Recent work by Lundeen et al. [Nature (London) 474, 188 (2011)] directly measured the wave function by weakly measuring a variable followed by a normal (i.e., “strong”) measurement of the complementary variable. We generalize this method to mixed states by considering the weak measurement of various products of these observables, thereby providing the density matrix an operational definition in terms of a procedure for its direct measurement. The method only requires measurements in two bases and can be performed in situ, determining the quantum state without destroying it.

We study a far-from-equilibrium system of interacting particles, hopping between sites of a 1D lattice with a rate which increases with the number of particles at interacting sites. We find that clusters of particles, which initially spontaneously form in the system, begin to move at increasing speed as they gain particles. Ultimately, they produce a moving condensate which comprises a finite fraction of the mass in the system. We show that, in contrast with previously studied models of condensation, the relaxation time to steady state decreases as an inverse power of $\ln L$ with system size $L$ and that condensation is instantaneous for $L\to \infty$.

We propose the generation of entangled states with trapped calcium ions using a combination of an rf dressed state and a spin-dependent force. By using this method, a decoherence-free entangled state of rf qubits can be directly generated, and ideally its fidelity is close to unity. We demonstrate an rf entangled state with a fidelity of $0.68\pm 0.08$, which has a coherence time of more than 200 ms by virtue of the fact that it is an eigenstate with energy gaps between adjacent levels. Using the same technique, we also produce a qutrit-qutrit entangled state with a fidelity of $0.77\pm 0.09$, which exceeds the threshold value for separability of $2/3$.

We study nonequilibrium steady states of lattice gases with nearest-neighbor interactions that are driven between two reservoirs. Density profiles in these systems exhibit oscillations close to the reservoirs. We demonstrate that an approach based on time-dependent density functional theory copes with these oscillations and predicts phase diagrams of bulk densities to a good approximation under arbitrary boundary-reservoir couplings. The minimum or maximum current principles can be applied only for specific bulk-adapted couplings. We show that they generally fail to give the correct topology of phase diagrams but can still be useful for getting insight into the mutual arrangement of different phases.

Weakly chaotic nonlinear maps with marginal fixed points have an infinite invariant measure. Time averages of integrable and nonintegrable observables remain random even in the long time limit. Temporal averages of integrable observables are described by the Aaronson-Darling-Kac theorem. We find the distribution of time averages of nonintegrable observables, for example, the time average position of the particle, $\overline{x}$. We show how this distribution is related to the infinite invariant density. We establish four identities between amplitude ratios controlling the statistics of the problem.

We investigate the ground states of a Bose-Einstein condensate of indirect excitons coupled to an electron gas. We show that in a properly designed system the crossing of a roton minimum into the negative energy domain can result in the appearance of the supersolid phase, characterized by periodicity in both real and reciprocal space. Accounting for the spin-dependent exchange interaction of excitons we obtain ferromagnetic supersolid domains. The Fourier spectra of excitations of weakly perturbed supersolids show pronounced diffraction maxima which may be detected experimentally.

We derive universal relations for the rf spectroscopy of a two-dimensional Fermi gas consisting of two spin states interacting through an $S$-wave scattering length. The rf transition rate has a high-frequency tail that is proportional to the contact and displays logarithmic scaling violations, decreasing asymptotically like $1/({\omega }^2{ln}^2\omega )$. Its coefficient is proportional to ${ln}^2(a_{2\mathrm{D}}^{\prime }/a_{2\mathrm{D}})$, where $a_{2\mathrm{D}}$ and $a_{2\mathrm{D}}^{\prime }$ are the two-dimensional scattering lengths associated with initial-state and final-state interactions. The clock shift is proportional to the contact and to $\ln (a_{2\mathrm{D}}^{\prime }/a_{2\mathrm{D}})$. If $|\ln (a_{2\mathrm{D}}^{\prime }/a_{2\mathrm{D}})|\gg 1$, the clock shift arises as a cancellation between much larger contributions proportional to ${ln}^2(a_{2\mathrm{D}}^{\prime }/a_{2\mathrm{D}})$ from bound-bound and bound-free rf transitions.

We characterize the entanglement contained in a pure three-qubit state via operational entanglement measures. To this end, we derive a new decomposition for arbitrary three-qubit states which is characterized by five parameters (up to local unitary operations). We show that these parameters are uniquely determined by bipartite entanglement measures. These quantities measure the entanglement required to generate the state following a particular preparation procedure and have a clear physical meaning. Moreover, we show that the classification of states obtained in this way is strongly related to the one obtained when considering general local operations and classical communication.

We introduce a new scheme for continuous-variable entanglement distillation that requires only linear temporal and constant physical or spatial resources. Distillation is the process by which high-quality entanglement may be distributed between distant nodes of a network in the unavoidable presence of decoherence. The known versions of this protocol scale exponentially in space and doubly exponentially in time. Our optimal scheme therefore provides exponential improvements over existing protocols. It uses a fixed-resource module—an entanglement distillery—comprising only four quantum memories of at most 50% storage efficiency and allowing a feasible experimental implementation. Tangible quantum advantages are obtainable by using existing off-resonant Raman quantum memories outside their conventional role of storage.

We demonstrate that a large ensemble of noiseless globally coupled-pinned oscillators is capable of rectifying spatial disorder with spontaneous current activated through a dynamical phase transition mechanism, either of first or second order, depending on the profile of the pinning potential. In the presence of an external weak drive, the same collective mechanism can result in an absolute negative mobility, which, though not immediately related to symmetry breaking, is most prominent at the phase transition. Our results apply to a tug-of-war by competing molecular motors for bidirectional cargo transport.

The effect of particle-nonconserving processes on the steady state of driven diffusive systems is studied within the context of a generalized $ABC$ model. It is shown that in the limit of slow nonconserving processes, the large deviation function of the overall particle density can be computed by making use of the steady-state density profile of the conserving model. In this limit one can define a chemical potential and identify first order transitions via Maxwell’s construction, similarly to what is done in equilibrium systems. This method may be applied to other driven models subjected to slow nonconserving dynamics.

We propose a practical entanglement classification scheme for general multipartite pure states in arbitrary dimensions under local unitary equivalence by exploiting the high order singular value decomposition technique and local symmetries of the states. By virtue of this scheme, the method of determining the local unitary equivalence of $n$-qubit states proposed by Kraus is extended to the case for arbitrary dimensional multipartite states.

A linear optical quantum computer relies on interference between photonic qubits for logic, and entanglement for near-deterministic operation. Here we measure the interference and entanglement properties of photons emitted by a quantum dot embedded within a light-emitting diode. We show that pairs of simultaneously generated photons are entangled, and indistinguishable from subsequently generated photons. We measure entanglement fidelity of 0.87 and two-photon-interference visibility of $0.60\pm 0.05$. The visibility, limited by detector jitter, could be improved by optical cavity designs.

A classical one-time pad allows two parties to send private messages over a public classical channel—an eavesdropper who intercepts the communication learns nothing about the message. A quantum one-time pad is a shared quantum state which allows two parties to send private messages or private quantum states over a public quantum channel. If the eavesdropper intercepts the quantum communication she learns nothing about the message. In the classical case, a one-time pad can be created using shared and partially private correlations. Here we consider the quantum case in the presence of an eavesdropper, and find the single-letter formula for the rate at which the two parties can send messages using a general quantum state as a quantum one-time pad. Surprisingly, the formula coincides with the distillable entanglement assisted by a symmetric channel, an important quantity in quantum information theory, but which lacked a clear operational meaning.

We study analytically the order statistics of a time series generated by the positions of a symmetric random walk of $n$ steps with step lengths of finite variance ${\sigma }^2$. We show that the statistics of the gap $d_{k,n}=M_{k,n}-M_{k+1,n}$ between the $k$th and the $(k+1)$th maximum of the time series becomes stationary, i.e., independent of $n$ as $n\to \infty$ and exhibits a rich, universal behavior. The mean stationary gap exhibits a universal algebraic decay for large $k$, $⟨d_{k,\infty }⟩/\sigma \sim 1/\sqrt{2\pi k}$, independent of the details of the jump distribution. Moreover, the probability density (pdf) of the stationary gap exhibits scaling, $\mathrm{Pr}(d_{k,\infty }=\delta )\simeq (\sqrt{k}/\sigma )P(\delta \sqrt{k}/\sigma )$, in the regime $\delta \sim ⟨d_{k,\infty }⟩$. The scaling function $P(x)$ is universal and has an unexpected power law tail, $P(x)\sim x^{-4}$ for large $x$. For $\delta \gg ⟨d_{k,\infty }⟩$ the scaling breaks down and the pdf gets cut off in a nonuniversal way. Consequently, the moments of the gap exhibit an unusual multiscaling behavior.

We consider Bell tests involving bipartite states shared between three parties. We show that the simple inclusion of a third part may greatly simplify the measurement scenario (in terms of the number of measurement settings per part) and allows the identification of previously unknown nonlocal resources.

Superactivation is the property that two channels with zero quantum capacity can be used together to yield a positive capacity. Here we demonstrate that this effect exists for a wide class of inequivalent channels, none of which can simulate each other. We also consider the case where one of two zero-capacity channels is applied, but the sender is ignorant of which one is applied. We find examples where the greater the entropy of mixing of the channels, the greater the lower bound for the capacity. Finally, we show that the effect of superactivation is rather generic by providing an example of superactivation using the depolarizing channel.

We derive the general form of a master equation describing the reduced time evolution of a sequence of subsystems “propagating” in an environment which can be described as a sequence of subenvironments. The interaction between subsystems and subenvironments is described in terms of a collision model, with the irreversible dynamics of the subenvironments between collisions explicitly taken into account. In the weak coupling regime, we show that the collisional model produces a correlated Markovian evolution for the joint density matrix of the multipartite system. The associated Lindblad superoperator contains pairwise terms describing cross correlation between the different subsystems. Such a model can describe a broad range of physical situations, ranging from quantum channels with memory to photon propagation in concatenated quantum optical systems.

Teleportation of a quantum state may be used for distributing entanglement between distant qubits in quantum communication and for quantum computation. Here we demonstrate the implementation of a teleportation protocol, up to the single-shot measurement step, with superconducting qubits coupled to a microwave resonator. Using full quantum state tomography and evaluating an entanglement witness, we show that the protocol generates a genuine tripartite entangled state of all three qubits. Calculating the projection of the measured density matrix onto the basis states of two qubits allows us to reconstruct the teleported state. Repeating this procedure for a complete set of input states we find an average output state fidelity of 86%.

Entanglement and nonlocality are both fundamental aspects of quantum theory, and play a prominent role in quantum information science. The exact relation between entanglement and nonlocality is, however, still poorly understood. Here we make progress in this direction by showing that, contrary to what previous work suggested, quantum nonlocality does not imply entanglement distillability. Specifically, we present analytically a 3-qubit entangled state that is separable along any bipartition. This implies that no bipartite entanglement can be distilled from this state, which is thus fully bound entangled. Then we show that this state nevertheless violates a Bell inequality. Our result also disproves the multipartite version of a long-standing conjecture made by Peres.