Recently, Pawlowski [Phys. Rev. A 82, 032313 (2010)] claimed to have proven the security of a quantum key distribution by using only the monogamy of Bell's inequality violations. In the proof, however, he tacitly assumed that the eavesdropper's outcome is binary. The assumption cannot be justified because Eve's (eavesdropper's) power can only be limited by natural principle. We provide a counterexample for a step of the proof.

In this reply, I address the comment by Hwang and Gittsovich on my paper [Phys. Rev. A 82, 032313 (2010)]. The authors of the Comment pointed out that I used an implicit assumption that the alphabet of the eavesdropper was binary. They claimed that such an assumption was unrealistic. Here, I show that, even without this assumption, the main result of my paper still holds.

We present a cascaded system consisting of three nondegenerate optical parametric amplifiers (NOPAs) for the generation and the enhancement of quantum entanglement of continuous variables. The entanglement of optical fields produced by the first NOPA is successively enhanced by the second and the third NOPAs from $-5.3$ to $-8.1$ dB below the quantum noise limit. The dependence of the enhanced entanglement on the physical parameters of the NOPAs and the reachable entanglement limitation for a given cascaded NOPA system are calculated. The calculation results are in good agreement with the experimental measurements.

We have obtained the wave function and time correlation of two $\gamma$ rays resulting from the annihilation of a spin-singlet positronium. We have modified the calculations made by Gauthier and Hawton [Phys. Rev. A 81, 062121 (2010)] in consideration of the real experimental conditions. It has been found that the time correlation is determined by the center-of-mass motion of the positronium, and that the exponential decay component shown by Gauthier and Hawton does not appear in the time-correlation function. We have also conducted an experiment focused on the exponential component in the time-correlation function. The experimental results are consistent with our calculation.

A scheme for measuring the purity of a quantum system with a finite number of levels is presented. The method makes use of two $\sqrt{\text{swap}}$ gates and hinges only on measurements performed on a reference system, prepared in a certain pure state and coupled with the target system. Neither tomographic methods, with the complete reconstruction of the state, nor interferometric setups are needed.

We present a detailed account of quantum state estimation by joint maximization of the likelihood and the entropy. After establishing the algorithms for both perfect and imperfect measurements, we apply the procedure to data from simulated and actual experiments. We demonstrate that the realistic situation of incomplete data from imperfect measurements can be handled successfully.

Two defect particles that couple to a harmonic chain, acting as common reservoir, can become entangled even when the two defects do not directly interact and the harmonic chain is effectively a thermal reservoir for each individual defect. This dynamics is encountered for sufficiently low temperatures of the chain and depends on the initial state of the two oscillators. In particular, when each defect is prepared in a squeezed state, entanglement can be found at time scales at which the steady state of a single defect is reached. We provide a microscopic description of the coupled quantum dynamics of chain and defects. By means of numerical simulations, we explore the parameter regimes for which entanglement is found under the specific assumption that both particles couple to the same ion of the chain. This model provides the microscopic setting where bath-induced entanglement can be observed.

We discuss an extension of the Hylleraas configuration-interaction method by incorporation of an exponentially correlated term. The necessary unlinked one-center, three- and four-electron integrals are derived in a closed form. No three- or four-electron auxiliary integrals appear in the final expressions. The evaluation scheme is an extension of the recent development of Ruiz [J. Math. Chem. 46, 1322 (2009)]. The prescription of combining diverged integrals to retrieve a finite value is avoided in the present approach.

We propose a method for producing entangled spin and orbital states in pairs of atoms resulting from the dissociation of diatomic molecules. The method employs the interference between a one-photon and a two-photon process to break the backward-forward symmetry of the dissociation processes. The spin entanglement of distant atom pairs makes use of excited spin-orbit-coupled (molecular) intermediate states. When the dissociating molecules are confined to a one-dimensional optical lattice, the method can be used to generate long sequences of (spin- and orbit-) entangled pairs of atoms.

Strongly interacting atoms trapped in optical lattices can be used to explore phase diagrams of Hubbard models. Spatial inhomogeneity due to trapping typically obscures distinguishing observables. We propose that measures using boson double occupancy avoid trapping effects to reveal two key correlation functions. We define a boson core compressibility and core superfluid stiffness in terms of double occupancy. We use quantum Monte Carlo on the Bose-Hubbard model to empirically show that these quantities intrinsically eliminate edge effects to reveal correlations near the trap center. The boson core compressibility offers a generally applicable tool that can be used to experimentally map out phase transitions between compressible and incompressible states.

The excitations of strongly interacting bosons confined in a two-dimensional square lattice are studied. Using a combined Bogoliubov method and the quantum-rotor approach, the Hamiltonian of strongly interacting bosons is mapped onto the $U\left(1\right)$-phase action. This allows to calculate the momentum- and energy-resolved one-particle spectral function and its dependence on the presence of the superfluid phase. It is shown that the destruction of the ordered phase leads to the opening of the gap in the excitation spectrum in $\mathbf{k}=\mathbf{0}$. On the other hand, superfluidity manifests itself as a sharp coherence peak resulting from the emergence of the long-range order. Correlation effects lead to the appearance of a smearing of the band structure of incoherent particles although the remnants of the Bogoliubov excitations are still present in the coherent part of the spectrum.

A one-dimensional magnetophotonic crystal with a nonlinear defect placed either symmetrically or asymmetrically inside the structure is considered. Simultaneous effects of time-reversal nonreciprocity and nonlinear spatial asymmetry in the structure are studied. Bistable response is demonstrated in a such system, accompanied by abrupt polarization switching between two circular or elliptical polarizations for transmitted and reflected waves. The effect is explained in terms of field localization at defect-mode spectral resonances and can be used in the design of thin-film optical isolators and polarization transformation devices.

We examine the response to the sudden switch of the pump parameter in a multimode semiconductor laser with intensity coupling on a model whose validity has been successfully compared to experimental results. We find the existence of a very slow modal evolution governed by a master mode, which reaches its steady state on a time scale that is a couple of orders of magnitude longer than that of the total intensity. The practical consequences for applications are examined, such as the temporal evolution of the spectral width of the laser emission and the time at which its steady state is attained. Issues related to modeling choices, such as the number of modes and their placement with respect to line center, are discussed.

We study nonlinear effects in an optomechanical system containing a quantum well. The nonlinearity due to the optomechanical coupling leads to a bistable behavior in the mean intracavity photon number and substantial squeezing in the transmitted field. We show that the optical bistability and the degree of squeezing can be controlled by tuning the power and frequency of the pump laser. The transmitted field intensity spectrum consists of six distinct peaks corresponding to optomechanical, polariton, and hybrid resonances. Interestingly, even though the quantum well and the mechanical modes are not directly coupled, their interaction with the common quantized cavity mode results in appearance of hybrid resonances.

An array of a finite number of waveguides, driven laterally by injecting light at the outer waveguides, is considered. The array is modeled by a discrete nonlinear Schrödinger equation. It has been shown [Phys. Rev. Lett. 94, 243902 (2005)] that, when the injected light is in the proximity of a bifurcation point, such a system can be sensitive to small disturbances, making it possible to act as a light detector. Here, the optimum intensity of the injected light is discussed, and an analytical approximation is presented.

We address the phase of a highly polarized Fermi gases across a narrow Feshbach resonance starting from the problem of a single down-spin fermion immersed in a Fermi sea of up spins. Both polaron and pairing states are considered using the variational wave function approach, and we find that the polaron-to-pairing transition will take place on the BCS side of the resonance, strongly in contrast to a wide resonance where the transition is located at the BEC side. For the pairing phase, we find the critical strength of the repulsive interaction between pairs above which the mixture of pairs and fermions will not phase separate. Therefore, nearby a narrow resonance, it is quite likely that magnetism can coexist with $s$-wave BCS superfluidity at large Zeeman fields, which is a remarkable property absent in conventional BCS superconductors (or fermion-pair superfluids).

The Heisenberg limit traditionally provides a lower bound on the phase uncertainty scaling as $1/\langle N\rangle$, where $\langle N\rangle$ is the mean number of photons in the probe. However, this limit has a number of loopholes which potentially might be exploited to achieve measurements with even greater accuracy. Here we close these loopholes by proving a completely rigorous form of the Heisenberg limit for the average error over all phase shifts, applicable to any estimate of a completely unknown phase shift. Our result gives a completely general, constraint-free, and nonasymptotic statement of the Heisenberg limit. It holds for all phase estimation schemes, including multiple passes, nonlinear phase shifts, multimode probes, and arbitrary measurements.

We consider the entanglement in a two-dimensional $XY$ model in an external magnetic field $h$. The model consists of a set of seven localized spin-$\frac{1}{2}$ particles in a two-dimensional triangular lattice coupled through nearest-neighbor exchange interaction $J$. We examine the effect of single and double impurities in the system as well as the degree of anisotropy on the nearest-neighbor entanglement and ergodicity of the system. We have found that the entanglement of the system at the different degrees of anisotropy mimics that of the one-dimensional spin systems at the extremely small and large values of the parameter $\lambda =h/J$. The entanglement of the Ising and partially anisotropic systems shows phase transition in the vicinity of $\lambda =2$, whereas, the entanglement of the isotropic system suddenly vanishes there. Also, we investigate the dynamic response of the system containing single and double impurities to an external exponential magnetic field at different degrees of anisotropy. We have demonstrated that the ergodicity of the system can be controlled by varying the strength and location of the impurities as well as the degree of anisotropy of the coupling.

We evaluate the degree of quantum correlation between two fermions (bosons) subject to continuous-time quantum walks in a one-dimensional (1D) ring lattice with periodic boundary conditions. In our approach, no particle-particle interaction is considered. We show that the interference effects due to exchange symmetry can result into the appearance of nonclassical correlations. The role played onto the appearance of quantum correlations by the quantum statistics of the particles, the boundary conditions, and the partition of the system is widely investigated. Quantum correlations have also been investigated in a model mimicking the ballistic evolution of two indistinguishable particles in a 1D continuous-space structure. Our results are consistent with recent quantum optics and electron quantum optics experiments where the showing up of two-particle nonclassical correlations has been observed even in the absence of mutual interaction between the particles.

Partial transposition of state operator is a well-known tool to detect quantum correlations between two parts of a composite system. In this paper, the global partial transpose (GPT) is linked to conceptually multipartite underlying structures in a state—the negativity fonts. If $K$-way negativity fonts with nonzero determinants exist, then selective partial transposition of a pure state, involving $K$ of the $N$ qubits ($K⩽N$), yields an operator with negative eigenvalues, identifying $K$-body correlations in the state. Expansion of GPT in terms of $K$-way partially transposed (KPT) operators reveals the nature of intricate intrinsic correlations in the state. Classification criteria for multipartite entangled states based on the underlying structure of global partial transpose of canonical state are proposed. The number of $N$-partite entanglement types for an $N$-qubit system is found to be $2^{N-1}-N+2$, while the number of major entanglement classes is $2^{N-1}-1$. Major classes for three- and four-qubit states are listed. Subclasses are determined by the number and type of negativity fonts in canonical states.