We relate the nonlocal properties of noisy entangled states to Grothendieck’s constant, a mathematical constant appearing in Banach space theory. For two-qubit Werner states ${\rho }_p^W=p\mid {\psi }^{-}⟩⟨{\psi }^{-}\mid +(1-p)\mathbb{1}∕4$, we show that there is a local model for projective measurements if and only if $p⩽1∕K_G\left(3\right)$, where $K_G\left(3\right)$ is Grothendieck’s constant of order 3. Known bounds on $K_G\left(3\right)$ prove the existence of this model at least for $p\lesssim 0.66$, quite close to the current region of Bell violation, $p\sim 0.71$. We generalize this result to arbitrary quantum states.

The optical theorem is applied to the process of electron-positron pair creation in the superposition of a nuclear Coulomb and a strong laser field. We derive representations for the total production rate as twofold integrals, both for circular laser polarization and for the general case of elliptic polarization. Our approach allows us to obtain, by analytical means, the asymptotic behavior of the pair creation rate for various limits of interest. In particular, we consider pair production by two-photon absorption and show that, close to the energetic threshold of this process, the rate obeys a power law in the laser frequency with different exponents for linear and circular laser polarization. With the help of the upcoming x-ray laser sources, our results could be tested experimentally.

A phase damping reservoir composed by $N$-bosons coupled to a system of interest through a cross-Kerr interaction is proposed and its effects on quantum superpositions are investigated. By means of analytical calculations we show that: (i) the reservoir induces a Gaussian decay of quantum coherences, and (ii) the inherent incommensurate character of the spectral distribution yields irreversibility. A state-independent decoherence time and a master equation are both derived analytically. These results, which have been extended for the thermodynamic limit, show that nondissipative decoherence can be suitably contemplated within the environment-induced decoherence (EID) approach. Finally, it is shown that the same mechanism yielding decoherence are also responsible for inducing dynamical disentanglement.

One of the most significant challenges facing the development of linear optics quantum computing (LOQC) is mode mismatch, whereby photon distinguishability is introduced within circuits, undermining quantum interference effects. We examine the effects of mode mismatch on the parity (or fusion) gate, the fundamental building block in several recent LOQC schemes. We derive simple error models for the effects of mode mismatch on its operation, and relate these error models to current fault-tolerant-threshold estimates.

We design linear-optics multiqubit quantum logic gates. We assume the traditional encoding of a qubit onto the state of a single photon in two modes (e.g., spatial or polarization). We suggest schemes allowing direct probabilistic realization of the fundamental Toffoli and Fredkin gates without resorting to a sequence of single- and two-qubit gates. This yields more compact schemes and potentially reduces the number of ancilla photons. The proposed setups involve passive linear optics, sources of auxiliary single photons or maximally entangled pairs of photons, and single-photon detectors. In particular, we propose an interferometric implementation of the Toffoli gate in the coincidence basis, which does not require any ancilla photons and is experimentally feasible with current technology.

We propose a natural generalization of bipartite Werner and isotropic states to multipartite systems consisting of an arbitrary even number of $d$-dimensional subsystems (qudits). These generalized states are invariant under the action of local unitary operations. We study basic properties of multipartite invariant states and present necessary and sufficient separability criteria.

We construct a class of multipartite states possessing orthogonal symmetry. This new class contains multipartite states which are invariant under the action of local unitary operations introduced in our preceding paper [Phys. Rev. A 73, 062314 (2006)]. We study basic properties of multipartite symmetric states: separability criteria and multi-PPT conditions.

We discuss the concept of polarization states of four-dimensional quantum systems based on the frequency nondegenerate biphoton field. Several quantum tomography protocols were developed and implemented for the measurement of an arbitrary state of ququart. A simple method that does not rely on the interferometric technique is used to generate and measure the sequence of states that can be used for quantum communication purposes.

We study nonlinear relaxation of the excited state in a system with two levels and a continuum. The process is first simulated in a one-dimensional waveguide array described by the discrete nonlinear Schrödinger equation. The results are interpreted in terms of degenerate four-wave mixing between the eigenmodes and diffraction properties of the array. We also show analytically that the role of the continuum can be played by a third bound state, with linear loss that replaces the diffraction in the continuum. This model enables derivation of the energy transfer rate and other parameters of the process.

A formula to evaluate the entanglement in a one-dimensional ferrimagnetic system is derived. Based on the formula, we find that the thermal entanglement in a small size spin-$1∕2$ and spin-$s$ ferrimagnetic chain is rather robust against temperature, and the threshold temperature may be arbitrarily high when $s$ is sufficiently large. This intriguing result answers unambiguously a fundamental question: “Can entanglement and quantum behavior in physical systems survive at arbitrary high temperatures?”

In a couple of papers [Phys. Rev. A, 63, 033818 (2001); 63, 023810 (2001)], P. Zhou, S. Swain, and L. You studied the cavity-induced modifications to the Autler-Townes spectrum of three-level atoms due to the phenomenon of quantum interference. They demonstrated that probe gain can occur in either of the Autler-Townes doublet due to the cavity-induced interference among spontaneous decay channels. In this Comment, we show that this conclusion is incorrect and it contradicts the thermodynamic equilibrium conditions of the atomic system in steady state.

We show that field-free molecular orientation induced by a half-cycle pulse may be considerably enhanced by an additional laser pulse inducing molecular antialignment. Two qualitatively different enhancement mechanisms are identified, depending on the pulse order, and their effects are optimized with the help of quasiclassical as well as fully quantum models.

We analyze the geometric phase for an open quantum system when computed by resorting to a stochastic unraveling of the reduced density matrix (quantum jump approach or stochastic Schrödinger equations). We show that the resulting phase strongly depends on the type of unraveling used for the calculations: as such, this phase is not a geometric object since it depends on nonphysical parameters, which are not related to the path followed by the density matrix during the evolution of the system.

We introduce the concept of a physical process that purifies a mixed quantum state, taken from a set of states, and investigate the conditions under which such a purification map exists. Here, a purification of a mixed quantum state is a pure state in a higher-dimensional Hilbert space, the reduced density matrix of which is identical to the original state. We characterize all sets of mixed quantum states, for which perfect purification is possible. Surprisingly, some sets of two noncommuting states are among them. Furthermore, we investigate the possibility of performing an imperfect purification.

We lay a comprehensive foundation for the study of redundant information storage in decoherence processes. Redundancy has been proposed as a prerequisite for objectivity, the defining property of classical objects. We consider two ensembles of states for a model universe consisting of one system and many environments: the first consisting of arbitrary states, and the second consisting of “singly branching” states consistent with a simple decoherence model. Typical states from the random ensemble do not store information about the system redundantly, but information stored in branching states has a redundancy proportional to the environment’s size. We compute the specific redundancy for a wide range of model universes, and fit the results to a simple first-principles theory. Our results show that the presence of redundancy divides information about the system into three parts: classical (redundant); purely quantum; and the borderline, undifferentiated or “nonredundant,” information.

The structure is investigated of all completely positive quantum operations that transform pure two-qubit input states of a given degree of entanglement in a covariant way. Special cases thereof are quantum NOT operations which transform entangled pure two-qubit input states of a given degree of entanglement into orthogonal states in an optimal way. Based on our general analysis all covariant optimal two-qubit quantum NOT operations are determined. In particular, it is demonstrated that only in the case of maximally entangled input states can these quantum NOT operations be performed perfectly.

We have observed attenuated total reflection at a glass/rubidium vapor interface in high precision. The atom density was from $3.8\times {10}^{20}\text{to}3.7\times {10}^{21}{\mathrm{m}}^{-3}$ and the angle of incidence was from 48.4 to 64.8°. Redshift and broadening of the reflection spectra were observed. The redshift depended on atom density, angle of incidence, light polarization and hyperfine structure. The observed broadening was attributed to the self-broadening of the resonance line. Calculation based on the Fresnel formula with a local index for the susceptibility of the vapor, which included the Lorentz local field correction and the modification of the wave vector of the evanescent light by the optically dense atomic vapor, was found to be in reasonable agreement with the experimental results.

We present a theoretical study of the effect of structural and base sequence disorders on the transport properties of nonthermal electron scattering within and from single strands of DNA. The calculations are based on our recently developed formalism to treat multiple elastic scattering from simplified pseudomolecular DNA subunits. Structural disorder is shown to increase both the elastic scattering cross section and the attachment probability on the bases at low energy. Sequence disorder, however, has no significant effect.

Doubly excited coherent elliptic states (DECESs) of an atom could be produced by exciting an atomic electron to a Rydberg state, applying the adiabatic field-switching technique to obtain a coherent elliptic state (CES) and by subsequent excitation of an atomic core electron into a low-lying excited state. The DECESs decay by autoionization and radiative transitions. As an example, the autoionization widths are calculated for DECESs in He. The dependence of the widths on the eccentricity of the CES, principal quantum number of the Rydberg electron, orientation of the inner electron orbital and electron exchange is studied and interpreted.

We have observed inner-shell photoionization of Be using synchrotron radiation in the energy region of the $1s\left(2s2p{}^{3}P\right)nl$ Rydberg states. We used a time-of-flight method to distinguish singly and doubly charged photoions and obtained the ${\mathrm{Be}}^{+}$ [$ns$; $n=5–12$, $\left({}^{1}P\right)3s$] and ${\mathrm{Be}}^{2+}$ [$ns$; $n=5–8$, $nd=5,6$, $\left({}^{1}P\right)3s$] ion spectra with high resolution corresponding to an instrumental bandpass of $13\mathrm{meV}$. Detailed analysis enabled the autoionization parameters, resonance energy position $E_0$, resonance width $\Gamma$, and Fano parameter $q$, to be obtained. From the resonance positions of the ${}^{3}Pnl$ series members, the series limit was determined to be $127.97\mathrm{eV}$, which is in good agreement with previous experiments.