We report on the generation of continuous-variable hyperentanglement of polarization and orbital angular momentum with a type II optical parametric oscillator. By compensating for the astigmatism between spatial modes, we produce an entangled pair of Hermite-Gauss beams. From correlations measurements, we verify the existence of continuous-variable hyperentanglement by the general entanglement criterion as well as by the continuous-variable version of the Peres-Horodecki criterion visualized on an equivalent Poincaré sphere.

We analyze theoretically the transport properties of a weakly interacting ultracold Bose gas enclosed in two reservoirs connected by a constriction. We assume that the transport of the superfluid part is hydrodynamic, and we describe the ballistic transport of the normal part using the Landauer-Büttiker formalism. Modeling the coupled evolution of the phase, atom number, and temperature mismatches between the reservoirs, we predict that Helmholtz (plasma) oscillations can be observed at nonzero temperatures below $T_c$. We show that, because of its strong compressibility, the Bose gas is characterized by a fast thermalization compared to the damping time for plasma oscillations, accompanied by a fast transfer of the normal component. This fast thermalization also affects the gas above $T_c$, where we present a comparison to the ideal fermionic case. Moreover, we outline the possible realization of a superleak through the inclusion of a disordered potential.

Tensor network states constitute an important variational set of quantum states for numerical studies of strongly correlated systems in condensed-matter physics, as well as in mathematical physics. This is specifically true for finitely correlated states or matrix-product operators, designed to capture mixed states of one-dimensional quantum systems. It is a well-known open problem to find an efficient algorithm that decides whether a given matrix-product operator actually represents a physical state that in particular has no negative eigenvalues. We address and answer this question by showing that the problem is provably undecidable in the thermodynamic limit and that the bounded version of the problem is NP-hard (nondeterministic-polynomial-time hard) in the system size. Furthermore, we discuss numerous connections between tensor network methods and (seemingly) different concepts treated before in the literature, such as hidden Markov models and tensor trains.

Quantum data locking is a protocol that allows for a small secret key to (un)lock an exponentially larger amount of information, hence yielding the strongest violation of the classical one-time pad encryption in the quantum setting. This violation mirrors a large gap existing between two security criteria for quantum cryptography quantified by two entropic quantities: the Holevo information and the accessible information. We show that the latter becomes a sensible security criterion if an upper bound on the coherence time of the eavesdropper’s quantum memory is known. Under this condition, we introduce a protocol for secret key generation through a memoryless qudit channel. For channels with enough symmetry, such as the $d$-dimensional erasure and depolarizing channels, this protocol allows secret key generation at an asymptotic rate as high as the classical capacity minus one bit.

Spatially entangled twin photons provide both promising resources for modern quantum information protocols, because of the high dimensionality of transverse entanglement, and a test of the Einstein-Podolsky-Rosen paradox in its original form of position versus impulsion. Usually, photons in temporal coincidence are selected and their positions recorded, resulting in a priori assumptions on their spatiotemporal behavior. In this Letter, we record, on two separate electron-multiplying charge coupled devices cameras, twin images of the entire flux of spontaneous down-conversion. This ensures a strict equivalence between the subsystems corresponding to the detection of either position (image or near-field plane) or momentum (Fourier or far-field plane). We report the highest degree of paradox ever reported and show that this degree corresponds to the number of independent degrees of freedom, or resolution cells, of the images.

We investigate the relation between the incompatibility of quantum measurements and quantum nonlocality. We show that a set of measurements is not jointly measurable (i.e., incompatible) if and only if it can be used for demonstrating Einstein-Podolsky-Rosen steering, a form of quantum nonlocality. Moreover, we discuss the connection between Bell nonlocality and joint measurability, and give evidence that both notions are inequivalent. Specifically, we exhibit a set of incompatible quantum measurements and show that it does not violate a large class of Bell inequalities. This suggests the existence of incompatible quantum measurements which are Bell local, similarly to certain entangled states which admit a local hidden variable model.

The fact that not all measurements can be carried out simultaneously is a peculiar feature of quantum mechanics and is responsible for many key phenomena in the theory, such as complementarity or uncertainty relations. For the special case of projective measurements, quantum behavior can be characterized by the commutator but for generalized measurements it is not easy to decide whether two measurements can still be understood in classical terms or whether the already show quantum features. We prove that a set of generalized measurements which does not satisfy the notion of joint measurability is nonclassical, as it can be used for the task of quantum steering. This shows that the notion of joint measurability is, among several definitions, the proper one to characterize quantum behavior. Moreover, the equivalence allows one to derive novel steering inequalities from known results on joint measurability and new criteria for joint measurability from known results on the steerability of states.

We investigate the relevant spectroscopic properties of the 795 nm ${}^3{\mathrm{H}}_6\leftrightarrow {}^3{\mathrm{H}}_4$ transition in 1% ${\mathrm{Tm}}^{3+}:{\mathrm{Y}}_3{\mathrm{Ga}}_5{\mathrm{O}}_{12}$ at temperatures as low as 1.2 K for optical quantum memories based on persistent spectral tailoring of narrow absorption features. Our measurements reveal that this transition has uniform coherence properties over a 56 GHz bandwidth, and a simple hyperfine structure split by $\pm 44\mathrm{MHz}/\mathrm{T}$ with lifetimes of up to hours. Furthermore, we find a ${{}^3\mathrm{F}}_4$ population lifetime of 64 ms—one of the longest lifetimes observed for an electronic level in a solid—and an exceptionally long coherence lifetime of $490\mu \mathrm{s}$—the longest ever observed for optical transitions of ${\mathrm{Tm}}^{3+}$ ions in a crystal. Our results suggest that this material allows realizing broadband quantum memories that enable spectrally multiplexed quantum repeaters.

We study theoretically and numerically the entanglement entropy of the $d$-dimensional free fermions whose one-body Hamiltonian is the Anderson model. Using the basic facts of the exponential Anderson localization, we show first that the disorder averaged entanglement entropy $⟨S_{\mathrm{\Lambda }}⟩$ of the $d$ dimension cube $\mathrm{\Lambda }$ of side length $l$ admits the area law scaling $⟨S_{\mathrm{\Lambda }}⟩\sim l^{(d-1)},l\gg 1$, even in the gapless case, thereby manifesting the area law in the mean for our model. For $d=1$ and $l\gg 1$ we obtain then asymptotic bounds for the entanglement entropy of typical realizations of disorder and use them to show that the entanglement entropy is not self-averaging, i.e., has nonvanishing random fluctuations even if $l\gg 1$.

We derive a hierarchy of stochastic evolution equations for pure states (quantum trajectories) for open quantum system dynamics with non-Markovian structured environments. This hierarchy of pure states (HOPS) is generally applicable and provides the exact reduced density operator as an ensemble average over normalized states. The corresponding nonlinear equations are presented. We demonstrate that HOPS provides an efficient theoretical tool and apply it to the spin-boson model, the calculation of absorption spectra of molecular aggregates, and energy transfer in a photosynthetic pigment-protein complex.

We theoretically propose and investigate an optical analogue of neutrino oscillations in a pair of vertically displaced binary waveguide arrays with longitudinally modulated effective refractive index. Optical propagation is modeled through coupled-mode equations, which in the continuous limit converge to two coupled Dirac equations for fermionic particles with different mass states, analogously to neutrinos. In addition to simulating neutrino oscillation in the noninteracting regime, our optical setting enables us to explore neutrino interactions in extreme regimes that are expected to play an important role in massive supernova stars. In particular, we predict the quenching of neutrino oscillations and the existence of topological defects, i.e., neutrino solitons, which in our photonic simulator should be observable as excitation of optical gap solitons propagating along the binary arrays at high excitation intensities.

Single-qubit operations on singlet-triplet qubits in GaAs double quantum dots have not yet reached the fidelities required for fault-tolerant quantum information processing. Considering experimentally important constraints and using measured noise spectra, we numerically minimize the effect of decoherence (including high-frequency $1/f$-like noise) and show, theoretically, that quantum gates with fidelities higher than 99.9% are achievable. We also present a self-consistent tuning protocol which should allow the elimination of individual systematic gate errors directly in an experiment.

In this Letter we exploit the recently solved conjecture on the bosonic minimum output entropy to show the optimality of Gaussian discord, so that the computation of quantum discord for bipartite Gaussian states can be restricted to local Gaussian measurements. We prove such optimality for a large family of Gaussian states, including all two-mode squeezed thermal states, which are the most typical Gaussian states realized in experiments. Our family also includes other types of Gaussian states and spans their entire set in a suitable limit where they become Choi matrices of Gaussian channels. As a result, we completely characterize the quantum correlations possessed by some of the most important bosonic states in quantum optics and quantum information.

We show that complete positivity is not only sufficient but also necessary for the validity of the quantum data-processing inequality. As a consequence, the reduced dynamics of a quantum system are completely positive, even in the presence of initial correlations with its surrounding environment, if and only if such correlations do not allow any anomalous backward flow of information from the environment to the system. Our approach provides an intuitive information-theoretic framework to unify and extend a number of previous results.

Einstein-Podolsky-Rosen (EPR) steering, a generalization of the original concept of “steering” proposed by Schrödinger, describes the ability of one system to nonlocally affect another system’s states through local measurements. Some experimental efforts to test EPR steering in terms of inequalities have been made, which usually require many measurement settings. Analogy to the “all-versus-nothing” (AVN) proof of Bell’s theorem without inequalities, testing steerability without inequalities would be more strong and require less resources. Moreover, the practical meaning of steering implies that it should also be possible to store the state information on the side to be steered, a result that has not yet been experimentally demonstrated. Using a recent AVN criterion for two-qubit entangled states, we experimentally implement a practical steering game using quantum memory. Furthermore, we develop a theoretical method to deal with the noise and finite measurement statistics within the AVN framework and apply it to analyze the experimental data. Our results clearly show the facilitation of the AVN criterion for testing steerability and provide a particularly strong perspective for understanding EPR steering.

It is well known that an unambiguous discrimination of the four optically encoded Bell states is possible with a probability of 50% at best, when using static, passive linear optics and arbitrarily many vacuum-mode ancillae. By adding unentangled single-photon ancillae, we are able to surpass this limit and reach a success probability of at least 75%. We discuss the error robustness of the proposed scheme and a generalization to reach a success probability arbitrarily close to 100%.