Abstract: We analyze the security and feasibility of a protocol for quantum key distribution (QKD) in a context where only one of the two parties trusts his measurement apparatus. This scenario lies naturally between standard QKD, where both parties trust their measurement apparatuses, and device-independent QKD (DI-QKD), where neither do, and can be a natural assumption in some practical situations. We show that the requirements for obtaining secure keys are much easier to meet than for DI-QKD, which opens promising experimental opportunities. We clarify the link between the security of this one-sided DI-QKD scenario and the demonstration of quantum steering, in analogy to the link between DI-QKD and the violation of Bell inequalities.

Abstract: The Fisher information $F$ gives a limit to the ultimate precision achievable in a phase estimation protocol. It has been shown recently that the Fisher information for a linear two-mode interferometer cannot exceed the number of particles if the input state is separable. As a direct consequence, with such input states the shot-noise limit is the ultimate limit of precision. In this work, we go a step further by deducing bounds on $F$ for several multiparticle entanglement classes. These bounds imply that genuine multiparticle entanglement is needed for reaching the highest sensitivities in quantum interferometry. We further compute similar bounds on the average Fisher information $\overline{F}$ for collective spin operators, where the average is performed over all possible spin directions. We show that these criteria detect different sets of states and illustrate their strengths by considering several examples, also using experimental data. In particular, the criterion based on $\overline{F}$ is able to detect certain bound entangled states.

Abstract: We present several entanglement criteria in terms of the quantum Fisher information that help to relate various forms of multipartite entanglement to the sensitivity of phase estimation. We show that genuine multipartite entanglement is necessary to reach the maximum sensitivity in some very general metrological tasks using a two-arm linear interferometer. We also show that it is needed to reach the maximum average sensitivity in a certain combination of such metrological tasks.

Abstract: We describe and expand upon the scalable randomized benchmarking protocol proposed in Phys. Rev. Lett. 106, 180504 (2011) which provides a method for benchmarking quantum gates and estimating the gate dependence of the noise. The protocol allows the noise to have weak time and gate dependence, and we provide a sufficient condition for the applicability of the protocol in terms of the average variation of the noise. We discuss how state-preparation and measurement errors are taken into account and provide a complete proof of the scalability of the protocol. We establish a connection in special cases between the error rate provided by this protocol and the error strength measured using the diamond norm distance.

Abstract: We analyze the optical properties of one-dimensional $\mathcal{PT}$-symmetric structures of arbitrary complexity. These structures violate normal unitarity (photon flux conservation) but are shown to satisfy generalized unitarity relations, which relate the elements of the scattering matrix and lead to a conservation relation in terms of the transmittance and (left and right) reflectances. One implication of this relation is that there exist anisotropic transmission resonances in $\mathcal{PT}$-symmetric systems, frequencies at which there is unit transmission and zero reflection, but only for waves incident from a single side. The spatial profile of these transmission resonances is symmetric, and they can occur even at $\mathcal{PT}$-symmetry-breaking points. The general conservation relations can be utilized as an experimental signature of the presence of $\mathcal{PT}$ symmetry and of $\mathcal{PT}$-symmetry-breaking transitions. The uniqueness of $\mathcal{PT}$-symmetry-breaking transitions of the scattering matrix is briefly discussed by comparing to the corresponding non-Hermitian Hamiltonians.

Abstract: In the study of open quantum systems, memory effects are usually ignored, and this leads to dynamical semigroups and Markovian dynamics. However, in practice, non-Markovian dynamics is the rule rather than the exception. With the recent emergence of quantum information theory, there is a flurry of investigations of non-Markovian dynamics, and several significant measures for non-Markovianity are introduced from various perspectives such as deviation from divisibility, information exchange between a system and its environment, or entanglement with the environment. In this work, by exploiting the correlations flow between a system and an arbitrary ancillary, we propose a considerably intuitive measure for non-Markovianity by use of correlations as quantified by the quantum mutual information rather than entanglement. The fundamental properties, physical significance, and differences and relations with existing measures for non-Markovianity are elucidated. The measure captures quite directly and deeply the characteristics of non-Markovianity from the perspective of information. A simplified version based on Jamio\l{}kowski-Choi isomorphism which encodes operations via bipartite states and does not involve any optimization is also proposed.

Abstract: We consider a $p$-polarized surface electromagnetic wave (a classical surface polariton) at the interface between the vacuum and a metal or left-handed medium. We show that the evanescent electromagnetic waves forming the surface polariton inevitably possess a backward spin energy flow, which, together with a superluminal orbital energy flow, form the total Poynting vector. This spin energy flow generates a well-defined (but not quantized) spin angular momentum of surface polaritons which is orthogonal to the propagation direction. The spin of evanescent waves arises from the imaginary longitudinal component of the electric field which makes the polarization effectively elliptical in the propagation plane. We also examine the connection between the spin and chirality of evanescent modes.

Abstract: We investigate dissipative phase transitions in an open central spin system. In our model the central spin interacts coherently with the surrounding many-particle spin environment and is subject to coherent driving and dissipation. We develop analytical tools based on a self-consistent Holstein-Primakoff approximation that enable us to determine the complete phase diagram associated with the steady states of this system. It includes first- and second-order phase transitions, as well as regions of bistability, spin squeezing, and altered spin-pumping dynamics. Prospects of observing these phenomena in systems such as electron spins in quantum dots or nitrogen-vacancy centers coupled to lattice nuclear spins are briefly discussed.

Abstract: We present an effective operator formalism for open quantum systems. Employing perturbation theory and adiabatic elimination of excited states for a weakly driven system, we derive an effective master equation which reduces the evolution to the ground-state dynamics. The effective evolution involves a single effective Hamiltonian and one effective Lindblad operator for each naturally occurring decay process. Simple expressions are derived for the effective operators which can be directly applied to reach effective equations of motion for the ground states. We compare our method with the hitherto existing concepts for effective interactions and present physical examples for the application of our formalism, including dissipative state preparation by engineered decay processes.

Abstract: We have theoretically and numerically investigated an analog of electromagnetically induced transparency (EIT) in plasmonic systems consisting of multiple cascaded nanodisk resonators, aperture-side-coupled to metal-insulator-metal bus waveguides. A simplified theoretical model is established to study spectral features in the plasmonic waveguide-resonator systems, and the calculated results are in good agreement with finite-difference time-domain simulations. The main dependent factors of EIT-like spectral response, namely, the resonance detuning, intrinsic Drude loss, and especially cavity-cavity separation, are discussed in detail. Similar to multiple EIT in quantum systems, multiple induced-transparency peaks are found in the areas of strong dispersion generated in our plasmonic system. The group indices and quality factors of transparency resonances with high transmission can reach levels of similar to 35 and similar to 200, respectively. These results pave a way toward dynamic control of light in the nanoscale domain, which can actualize some new devices for fundamental study and applications of plasmonic nanostructures.

Abstract: We propose a family of error-detecting stabilizer codes with an encoding rate of $1/3$ that permit a transversal implementation of the gate $T=\mathrm{exp}(\ensuremath{-}i\ensuremath{\pi}Z/8)$ on all logical qubits. These codes are used to construct protocols for distilling high-quality ``magic'' states $T\left|+\right\ensuremath{\rangle}$ by Clifford group gates and Pauli measurements. The distillation overhead scales as $O({\mathrm{log}}^{\ensuremath{\gamma}}(1/\ensuremath{\epsilon}))$, where $\ensuremath{\epsilon}$ is the output accuracy and $\ensuremath{\gamma}={\mathrm{log}}_{2}(3)\ensuremath{\approx}1.6$. To construct the desired family of codes, we introduce the notion of a triorthogonal matrix, a binary matrix in which any pair and any triple of rows have even overlap. Any triorthogonal matrix gives rise to a stabilizer code with a transversal $T$ gate on all logical qubits, possibly augmented by Clifford gates. A powerful numerical method for generating triorthogonal matrices is proposed. Our techniques lead to a twofold overhead reduction for distilling magic states with accuracy $\ensuremath{\epsilon}\ensuremath{\sim}{10}^{\ensuremath{-}12}$ compared with previously known protocols.

Abstract: A no-signalling channel transforming quantum systems in Alice's and Bob's local laboratories is compatible with two different causal structures: ($A⪯B$) Alice's output causally precedes Bob's input and ($B⪯A$) Bob's output causally precedes Alice's input. Here I prove that two no-signalling channels that are not perfectly distinguishable in any ordinary quantum circuit can become perfectly distinguishable through the quantum superposition of circuits with different causal structures.

Abstract: We theorize the spin Hall effect of light (SHEL) on a nanometal film and demonstrate it experimentally via weak measurements. A general propagation model to describe the relationship between the spin-orbit coupling and the thickness of the metal film is established. It is revealed that the spin-orbit coupling in the SHEL can be effectively modulated by adjusting the thickness of the metal film, and the transverse displacement is sensitive to the thickness of metal film in a certain range for horizontal polarization light. Importantly, a large negative transverse shift can be observed as a consequence of the combined contribution of the ratio and the phase difference of Fresnel coefficients.

Abstract: Within extended coherent states, a recent exact solution to the quantum Rabi model (QRM) [D. Braak, Phys. Rev. Lett. 107, 100401 (2011)] can be recovered in an alternative simpler and more physical way, without use of any extra conditions. In the same framework, the two-photon QRM is solved exactly by treating extended squeezed states on an equal footing. Concise transcendental functions responsible for the exact solutions are derived. The isolated Juddian solutions are also analytically obtained in terms of degeneracy. Both the extended coherent states and squeezed states employed here are essentially Fock states in the space of the corresponding Bogoliubov operators, which result in free-particle number operators. The present approach can be summarized concisely in a unified way and easily extended to various spin-boson systems with multiple levels, even multiple modes.

Abstract: We investigate correlations among complementary observables. In particular, we show how to take advantage of mutually unbiased bases for the efficient detection of entanglement in arbitrarily high-dimensional, multipartite, and continuous-variable quantum systems. The introduced entanglement criteria are relatively easy to implement experimentally since they require only a few local measurement settings. In addition, we establish a link between the separability problem and the maximum number of mutually unbiased bases---opening an additional avenue in this long-standing open problem.

Abstract: Entanglement swapping is a process bywhich two initially independent quantum systems can become entangled and generate nonlocal correlations. To characterize such correlations, we compare them to those predicted by bilocal models, where systems that are initially independent are described by uncorrelated states. We extend in this paper the analysis of bilocal correlations initiated in [Phys. Rev. Lett. 104, 170401 (2010)]. In particular, we derive new Bell-type inequalities based on the bilocality assumption in different scenarios, we study their possible quantum violations, and we analyze their resistance to experimental imperfections. The bilocality assumption, being stronger than Bell’s standard local causality assumption, lowers the requirements for the demonstration of quantumness in entanglement-swapping experiments.

Abstract: The observation of $\mathcal{PT}$ symmetry in a coupled optical waveguide system that involves a complex refractive index has been demonstrated impressively in the experiment by R\"uter et al. [Nat. Phys. 6, 192 (2010)]. This is, however, only an optical analog of a quantum system, and it would be highly desirable to observe the manifestation of $\mathcal{PT}$ symmetry and the resulting properties also in a real, experimentally accessible, quantum system. Following a suggestion by Klaiman et al. [Phys. Rev. Lett. 101, 080402 (2008)], we investigate a $\mathcal{PT}$-symmetric arrangement of a Bose-Einstein condensate in a double-well potential, where in one well cold atoms are injected while in the other particles are extracted from the condensate. We investigate, in particular, the effects of the nonlinearity in the Gross-Pitaevskii equation on the $\mathcal{PT}$ properties of the condensate. To study these effects we analyze a simple one-dimensional model system in which the condensate is placed into two $\mathcal{PT}$-symmetric $\ensuremath{\delta}$-function traps. The analysis will serve as a useful guide for studies of the behavior of Bose-Einstein condensates in realistic $\mathcal{PT}$-symmetric double wells.

Abstract: We study the metastability and decay of multiply-charged superflow in a ring-shaped atomic Bose-Einstein condensate. Supercurrent corresponding to a giant vortex with topological charge up to q=10 is phase-imprinted optically and detected both interferometrically and kinematically. We observe q=3 superflow persisting for up to a minute and clearly resolve a cascade of quantised steps in its decay. These stochastic decay events, associated with vortex-induced $2 \pi$ phase slips, correspond to collective jumps of atoms between discrete q values. We demonstrate the ability to detect quantised rotational states with > 99 % fidelity, which allows a detailed quantitative study of time-resolved phase-slip dynamics. We find that the supercurrent decays rapidly if the superflow speed exceeds a critical velocity in good agreement with numerical simulations, and we also observe rare stochastic phase slips for superflow speeds below the critical velocity.

Abstract: Higher-order sidebands in optomechanically induced transparency are discussed in a generic optomechanical system. We take account of nonlinear terms and give an effective method to deal with such problems. It is shown that, if a strong control field with frequency ${\ensuremath{\omega}}_{1}$ and a weak probe field with frequency ${\ensuremath{\omega}}_{p}$ are incident upon the optomechanical system, then there are output fields with frequencies ${\ensuremath{\omega}}_{1}\ifmmode\pm\else\textpm\fi{}2\ensuremath{\Omega}$ generated, where $\ensuremath{\Omega}={\ensuremath{\omega}}_{p}\ensuremath{-}{\ensuremath{\omega}}_{1}$. We analyze the amplitude of the output field ${\ensuremath{\omega}}_{1}+2\ensuremath{\Omega}$ and look at how it varies with the control field and show that the amplitude of the second-order sideband can be controlled by the strong control field.

Abstract: We design, by invariant-based inverse engineering, resonant laser pulses to perform fast population transfers in three-level systems. The laser intensities to improve the fidelity or to achieve a perfect transfer are examined for different protocols. They can be reduced by populating the intermediate state and by multimode driving.

Abstract: Practical schemes for measurement-device-independent quantum key distribution using phase and path or time encoding are presented. In addition to immunity to existing loopholes in detection systems, our setup employs simple encoding and decoding modules without relying on polarization maintenance or optical switches. Moreover, by employing a modified sifting technique to handle the dead-time limitations in single-photon detectors, our scheme can be run with only two single-photon detectors. With a phase-post-selection technique, a decoy-state variant of our scheme is also proposed, whose key generation rate scales linearly with the channel transmittance.

Abstract: We study the existence of absolutely maximally entangled (AME) states in quantum mechanics and its applications to quantum information. AME states are characterized by being maximally entangled for all bipartitions of the system and exhibit genuine multipartite entanglement. With such states, we present a parallel teleportation protocol which teleports multiple quantum states between groups of senders and receivers. The notable features of this protocol are that (i) the partition into senders and receivers can be chosen after the state has been distributed, and (ii) one group has to perform joint quantum operations while the parties of the other group only have to act locally on their system. We also prove the equivalence between pure state quantum secret sharing schemes and AME states with an even number of parties.

Abstract: As quantum key distribution becomes a mature technology, it appears clearly that some assumptions made in the security proofs cannot be justified in practical implementations. This might open the door to possible side-channel attacks. We examine several discrepancies between theoretical models and experimental setups in the case of continuous-variable quantum key distribution. We study in particular the impact of an imperfect modulation on the security of Gaussian protocols and show that approximating the theoretical Gaussian modulation with a discrete one is sufficient in practice. We also address the issue of properly calibrating the detection setup and in particular the value of the shot noise. Finally, we consider the influence of phase noise in the preparation stage of the protocol and argue that taking this noise into account can improve the secret key rate because this source of noise is not controlled by the eavesdropper.

Abstract: Motivated by experiments observing self-organization of cold atoms in optical cavities, we investigate the collective dynamics of the associated nonequilibrium Dicke model. The model displays a rich semiclassical phase diagram of long-time attractors including distinct superradiant fixed points, bistable and multistable coexistence phases, and regimes of persistent oscillations. We explore the intrinsic time scales for reaching these asymptotic states and discuss the implications for finite-duration experiments. On the basis of a semiclassical analysis of the effective Dicke model, we find that sweep measurements over 200 ms may be required in order to access the asymptotic regime. We briefly comment on the corrections that may arise due to quantum fluctuations and states outside of the effective two-level Dicke model description.

Abstract: We derive exact relations for $N$ spin-1/2 fermions with zero-range or short-range interactions, in continuous space or on a lattice, in $2D$ or in $3D$, in any external potential. Some of them generalize known relations between energy, momentum distribution $n(k)$, pair distribution function $g^{(2)}(r)$, derivative of the energy with respect to the scattering length $a$. Expressions are found for the second order derivative of the energy with respect to $1/a$ (or to $\ln a$ in $2D$). Also, it is found that the leading energy corrections due to a finite interaction range, are proportional to the effective range $r_e$ in $3D$ (and to $r_e^2$ in $2D$) with exprimable model-independent coefficients, that give access to the subleading short distance behavior of $g^{(2)}(r)$ and to the subleading $1/k^6$ tail of $n(k)$. This applies to lattice models for some magic dispersion relations, an example of which is given. Corrections to exactly solvable two-body and three-body problems are obtained. For the trapped unitary gas, the variation of the finite-$1/a$ and finite $r_e$ energy corrections within each $SO(2,1)$ energy ladder is obtained; it gives the frequency shift and the collapse time of the breathing mode. For the bulk unitary gas, we compare to fixed-node Monte Carlo data, and we estimate the experimental uncertainty on the Bertsch parameter due to a finite $r_e$.

Abstract: We propose a potentially practical scheme to precisely measure the charge number of small charged objects by using optomechanically induced transparency (OMIT) in optomechanical systems. In contrast to conventional measurements based on noise backaction on optomechanical systems, our scheme presents an alternative way to detect the charge number exactly, by monitoring small deformation of the mechanical resonator sensitive to the charge number of nearby charged object. The relationship between the charge number and the OMIT window width is investigated and the feasibility of the scheme is justified by numerical simulation with currently available experimental values.

Abstract: We propose a general method by which experiments on ultracold gases can be used to determine the topological properties of the energy bands of optical lattices, as represented by the map of the Berry curvature across the Brillouin zone. The Berry curvature modifies the semiclassical dynamics and hence the trajectory of a wave packet undergoing Bloch oscillations. However, in two dimensions these trajectories may be complicated Lissajous-like figures, making it difficult to extract the effects of Berry curvature in general. We propose how this can be done using a ``time-reversal'' protocol. This compares the velocity of a wave packet under positive and negative external force, and allows a clean measurement of the Berry curvature over the Brillouin zone. We discuss how this protocol may be implemented and explore the semiclassical dynamics for three specific systems: the asymmetric hexagonal lattice and two ``optical flux'' lattices in which the Chern number is nonzero. Finally, we discuss general experimental considerations for observing Berry curvature effects in ultracold gases.

Abstract: We provide a general method to find the Hamiltonian of a linear circuit in the presence of a nonlinearity. Focusing on the case of a Josephson junction embedded in a transmission-line resonator, we solve for the normal modes of the system by taking into account exactly the effect of the quadratic (i.e., inductive) part of the Josephson potential. The nonlinearity is then found to lead to self and cross-Kerr effects, as well as beam-splitter-type interactions between modes. By adjusting the parameters of the circuit, the Kerr coefficient $K$ can be made to reach values that are weak ($Kl\ensuremath{\kappa}$), strong ($Kg\ensuremath{\kappa}$), or even very strong ($K\ensuremath{\gg}\ensuremath{\kappa}$) with respect to the photon-loss rate $\ensuremath{\kappa}$. In the latter case, the $\mathrm{resonator}+\mathrm{junction}$ circuit corresponds to an in-line version of the transmon. By replacing the single junction by a SQUID, the Kerr coefficient can be tuned in situ, allowing, for example, the fast generation of Schr\"odinger cat states of microwave light. Finally, we explore the maximal strength of qubit-resonator coupling that can be reached in this setting.

Abstract: We present a space-time generalization of the known spatial (monochromatic) wave vortex beams carrying intrinsic orbital angular momentum (OAM) along the propagation direction. Generic spatiotemporal vortex beams are polychromatic and can carry intrinsic OAM at an arbitrary angle to the mean momentum. Applying either (i) a transverse wave-vector shift or (ii) a Lorentz boost to a monochromatic Bessel beam, we construct a family of either (i) time-diffracting or (ii) nondiffracting spatiotemporal Bessel beams, which are exact solutions of the Klein-Gordon wave equations. The proposed spatiotemporal OAM states are able to describe either photon or electron vortex states (both relativistic and nonrelativistic) and have potential applications in particle collisions, optics of moving media, quantum communications, and astrophysics.