Approximating incompatible von Neumann measurements simultaneously

We study the problem of performing orthogonal qubit measurements simultaneously. Since these measurements are incompatible, one has to accept additional imprecision. An optimal joint measurement is the one with the least possible imprecision. All earlier considerations of this problem have concerned only joint measurability of observables, while in this work we also take into account conditional state transformations (i.e., instruments). We characterize the optimal joint instrument for two orthogonal von Neumann instruments as being the Luders instrument of the optimal joint observable.Comment: 9 pages, 4 figures; v2 has a more extensive introduction + other minor correction

Tumbleweeds and airborne gravitational noise sources for LIGO

Gravitational-wave detectors are sensitive not only to astrophysical gravitational waves, but also to the fluctuating Newtonian gravitational forces of moving masses in the ground and air around the detector. This paper studies the gravitational effects of density perturbations in the atmosphere, and from massive airborne objects near the detector. These effects were previously considered by Saulson; in this paper I revisit these phenomena, considering transient atmospheric shocks, and the effects of sound waves or objects colliding with the ground or buildings around the test masses. I also consider temperature perturbations advected past the detector as a source of gravitational noise. I find that the gravitational noise background is below the expected noise floor even of advanced interferometric detectors, although only by an order of magnitude for temperature perturbations carried along turbulent streamlines. I also find that transient shockwaves in the atmosphere could potentially produce large spurious signals, with signal-to-noise ratios in the hundreds in an advanced interferometric detector. These signals could be vetoed by means of acoustic sensors outside of the buildings. Massive wind-borne objects such as tumbleweeds could also produce gravitational signals with signal-to-noise ratios in the hundreds if they collide with the interferometer buildings, so it may be necessary to build fences preventing such objects from approaching within about 30m of the test masses.Comment: 15 pages, 10 PostScript figures, uses REVTeX4.cls and epsfig.st

The Standard Model of Quantum Measurement Theory: History and Applications

The standard model of the quantum theory of measurement is based on an interaction Hamiltonian in which the observable-to-be-measured is multiplied with some observable of a probe system. This simple Ansatz has proved extremely fruitful in the development of the foundations of quantum mechanics. While the ensuing type of models has often been argued to be rather artificial, recent advances in quantum optics have demonstrated their prinicpal and practical feasibility. A brief historical review of the standard model together with an outline of its virtues and limitations are presented as an illustration of the mutual inspiration that has always taken place between foundational and experimental research in quantum physics.Comment: 22 pages, to appear in Found. Phys. 199

SIC-POVMs and the Extended Clifford Group

We describe the structure of the extended Clifford Group (defined to be the group consisting of all operators, unitary and anti-unitary, which normalize the generalized Pauli group (or Weyl-Heisenberg group as it is often called)). We also obtain a number of results concerning the structure of the Clifford Group proper (i.e. the group consisting just of the unitary operators which normalize the generalized Pauli group). We then investigate the action of the extended Clifford group operators on symmetric informationally complete POVMs (or SIC-POVMs) covariant relative to the action of the generalized Pauli group. We show that each of the fiducial vectors which has been constructed so far (including all the vectors constructed numerically by Renes et al) is an eigenvector of one of a special class of order 3 Clifford unitaries. This suggests a strengthening of a conjuecture of Zauner's. We give a complete characterization of the orbits and stability groups in dimensions 2-7. Finally, we show that the problem of constructing fiducial vectors may be expected to simplify in the infinite sequence of dimensions 7, 13, 19, 21, 31,... . We illustrate this point by constructing exact expressions for fiducial vectors in dimensions 7 and 19.Comment: 27 pages. Version 2 contains some additional discussion of Zauner's original conjecture, and an alternative, possibly stronger version of the conjecture in version 1 of this paper; also a few other minor improvement

Low-density, one-dimensional quantum gases in a split trap

We investigate degenerate quantum gases in one dimension trapped in a harmonic potential that is split in the centre by a pointlike potential. Since the single particle eigenfunctions of such a system are known for all strengths of the central potential, the dynamics for non-interacting fermionic gases and low-density, strongly interacting bosonic gases can be investigated exactly using the Fermi-Bose mapping theorem. We calculate the exact many-particle ground-state wave-functions for both particle species, investigate soliton-like solutions, and compare the bosonic system to the well-known physics of Bose gases described by the Gross-Pitaevskii equation. We also address the experimentally important questions of creation and detection of such states.Comment: 7 pages, 5 figure

Does My Stigma Look Big in This? Considering the acceptability and desirability in the inclusive design of technology products

This paper examines the relationship between stigmatic effects of design of technology products for the older and disabled and contextualizes this within wider social themes such as the functional, social, medical and technology models of disability. Inclusive design approaches are identified as unbiased methods for designing for the wider population that may accommodate the needs and desires of people with impairments, therefore reducing ’aesthetic stigma’. Two case studies illustrate stigmatic and nonstigmatic designs

Pb and Bi L-Subshell Ionization Cross-Section Ratios Versus Proton Bombarding Energy from 0.5 to 4 MeV

Experimental ratios of L-subshell cross sections are given for ionization of lead and bismuth by 0.5-4-MeV-proton bombardment. The ratio of the LII to LI cross sections exhibits a maximum near 1.75 MeV. Individual subshell cross sections are obtained from the experimental ratios and previous total-cross-section data. These subshell ratios and cross sections are compared with the theoretical predictions of the plane-wave Born approximation using nonrelativistic hydrogenic wave functions, of the binary-encounter approximation scaled from Mg K-shell cross sections, and of the binary-encounter approximation scaled from cross sections obtained using L-shell velocity distributions. It was found that both approximations predict the trend of the data for the LII and LIII subshells, but that only the plane-wave Born approximation gave the proper behavior for the LI subshell

Excitation spectrum and instability of a two-species Bose-Einstein condensate

We numerically calculate the density profile and excitation spectrum of a two-species Bose-Einstein condensate for the parameters of recent experiments. We find that the ground state density profile of this system becomes unstable in certain parameter regimes, which leads to a phase transition to a new stable state. This state displays spontaneously broken cylindrical symmetry. This behavior is reflected in the excitation spectrum: as we approach the phase transition point, the lowest excitation frequency goes to zero, indicating the onset of instability in the density profile. Following the phase transition, this frequency rises again.Comment: 8 pages, 5 figures, uses REVTe

Self-adjoint Lyapunov variables, temporal ordering and irreversible representations of Schroedinger evolution

In non relativistic quantum mechanics time enters as a parameter in the Schroedinger equation. However, there are various situations where the need arises to view time as a dynamical variable. In this paper we consider the dynamical role of time through the construction of a Lyapunov variable - i.e., a self-adjoint quantum observable whose expectation value varies monotonically as time increases. It is shown, in a constructive way, that a certain class of models admit a Lyapunov variable and that the existence of a Lyapunov variable implies the existence of a transformation mapping the original quantum mechanical problem to an equivalent irreversible representation. In addition, it is proved that in the irreversible representation there exists a natural time ordering observable splitting the Hilbert space at each t>0 into past and future subspaces.Comment: Accepted for publication in JMP. Supercedes arXiv:0710.3604. Discussion expanded to include the case of Hamiltonians with an infinitely degenerate spectru

Symmetric Informationally Complete Quantum Measurements

We consider the existence in arbitrary finite dimensions d of a POVM comprised of d^2 rank-one operators all of whose operator inner products are equal. Such a set is called a ``symmetric, informationally complete'' POVM (SIC-POVM) and is equivalent to a set of d^2 equiangular lines in C^d. SIC-POVMs are relevant for quantum state tomography, quantum cryptography, and foundational issues in quantum mechanics. We construct SIC-POVMs in dimensions two, three, and four. We further conjecture that a particular kind of group-covariant SIC-POVM exists in arbitrary dimensions, providing numerical results up to dimension 45 to bolster this claim.Comment: 8 page