Commitment as investment under uncertainty

An explanation of how irreversible investment and the techniques associated with pricing real options can apply to a broad range of problems in finance, macroeconomics, and trade policy.Economic policy ; Macroeconomics

Dynamic commitment and imperfect policy rules

An examination of the dynamics of commitment, showing that because the decision regarding rules versus discretion occurs in real time, opting for discretion is often the better choice, since it leaves open the possibility of adopting rules later on.Monetary policy

Dynamic commitment and imperfect policy rules

Considering the dynamics of commitment highlights, some neglected features of time inconsistency problems. We modify the standard rules-versus-discretion question in three ways: (1) A government that does not commit today retains the option to do so tomorrow, (2) the government's commitment capability is restricted to a class of simple rules, and (3) the government's ability to make irrevocable commitments is restricted. Three results stand out. First, the option to wait makes the incumbent regime (rules or discretion) relatively more attractive. Second, the option to wait means that increased uncertainly makes the incumbent regime more attractive. Third, because the commitment decision takes place in 'real time,' policy choice displays hysteresis.Monetary policy

Quantum Channels and Representation Theory

In the study of d-dimensional quantum channels $(d \geq 2)$, an assumption which is not very restrictive, and which has a natural physical interpretation, is that the corresponding Kraus operators form a representation of a Lie algebra. Physically, this is a symmetry algebra for the interaction Hamiltonian. This paper begins a systematic study of channels defined by representations; the famous Werner-Holevo channel is one element of this infinite class. We show that the channel derived from the defining representation of SU(n) is a depolarizing channel for all $n$, but for most other representations this is not the case. Since the Bloch sphere is not appropriate here, we develop technology which is a generalization of Bloch's technique. Our method works by representing the density matrix as a polynomial in symmetrized products of Lie algebra generators, with coefficients that are symmetric tensors. Using these tensor methods we prove eleven theorems, derive many explicit formulas and show other interesting properties of quantum channels in various dimensions, with various Lie symmetry algebras. We also derive numerical estimates on the size of a generalized ``Bloch sphere'' for certain channels. There remain many open questions which are indicated at various points through the paper.Comment: 28 pages, 1 figur

Decoherence-protected memory for a single-photon qubit

The long-lived, efficient storage and retrieval of a qubit encoded on a photon is an important ingredient for future quantum networks. Although systems with intrinsically long coherence times have been demonstrated, the combination with an efficient light-matter interface remains an outstanding challenge. In fact, the coherence times of memories for photonic qubits are currently limited to a few milliseconds. Here we report on a qubit memory based on a single atom coupled to a high-finesse optical resonator. By mapping and remapping the qubit between a basis used for light-matter interfacing and a basis which is less susceptible to decoherence, a coherence time exceeding 100 ms has been measured with a time-independant storage-and-retrieval efficiency of 22%. This demonstrates the first photonic qubit memory with a coherence time that exceeds the lower bound needed for teleporting qubits in a global quantum internet.Comment: 3 pages, 4 figure

Multi-Modal Human-Machine Communication for Instructing Robot Grasping Tasks

A major challenge for the realization of intelligent robots is to supply them with cognitive abilities in order to allow ordinary users to program them easily and intuitively. One way of such programming is teaching work tasks by interactive demonstration. To make this effective and convenient for the user, the machine must be capable to establish a common focus of attention and be able to use and integrate spoken instructions, visual perceptions, and non-verbal clues like gestural commands. We report progress in building a hybrid architecture that combines statistical methods, neural networks, and finite state machines into an integrated system for instructing grasping tasks by man-machine interaction. The system combines the GRAVIS-robot for visual attention and gestural instruction with an intelligent interface for speech recognition and linguistic interpretation, and an modality fusion module to allow multi-modal task-oriented man-machine communication with respect to dextrous robot manipulation of objects.Comment: 7 pages, 8 figure

Evolution of spin correlations in SrDy2O4 in an applied magnetic field

The development of short- and long-range magnetic order induced in a frustrated zig-zag ladder compound SrDy2O4 by an applied field is studied using neutron diffraction techniques. In zero field, SrDy2O4 lacks long-range magnetic order down to temperatures as low as 60 mK, and the observed powder neutron diffraction (PND) patterns are dominated by very broad diffuse scattering peaks. Single crystal neutron diffraction reveals that the zero-field magnetic structure consists of a collection of antiferromagnetic chains running along the c axis and that there is very little correlation between the chains in the ab plane. In an applied magnetic field, the broad diffuse scattering features in PND are gradually replaced by much sharper peaks, however, the pattern remains rather complex, reflecting the highly anisotropic nature of SrDy2O4. Single crystal neutron diffraction shows that a moderate field applied along the b axis induces an up-up-down magnetic order associated with a 1/3-magnetisation plateau, in which magnetic correlation length in the ab plane is significantly increased, but it nevertheless remains finite. The resolution limited k = 0 peaks associated with a ferromagnetic arrangement appear in powder and single crystal neutron diffraction patterns in fields of 2.5 T and above.Comment: 10 pages, 11 figure

On the number of representations providing noiseless subsystems

This paper studies the combinatoric structure of the set of all representations, up to equivalence, of a finite-dimensional semisimple Lie algebra. This has intrinsic interest as a previously unsolved problem in representation theory, and also has applications to the understanding of quantum decoherence. We prove that for Hilbert spaces of sufficiently high dimension, decoherence-free subspaces exist for almost all representations of the error algebra. For decoherence-free subsystems, we plot the function $f_d(n)$ which is the fraction of all $d$-dimensional quantum systems which preserve $n$ bits of information through DF subsystems, and note that this function fits an inverse beta distribution. The mathematical tools which arise include techniques from classical number theory.Comment: 17 pp, 4 figs, accepted for Physical Review