New from quant-ph

Physical interactions in quantum many-body systems are typically local: Individual constituents interact mainly with their few nearest neighbors. This locality of interactions is inherited by a decay of correlation functions, but also reflected by scaling laws of a quite profound quantity: The entanglement entropy of ground states. This entropy of the reduced state of a subregion often merely grows like the boundary area of the subregion, and not like its volume, in sharp contrast with an expected extensive behavior. Such "area laws" for the entanglement entropy and related quantities have received considerable attention in recent years. They emerge in several seemingly unrelated fields, in the context of black hole physics, quantum information science, and quantum many-body physics where they have important implications on the numerical simulation of lattice models. In this Colloquium we review the current status of area laws in these fields. Center stage is taken by rigorous results on lattice models in one and higher spatial dimensions. The differences and similarities between bosonic and fermionic models are stressed, area laws are related to the velocity of information propagation, and disordered systems, non-equilibrium situations, classical correlation concepts, and topological entanglement entropies are discussed. A significant proportion of the article is devoted to the quantitative connection between the entanglement content of states and the possibility of their efficient numerical simulation. We discuss matrix-product states, higher-dimensional analogues, and states from entanglement renormalization and conclude by highlighting the implications of area laws on quantifying the effective degrees of freedom that need to be considered in simulations.

We briefly review the most relevant aspects of complete integrability for classical systems and identify those aspects which should be present in a definition of quantum integrability.

We show that a naive extension of classical concepts to the quantum framework would not work because all infinite dimensional Hilbert spaces are unitarily isomorphic and, as a consequence, it would not be easy to define degrees of freedom. We argue that a geometrical formulation of quantum mechanics might provide a way out.

We show that a scaling law exists for the near resonant dynamics of cold kicked atoms in the presence of a randomly fluctuating pulse amplitude. Analysis of a quasi-classical phase-space representation of the quantum system with noise allows a new scaling law to be deduced. The scaling law and associated stability are confirmed by comparison with quantum simulations and experimental data.

We investigate a state discrimination problem in generic probability models which include both classical and quantum theory. Closely related family of ensembles (which we call a Helstrom family of ensembles) with the problem is introduced and we provide a geometrical method to find an optimal measurement for state discrimination by means of Bayesian strategy. We illustrate our method in 2-level quantum systems, and reproduce the optimal success probabilities for binary state discrimination and N numbers of symmetric quantum states. The existences of families of ensembles in binary cases are shown both in classical and quantum theories in any generic cases.

The set of 63 real generalized Pauli matrices of three-qubits can be factored into two subsets of 35 symmetric and 28 antisymmetric elements. This splitting is shown to be completely embodied in the properties of the Fano plane; the elements of the former set being in a bijective correspondence with the 7 points, 7 lines and 21 flags, whereas those of the latter set having their counterparts in 28 anti-flags of the plane. This representation naturally extends to the one in terms of the split Cayley hexagon of order two. 63 points of the hexagon split into 9 orbits of 7 points (operators) each under the action of an automorphism of order 7. 63 lines of the hexagon carry three points each and represent the triples of operators such that the product of any two gives, up to a sign, the third one. Since this hexagon admits a full embedding in a projective 5-space over GF(2), the 35 symmetric operators are also found to answer to the points of a Klein quadric in such space. The 28 antisymmetric matrices can be associated with the 28 vertices of the Coxeter graph, one of two distinguished subgraphs of the hexagon. The PSL_{2}(7) subgroup of the automorphism group of the hexagon is discussed in detail and the Coxeter sub-geometry is found to be intricately related to the E_7-symmetric black-hole entropy formula in string theory. It is also conjectured that the full geometry/symmetry of the hexagon should manifest itself in the corresponding black-hole solutions. Finally, an intriguing analogy with the case of Hopf sphere fibrations and a link with coding theory are briefly mentioned.

Within the framework of quantum memory channels we introduce the notion of repeatability of quantum channels. In particular, a quantum channel is called repeatable if there exist a memory device implementing the same channel on each individual input. We show that random unitary channels can be implemented in a repeatable fashion, whereas the nonunital channels cannot.

A group of non-uniform quantum lattice Hamiltonians in one dimension is introduced, which is related to the hyperbolic $1 + 1$-dimensional space. The Hamiltonians contain only nearest neighbor interactions whose strength is proportional to $\cosh j \lambda$, where $j$ is the lattice index and where $\lambda \ge 0$ is a deformation parameter. In the limit $\lambda \to 0$ the Hamiltonians become uniform. Spacial translation of the deformed Hamiltonians is induced by the corner Hamiltonians. As a simple example, we investigate the ground state of the deformed $S = 1/2$ Heisenberg spin chain by use of the density matrix renormalization group (DMRG) method. It is shown that the ground state is dimerized when $\lambda$ is finite. Spin correlation function show exponential decay, and the boundary effect decreases with increasing $\lambda$.

We investigate the entanglement properties of pure quantum states describing $n$ qubits. We characterize all multipartite states which can be maximally entangled to local auxiliary systems using controlled operations. A state has this property iff one can construct out of it an orthonormal basis by applying independent local unitary operations. This implies that those states can be used to encode locally the maximum amount of $n$ bits. Examples of these states are the so--called stabilizer states, which are used for quantum error correction and one--way quantum computing. We give a simple characterization of these states and construct a complete set of commuting unitary observables which characterize the state uniquely. Furthermore we show how these states can be prepared and discuss their applications.

Ping-Pong protocol is a type of quantum key distribution which makes use of two entangled photons in the EPR state. Its security is based on the randomization of the operations that Alice performs on the travel photon (qubit), and on the anti-correlation between the two photons in the EPR state. In this paper, we study the security of this protocol against some known quantum attacks, and present a scheme that may enhance its security to some degree.

We show that the transition from regular to chaotic spectral statistics in interacting many-body quantum systems has an unambiguous signature in the distribution of Schmidt coefficients dynamically generated from a generic initial state, and thus limits the efficiency of the t-DMRG algorithm.

We study the effect of strong radio-frequency (rf) fields on a chromium Bose-Einstein condensate, in a regime where the rf frequency is much larger than the Larmor frequency. We show that the Lande factor of the atoms is lowered by the presence of the rf, and can be even set to zero for a proper combination of the rf power and frequency. The trajectories of the atoms under the influence of magnetic potentials are thus greatly modified. We study the criteria for adiabaticity of the rf dressing process leading to such a modification of the atom magnetic susceptibility. We also measure the lifetime of the rf dressed BECs.

Sub-wavelength diameter tapered optical fibers surrounded by rubidium vapor can undergo a substantial decrease in transmission at high atomic densities due to the accumulation of rubidium atoms on the surface of the fiber. Here we demonstrate the ability to control these changes in transmission using light guided within the taper. We observe transmission through a tapered fiber that is a nonlinear function of the incident power. This effect can also allow a strong control beam to change the transmission of a weak probe beam.

We imagine an experiment on an unknown quantum mechanical system in which the system is prepared in various ways and a range of measurements are performed. For each measurement M and preparation rho the experimenter can determine, given enough time, the probability of a given outcome a: p(a|M,rho). How large does the Hilbert space of the quantum system have to be in order to allow us to find density matrices and measurement operators that will reproduce the given probability distribution? In this note, we prove a simple lower bound for the dimension of the Hilbert space. The main insight is to relate this problem to the construction of quantum random access codes, for which interesting bounds on Hilbert space dimension already exist. We discuss several applications of our result to hidden variable, or ontological models, to Bell inequalities and to properties of the smooth min-entropy.

The Casimir force due to a massless scalar field satisfying Dirichlet boundary conditions may attract or repel a piston in the neck of a flask-like container. Using the world-line formalism this behavior is related to the competing contribution to the interaction energy of two types of Brownian bridges. It qualitatively is also expected from attractive long-range two-body forces between constituents of the boundary. A geometric subtraction scheme is presented that avoids divergent contributions to the interaction energy and classifies the Brownian bridges that contribute to the force. These are all of finite length and the Casimir force can be analyzed and in principle accurately computed without resorting to regularization or analytic continuation. The world-line analysis is robust with respect to variations in the shape of the piston and the flask and the analogy with long-range forces suggests that neutral atoms and particles are also drawn into open-ended pipes (or nano-tubes) by Casimir forces of electromagnetic origin.

Being able to quantify the level of coherent control in a proposed device implementing a quantum information processor (QIP) is an important task for both comparing different devices and assessing a device's prospects with regards to achieving fault-tolerant quantum control. We implement in a liquid-state nuclear magnetic resonance QIP the randomized benchmarking protocol presented by Knill et al (PRA 77: 012307 (2008)). We report an error per randomized $\frac{\pi}{2}$ pulse of $1.3 \pm 0.1 \times 10^{-4}$ with a single qubit QIP and show an experimentally relevant error model where the randomized benchmarking gives a signature fidelity decay which is not possible to interpret as a single error per gate. We explore and experimentally investigate multi-qubit extensions of this protocol and report an average error rate for one and two qubit gates of $4.7 \pm 0.3 \times 10^{-3}$ for a three qubit QIP. We estimate that these error rates are still not decoherence limited and thus can be improved with modifications to the control hardware and software.

We study numerically the Coulomb interacting two-particle stationary states of the Schr\"odinger equation, where the particles are confined in a two-dimensional infinite square well. Inside the domain the particles are subjected to a steeply increasing isotropic harmonic potential, resembling that in a nucleus. For these circumstances we have developed a fully discretized finite difference method of the Numerov-type that approximates the four-dimensional Laplace operator, and thus the whole Schr\"odinger equation, with a local truncation error of $\mathcal{O}(h^6)$, with $h$ being the uniform step size. The method is built on a 89-point central difference scheme in the four-dimensional grid. As expected from the general theorem by Keller [Num.\ Math. \textbf{7}, 412 (1965)], the error of eigenvalues so obtained are found to be the same order of magnitude which we have proved analytically as well.

Why do we not experience a violation of macroscopic realism in every-day life? Normally, no violation can be seen either because of decoherence or the restriction of coarse-grained measurements, transforming the time evolution of any quantum state into a classical time evolution of a statistical mixture. We find the sufficient condition for these classical evolutions for spin systems under coarse-grained measurements. Then we demonstrate that there exist "non-classical" Hamiltonians whose time evolution cannot be understood classically, although at every instant of time the quantum spin state appears as a classical mixture. We suggest that such Hamiltonians are unlikely to be realized in nature because of their high computational complexity.

We demonstrate that two remote qubits can be entangled through an optically active intermediary even if the coupling strengths between mediator and qubits are different. This is true for a broad class of interactions. We consider two contrasting scenarios. First, we extend the analysis of a previously studied gate operation which relies on pulsed, dynamical control of the optical state and which may be performed quickly. We show that remote spins can be entangled in this case even when the intermediary coupling strengths are unequal. Second, we propose an alternative adiabatic control procedure, and find that the system requirements become even less restrictive in this case. The scheme could be tested immediately in a range of systems including molecules, quantum dots, or defects in crystals.

In order to study the resonance spectra of chaotic cavities subject to some damping (which can be due to absorption or partial reflection at the boundaries), we use a model of damped quantum maps. In the high-frequency limit, the distribution of (quantum) decay rates is shown to cluster near a ``typical'' value, which is larger than the classical decay rate of the corresponding damped ray dynamics. The speed of this clustering may be quite slow, which could explain why it has not been detected in previous numerical data.

We demonstrate the generation of multi-photon quantum states of light by cavity-enhanced parametric down-conversion in the high-repetition-rate pulsed regime. An external enhancement cavity resonant with the spectral comb of modes of a mode-locked pump laser provides a coherent build-up of the pump intensity and greatly enhances the parametric gain without sacrificing its high repetition rate and comb structure. We probe the parametric gain enhancement by the conditional generation and tomographic analysis of two-photon Fock states. Besides its potential impact to efficiently generate highly-nonclassical or entangled multi-photon states in many existing experimental setups, this scheme opens new and exciting perspectives towards the combination of quantum and comb technologies for enhanced measurements and advanced quantum computation protocols.