27,985 research outputs found
Bell's inequality and the coincidence-time loophole
This paper analyzes effects of time-dependence in the Bell inequality. A
generalized inequality is derived for the case when coincidence and
non-coincidence [and hence whether or not a pair contributes to the actual
data] is controlled by timing that depends on the detector settings. Needless
to say, this inequality is violated by quantum mechanics and could be violated
by experimental data provided that the loss of measurement pairs through
failure of coincidence is small enough, but the quantitative bound is more
restrictive in this case than in the previously analyzed "efficiency loophole."Comment: revtex4, 3 figures, v2: epl document class, reformatted w slight
change
Comment on "Exclusion of time in the theorem of Bell" by K. Hess and W. Philipp
A recent Letter by Hess and Philipp claims that Bell's theorem neglects the
possibility of time-like dependence in local hidden variables, hence is not
conclusive. Moreover the authors claim that they have constructed, in an
earlier paper, a local realistic model of the EPR correlations. However, they
themselves have neglected the experimenter's freedom to choose settings, while
on the other hand, Bell's theorem can be formulated to cope with time-like
dependence. This in itself proves that their toy model cannot satisfy local
realism, but we also indicate where their proof of its local realistic nature
fails.Comment: Latex needs epl.cl
A geometric proof of the Kochen-Specker no-go theorem
We give a short geometric proof of the Kochen-Specker no-go theorem for
non-contextual hidden variables models. Note added to this version: I
understand from Jan-Aake Larsson that the construction we give here actually
contains the original Kochen-Specker construction as well as many others (Bell,
Conway and Kochen, Schuette, perhaps also Peres).Comment: This paper appeared some years ago, before the author was aware of
quant-ph. It is relevant to recent developments concerning Kochen-Specker
theorem
Fisher information in quantum statistics
Braunstein and Caves (1994) proposed to use Helstrom's {\em quantum
information} number to define, meaningfully, a metric on the set of all
possible states of a given quantum system. They showed that the quantum
information is nothing else than the maximal Fisher information in a
measurement of the quantum system, maximized over all possible measurements.
Combining this fact with classical statistical results, they argued that the
quantum information determines the asymptotically optimal rate at which
neighbouring states on some smooth curve can be distinguished, based on
arbitrary measurements on identical copies of the given quantum system.
We show that the measurement which maximizes the Fisher information typically
depends on the true, unknown, state of the quantum system. We close the
resulting loophole in the argument by showing that one can still achieve the
same, optimal, rate of distinguishability, by a two stage adaptive measurement
procedure.
When we consider states lying not on a smooth curve, but on a manifold of
higher dimension, the situation becomes much more complex. We show that the
notion of ``distinguishability of close-by states'' depends strongly on the
measurement resources one allows oneself, and on a further specification of the
task at hand. The quantum information matrix no longer seems to play a central
role.Comment: This version replaces the previous versions of February 1999 (titled
'An Example of Non-Attainability of Expected Quantum Information') and that
of November 1999. Proofs and results are much improved. To appear in J. Phys.
Mechanism of the photovoltaic effect in 2-6 compounds Progress report, 1 Oct. 1968 - 31 Mar. 1969
Heat treatment, illumination and darkness effects, and photovoltaic properties of Cu2S-CdS heterojunction
An invitation to quantum tomography (II)
The quantum state of a light beam can be represented as an infinite
dimensional density matrix or equivalently as a density on the plane called the
Wigner function. We describe quantum tomography as an inverse statistical
problem in which the state is the unknown parameter and the data is given by
results of measurements performed on identical quantum systems. We present
consistency results for Pattern Function Projection Estimators as well as for
Sieve Maximum Likelihood Estimators for both the density matrix of the quantum
state and its Wigner function. Finally we illustrate via simulated data the
performance of the estimators. An EM algorithm is proposed for practical
implementation. There remain many open problems, e.g. rates of convergence,
adaptation, studying other estimators, etc., and a main purpose of the paper is
to bring these to the attention of the statistical community.Comment: An earlier version of this paper with more mathematical background
but less applied statistical content can be found on arXiv as
quant-ph/0303020. An electronic version of the paper with high resolution
figures (postscript instead of bitmaps) is available from the authors. v2:
added cross-validation results, reference
Estimation in a growth study with irregular measurement times
Between 1982 and 1988 a growth study was carried out at the Division of Pediatric Oncology of the University Hospital of Groningen. A special feature of the project was that sample sizes are small and that ages at entry may be very different. In addition the intended design was not fully complied with. This paper highlights some aspects of the statistical analysis which is based on (1) reference scores, (2) statistical procedures allowing for an irregular pattern of measurement times caused by missing data and shifted measurement times
Anna Karenina and The Two Envelopes Problem
The Anna Karenina principle is named after the opening sentence in the
eponymous novel: Happy families are all alike; every unhappy family is unhappy
in its own way. The Two Envelopes Problem (TEP) is a much-studied paradox in
probability theory, mathematical economics, logic, and philosophy. Time and
again a new analysis is published in which an author claims finally to explain
what actually goes wrong in this paradox. Each author (the present author
included) emphasizes what is new in their approach and concludes that earlier
approaches did not get to the root of the matter. We observe that though a
logical argument is only correct if every step is correct, an apparently
logical argument which goes astray can be thought of as going astray at
different places. This leads to a comparison between the literature on TEP and
a successful movie franchise: it generates a succession of sequels, and even
prequels, each with a different director who approaches the same basic premise
in a personal way. We survey resolutions in the literature with a view to
synthesis, correct common errors, and give a new theorem on order properties of
an exchangeable pair of random variables, at the heart of most TEP variants and
interpretations. A theorem on asymptotic independence between the amount in
your envelope and the question whether it is smaller or larger shows that the
pathological situation of improper priors or infinite expectation values has
consequences as we merely approach such a situation.Comment: Final corrections (fingers crossed
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