7,104 research outputs found
Universal joint-measurement uncertainty relation for error bars
We formulate and prove a new, universally valid uncertainty relation for the necessary error bar widths in any approximate joint measurement of position and momentum
Time-of-arrival probabilities and quantum measurements: II Application to tunneling times
We formulate quantum tunneling as a time-of-arrival problem: we determine the
detection probability for particles passing through a barrier at a detector
located a distance L from the tunneling region. For this purpose, we use a
Positive-Operator-Valued-Measure (POVM) for the time-of-arrival determined in
quant-ph/0509020 [JMP 47, 122106 (2006)]. This only depends on the initial
state, the Hamiltonian and the location of the detector. The POVM above
provides a well-defined probability density and an unambiguous interpretation
of all quantities involved. We demonstrate that for a class of localized
initial states, the detection probability allows for an identification of
tunneling time with the classic phase time. We also establish limits to the
definability of tunneling time.
We then generalize these results to a sequential measurement set-up: the
phase space properties of the particles are determined by an unsharp sampling
before their attempt to cross the barrier. For such measurements the tunneling
time is defined as a genuine observable. This allows us to construct a
probability distribution for its values that is definable for all initial
states and potentials. We also identify a regime, in which these probabilities
correspond to a tunneling-time operator.Comment: 26 pages--revised version, small changes, to appear in J. Math. Phy
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
Unsharp Quantum Reality
The positive operator (valued) measures (POMs) allow one to generalize the notion of observable beyond the traditional one based on projection valued measures (PVMs). Here, we argue that this generalized conception of observable enables a consistent notion of unsharp reality and with it an adequate concept of joint properties. A sharp or unsharp property manifests itself as an element of sharp or unsharp reality by its tendency to become actual or to actualize a specific measurement outcome. This actualization tendency-or potentiality-of a property is quantified by the associated quantum probability. The resulting single-case interpretation of probability as a degree of reality will be explained in detail and its role in addressing the tensions between quantum and classical accounts of the physical world will be elucidated. It will be shown that potentiality can be viewed as a causal agency that evolves in a well-defined way
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
A dilemma in representing observables in quantum mechanics
There are self-adjoint operators which determine both spectral and
semispectral measures. These measures have very different commutativity and
covariance properties. This fact poses a serious question on the physical
meaning of such a self-adjoint operator and its associated operator measures.Comment: 10 page
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
Inequalities that test locality in quantum mechanics
Quantum theory violates Bell's inequality, but not to the maximum extent that
is logically possible. We derive inequalities (generalizations of Cirel'son's
inequality) that quantify the upper bound of the violation, both for the
standard formalism and the formalism of generalized observables (POVMs). These
inequalities are quantum analogues of Bell inequalities, and they can be used
to test the quantum version of locality. We discuss the nature of this kind of
locality. We also go into the relation of our results to an argument by Popescu
and Rohrlich (Found. Phys. 24, 379 (1994)) that there is no general connection
between the existence of Cirel'son's bound and locality.Comment: 5 pages, 1 figure; the argument has been made clearer in the revised
version; 1 reference adde
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
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