) biseparable $B\text{−}CA$, (2c) biseparable $C\text{−}AB$, (3) $W$, and (4) Greenberger-Horne-Zeilinger, correspond respectively to ranks 0, 1, 2a, 2b, 2c, 3, and 4 of a Freudenthal triple system defined over the Jordan algebra $\mathbb{C}\oplus \mathbb{C}\oplus \mathbb{C}$. We also compute the corresponding stochastic local operations and classical communication orbits.

Measurements of the grand total and positronium-formation cross sections for positrons scattered by helium within the impact energy range from 10 to 60 eV are presented. All measurements presented here use a high-resolution $\left(\sim 70\text{meV}\right)$ trap-based pulsed positron beam. Scattering is studied using a high-magnetic field, and absolute measurements of the scattering cross sections are obtained without the need for normalization to other cross sections. We also present single center, convergent close coupling calculations of the total cross section. A detailed study of the cross section to investigate the possibility of scattering resonances and channel coupling has been made. Comparisons with previous cross-section measurements and theoretical calculations are also included.