We present a continuous-variable quantum key distribution protocol combining a discrete modulation and reverse reconciliation. This protocol is proven unconditionally secure and allows the distribution of secret keys over long distances, thanks to a reverse reconciliation scheme efficient at very low signal-to-noise ratio.

The information transmission is studied for quantum channels in which the noise includes dissipative effects, more specifically, nonunitality. Noise is usually a nuisance but can sometimes be helpful. For these channels, the communication capacity is shown to increase with the dissipative component of the noise and may exhibit transitions beyond which it increases faster. The optimal states are constructed analytically as well as the pertaining “phase” diagram.

We provide a simple way to obtain the fusion rules associated with elementary quasiholes over quantum Hall wave functions, in terms of domain walls. The knowledge of the fusion rules is helpful in the identification of the underlying conformal field theory describing the wave functions. We show that, for a certain two-parameter family $(k,r)$ of wave functions, the fusion rules are those of $su(r{)}_k$. In addition, we give an explicit conformal field theory construction of these states, based on the ${\mathcal{M}}_k(k+1,k+r)$ “minimal” theories. For $r=2$, these states reduce to the Read-Rezayi states. The “Gaffnian” wave function is the prototypical example for $r>2$, in which case the conformal field theory is nonunitary.

In some of the earliest work on quantum computing, Feynman showed how to implement universal quantum computation with a time-independent Hamiltonian. I show that this remains possible even if the Hamiltonian is restricted to be the adjacency matrix of a low-degree graph. Thus quantum walk can be regarded as a universal computational primitive, with any quantum computation encoded in some graph. The main idea is to implement quantum gates by scattering processes.

We consider whether two copies of a noisy entangled state can be purified into a single copy with less noise using local operations and classical communication. We show that this is impossible to achieve with certainty when the states form a one parameter twirlable family (i.e., a local twirling operation exists that maps all states into the family, yet leaves the family itself invariant). This implies that two copies of a Werner state cannot be deterministically purified. Furthermore, due to the nature of the proof, it will hold not only in quantum theory, but in any nonlocal probabilistic theory. Hence two noisy Popescu-Rohrlich boxes (hypothetical devices more nonlocal than any quantum state) also cannot be purified.

The absence of vacuum Cherenkov radiation for 104.5 GeV electrons and positrons at the LEP collider at CERN combined with the observed stability of 300 GeV photons at the Tevatron constrains deviations of the speed of light relative to the maximal attainable speed of electrons. Within the standard-model extension, the limit $-5.8\times {10}^{-12}\le {\tilde{\kappa }}_{\mathrm{tr}}-\frac{4}{3}{c}_e^{00}\le 1.2\times {10}^{-11}$ is extracted, which sharpens previous bounds by more than 3 orders of magnitude. The potential for further refinements of this limit with terrestrial experiments and astrophysical observations is discussed.

We study the separability of permutationally symmetric quantum states. We show that for bipartite symmetric systems most of the relevant entanglement criteria coincide. However, we provide a method to generate examples of bound entangled states in symmetric systems, for the bipartite and the multipartite case. These states shed some new light on the nature of bound entanglement.

We study the generic scaling properties of the mutual information between two disjoint intervals, in a class of one-dimensional quantum critical systems described by the $c=1$ bosonic field theory. A numerical analysis of a spin-chain model reveals that the mutual information is scale invariant and depends directly on the boson radius. We interpret the results in terms of correlation functions of branch-point twist fields. The present study provides a new way to determine the boson radius, and furthermore demonstrates the power of the mutual information to extract more refined information of conformal field theory than the central charge.

We describe a scalable, high-speed, and robust architecture for measurement-based quantum computing with trapped ions. Measurement-based architectures offer a way to speed up operation of a quantum computer significantly by parallelizing the slow entangling operations and transferring the speed requirement to fast measurement of qubits. We show that a 3D cluster state suitable for fault-tolerant measurement-based quantum computing can be implemented on a 2D array of ion traps. We propose the projective measurement of ions via multiphoton photoionization for nanosecond operation and discuss the viability of such a scheme for Ca ions.

We demonstrate theoretically a parallelized C-NOT gate which allows us to entangle a mesoscopic ensemble of atoms with a single control atom in a single step, with high fidelity and on a microsecond time scale. Our scheme relies on the strong and long-ranged interaction between Rydberg atoms triggering electromagnetically induced transparency. By this we can robustly implement a conditional transfer of all ensemble atoms between two logical states, depending on the state of the control atom. We outline a many-body interferometer which allows a comparison of two many-body quantum states by performing a measurement of the control atom.

Some materials remain solids even if they are heated beyond the temperature of their melting points. In condensed matter physics, this rare phenomenon is called superheating. Here we report the analogous phenomenon in granular matter: a strongly vibrated monolayer that instead of being a gas persists as a crystal for some time. Eventually, it spontaneously evaporates. We found that the system has thermodynamiclike features like coexistence and metastability. We show how the observed metastable phase is linked to energy dissipation.

We present experimental results on a Bose gas in a quasi-2D geometry near the Berezinskii, Kosterlitz, and Thouless (BKT) transition temperature. By measuring the density profile after time of flight and the coherence length, we identify different states of the gas. We observe that the gas develops a bimodal distribution without long range order. In this regime, the gas presents a longer coherence length than the thermal cloud; it is quasicondensed but is not superfluid. Experimental evidence indicates that we also observe the superfluid transition (BKT transition). For a sufficiently long time of flight, we observe a trimodal distribution when the gas has developed a superfluid component.

We first present a protocol for deterministically distilling nonlocality, building upon a recent result of Forster et al. [Phys. Rev. Lett. 102, 120401 (2009)]. Our protocol, which is optimal for two-copy distillation, works efficiently for a specific class of postquantum nonlocal boxes, which we term correlated nonlocal boxes. In the asymptotic limit, all correlated nonlocal boxes are distilled to the maximally nonlocal box of Popescu and Rohrlich. Then, taking advantage of a result of Brassard et al. [Phys. Rev. Lett. 96, 250401 (2006)] we show that all correlated nonlocal boxes make communication complexity trivial, and therefore appear very unlikely to exist in nature. Astonishingly, some of these nonlocal boxes are arbitrarily close to the set of classical correlations. This result therefore gives new insight to the problem of why quantum nonlocality is limited.

Discrimination between unknown processes chosen from a finite set is experimentally shown to be possible even in the case of nonorthogonal processes. We demonstrate unambiguous deterministic quantum process discrimination of nonorthogonal processes using properties of entanglement, additional known unitaries, or classical communication. Single qubit measurement and unitary processes and multipartite unitaries (where the unitary acts nonseparably across two distant locations) acting on photons are discriminated with a confidence of $\ge 97\%$ in all cases.

We define a new class of random walk processes which maximize entropy. This maximal entropy random walk is equivalent to generic random walk if it takes place on a regular lattice, but it is not if the underlying lattice is irregular. In particular, we consider a lattice with weak dilution. We show that the stationary probability of finding a particle performing maximal entropy random walk localizes in the largest nearly spherical region of the lattice which is free of defects. This localization phenomenon, which is purely classical in nature, is explained in terms of the Lifshitz states of a certain random operator.

Using a high temperature virial expansion, we present a controllable study of the thermodynamics of strongly correlated Fermi gases near the BEC-BCS crossover region. We propose a practical way to determine the expansion coefficients for both harmonically trapped and homogeneous cases, and calculate the third order coefficient $b_3(T)$ at finite temperatures $T$. At resonance, a $T$-independent coefficient $b_{3,\infty }^{\mathrm{hom}}\approx -0.29095295$ is determined in free space. These results are compared with a recent thermodynamic measurement of ${}^6\mathrm{Li}$ atoms, at temperatures below the degeneracy temperature, and with Monte Carlo simulations.

We present an exact analytical solution of the fundamental systems of quasi-one-dimensional spin-$1/2$ fermions with infinite repulsion for an arbitrary confining potential. The eigenfunctions are constructed by the combination of Girardeau’s hard-core contacting boundary condition and group theoretical method, which guarantees the obtained states to be simultaneously the eigenstates of $S$ and $S_z$ and satisfy antisymmetry under odd permutation. We show that the total ground-state density profile behaves like the polarized noninteracting fermions, whereas the spin-dependent densities display different properties for different spin configurations. We also discuss the splitting of the ground states for large but finite repulsion.

We address, on the example of a simple solvable model, the issue of whether the stationary state of dissipative systems converges to an equilibrium state in the low dissipation limit. We study a driven dissipative zero range process on a tree, in which particles are interpreted as finite amounts of energy exchanged between degrees of freedom. The tree structure mimics the hierarchy of length scales; energy is injected at the top of the tree (large scales), transferred through the tree, and dissipated mostly in the deepest branches of the tree (small scales). Varying a parameter characterizing the transfer dynamics, a transition is observed, in the low dissipation limit, between a quasiequilibrated regime and a far-from-equilibrium one, where the dissipated flux does not vanish.

Within a generalized Caldeira-Leggett model, we analyze the conditions under which a bosonic heat bath can entangle two microscopic quantum systems at a distance $r$. We find that the attainable entanglement is extremely distance-sensitive. Significant entanglement can only be achieved if the systems are within a microscopic distance that is of order of the cutoff wavelength $\lambda$ of the system-bath interaction. At larger distances, the maximal entanglement is exponentially suppressed with a decay length of order $\lambda$. We conclude that entanglement generation via a heat bath is not suitable for entangling remote objects.

We investigate electron-positron pair production from vacuum for short laser pulses with a subcycle structure, in the nonperturbative regime (Schwinger pair production). We use the nonequilibrium quantum kinetic approach and show that the momentum spectrum of the created electron-positron pairs is extremely sensitive to the subcycle dynamics—depending on the laser frequency $\omega$, the pulse length $\tau$, and the carrier phase $\varphi$—and shows several distinctive new signatures. This observation could not only help in the design of laser pulses to optimize the experimental signature of Schwinger pair production but also ultimately lead to new probes of light pulses at extremely short time scales.