225 research outputs found
Entanglement of a Double Dot with a Quantum Point Contact
Entanglement between particle and detector is known to be inherent in the
measurement process. Gurvitz recently analyzed the coupling of an electron in a
double dot (DD) to a quantum point contact (QPC) detector. In this paper we
examine the dynamics of entanglement that result between the DD and QPC. The
rate of entanglement is optimized as a function of coupling when the electron
is initially in one of the dots. It decreases asymptotically towards zero with
increased coupling. The opposite behavior is observed when the DD is initially
in a superposition: the rate of entanglement increases unboundedly as the
coupling is increased. The possibility that there are conditions for which
measurement occurs versus entanglement is considered
Quantum measurement problem and cluster separability
A modified Beltrametti-Cassinelli-Lahti model of measurement apparatus that
satisfies both the probability reproducibility condition and the
objectification requirement is constructed. Only measurements on microsystems
are considered. The cluster separability forms a basis for the first working
hypothesis: the current version of quantum mechanics leaves open what happens
to systems when they change their separation status. New rules that close this
gap can therefore be added without disturbing the logic of quantum mechanics.
The second working hypothesis is that registration apparatuses for microsystems
must contain detectors and that their readings are signals from detectors. This
implies that separation status of a microsystem changes during both preparation
and registration. A new rule that specifies what happens at these changes and
that guarantees the objectification is formulated and discussed. A part of our
result has certain similarity with 'collapse of the wave function'.Comment: 31 pages, no figure. Published versio
On the nature of continuous physical quantities in classical and quantum mechanics
Within the traditional Hilbert space formalism of quantum mechanics, it is
not possible to describe a particle as possessing, simultaneously, a sharp
position value and a sharp momentum value. Is it possible, though, to describe
a particle as possessing just a sharp position value (or just a sharp momentum
value)? Some, such as Teller (Journal of Philosophy, 1979), have thought that
the answer to this question is No -- that the status of individual continuous
quantities is very different in quantum mechanics than in classical mechanics.
On the contrary, I shall show that the same subtle issues arise with respect to
continuous quantities in classical and quantum mechanics; and that it is, after
all, possible to describe a particle as possessing a sharp position value
without altering the standard formalism of quantum mechanics.Comment: 26 pages, LaTe
Generalized Husimi Functions: Analyticity and Information Content
The analytic properties of a class of generalized Husimi functions are
discussed, with particular reference to the problem of state reconstruction.
The class consists of the subset of Wodkiewicz's operational probability
distributions for which the filter reference state is a squeezed vacuum state.
The fact that the function is analytic means that perfectly precise knowledge
of its values over any small region of phase space provides enough information
to reconstruct the density matrix. If, however, one only has imprecise
knowledge of its values, then the amplification of statistical errors which
occurs when one attempts to carry out the continuation seriously limits the
amount of information which can be extracted. To take account of this fact a
distinction is made between explicate, or experimentally accessible
information, and information which is only present in implicate, experimentally
inaccessible form. It is shown that an explicate description of various aspects
of the system can be found localised on various 2 real dimensional surfaces in
complexified phase space. In particular, the continuation of the function to
the purely imaginary part of complexified phase space provides an explicate
description of the Wigner function.Comment: 16 pages, 2 figures, AMS-latex. Replaced with published versio
Models of wave-function collapse, underlying theories, and experimental tests
We describe the state of the art in preparing, manipulating and detecting coherent molecular matter. We focus on experimental methods for handling the quantum motion of compound systems from diatomic molecules to clusters or biomolecules.Molecular quantum optics offers many challenges and innovative prospects: already the combination of two atoms into one molecule takes several well-established methods from atomic physics, such as for instance laser cooling, to their limits. The enormous internal complexity that arises when hundreds or thousands of atoms are bound in a single organic molecule, cluster or nanocrystal provides a richness that can only be tackled by combining methods from atomic physics, chemistry, cluster physics, nanotechnology and the life sciences.We review various molecular beam sources and their suitability for matter-wave experiments. We discuss numerous molecular detection schemes and give an overview over diffraction and interference experiments that have already been performed with molecules or clusters.Applications of de Broglie studies with composite systems range from fundamental tests of physics up to quantum-enhanced metrology in physical chemistry, biophysics and the surface sciences.Nanoparticle quantum optics is a growing field, which will intrigue researchers still for many years to come. This review can, therefore, only be a snapshot of a very dynamical process
Kochen-Specker Vectors
We give a constructive and exhaustive definition of Kochen-Specker (KS)
vectors in a Hilbert space of any dimension as well as of all the remaining
vectors of the space. KS vectors are elements of any set of orthonormal states,
i.e., vectors in n-dim Hilbert space, H^n, n>3 to which it is impossible to
assign 1s and 0s in such a way that no two mutually orthogonal vectors from the
set are both assigned 1 and that not all mutually orthogonal vectors are
assigned 0. Our constructive definition of such KS vectors is based on
algorithms that generate MMP diagrams corresponding to blocks of orthogonal
vectors in R^n, on algorithms that single out those diagrams on which algebraic
0-1 states cannot be defined, and on algorithms that solve nonlinear equations
describing the orthogonalities of the vectors by means of statistically
polynomially complex interval analysis and self-teaching programs. The
algorithms are limited neither by the number of dimensions nor by the number of
vectors. To demonstrate the power of the algorithms, all 4-dim KS vector
systems containing up to 24 vectors were generated and described, all 3-dim
vector systems containing up to 30 vectors were scanned, and several general
properties of KS vectors were found.Comment: 19 pages, 6 figures, title changed, introduction thoroughly
rewritten, n-dim rotation of KS vectors defined, original Kochen-Specker 192
(117) vector system translated into MMP diagram notation with a new graphical
representation, results on Tkadlec's dual diagrams added, several other new
results added, journal version: to be published in J. Phys. A, 38 (2005). Web
page: http://m3k.grad.hr/pavici
Classical and quantum: a conflict of interest
We highlight three conflicts between quantum theory and classical general
relativity, which make it implausible that a quantum theory of gravity can be
arrived at by quantising classical gravity. These conflicts are: quantum
nonlocality and space-time structure; the problem of time in quantum theory;
and the quantum measurement problem. We explain how these three aspects bear on
each other, and how they point towards an underlying noncommutative geometry of
space-time.Comment: 15 pages. Published in `Gravity and the quantum' [Essays in honour of
Thanu Padmanabhan on the occasion of his sixtieth birthday] Eds. Jasjeet
Singh Bagla and Sunu Engineer (Springer, 2017
Decoherence, the measurement problem, and interpretations of quantum mechanics
Environment-induced decoherence and superselection have been a subject of
intensive research over the past two decades, yet their implications for the
foundational problems of quantum mechanics, most notably the quantum
measurement problem, have remained a matter of great controversy. This paper is
intended to clarify key features of the decoherence program, including its more
recent results, and to investigate their application and consequences in the
context of the main interpretive approaches of quantum mechanics.Comment: 41 pages. Final published versio
(Never) Mind your p's and q's: Von Neumann versus Jordan on the Foundations of Quantum Theory
In two papers entitled "On a new foundation [Neue Begr\"undung] of quantum
mechanics," Pascual Jordan (1927b,g) presented his version of what came to be
known as the Dirac-Jordan statistical transformation theory. As an alternative
that avoids the mathematical difficulties facing the approach of Jordan and
Paul A. M. Dirac (1927), John von Neumann (1927a) developed the modern Hilbert
space formalism of quantum mechanics. In this paper, we focus on Jordan and von
Neumann. Central to the formalisms of both are expressions for conditional
probabilities of finding some value for one quantity given the value of
another. Beyond that Jordan and von Neumann had very different views about the
appropriate formulation of problems in quantum mechanics. For Jordan, unable to
let go of the analogy to classical mechanics, the solution of such problems
required the identication of sets of canonically conjugate variables, i.e., p's
and q's. For von Neumann, not constrained by the analogy to classical
mechanics, it required only the identication of a maximal set of commuting
operators with simultaneous eigenstates. He had no need for p's and q's. Jordan
and von Neumann also stated the characteristic new rules for probabilities in
quantum mechanics somewhat differently. Jordan (1927b) was the first to state
those rules in full generality. Von Neumann (1927a) rephrased them and, in a
subsequent paper (von Neumann, 1927b), sought to derive them from more basic
considerations. In this paper we reconstruct the central arguments of these
1927 papers by Jordan and von Neumann and of a paper on Jordan's approach by
Hilbert, von Neumann, and Nordheim (1928). We highlight those elements in these
papers that bring out the gradual loosening of the ties between the new quantum
formalism and classical mechanics.Comment: New version. The main difference with the old version is that the
introduction has been rewritten. Sec. 1 (pp. 2-12) in the old version has
been replaced by Secs. 1.1-1.4 (pp. 2-31) in the new version. The paper has
been accepted for publication in European Physical Journal
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