1,472 research outputs found
An Evolutionary Formalism for Weak Quantum Measurements
Unitary evolution and projective measurement are fundamental axioms of
quantum mechanics. Even though projective measurement yields one of the
eigenstates of the measured operator as the outcome, there is no theory that
predicts which eigenstate will be observed in which experimental run. There
exists only an ensemble description, which predicts probabilities of various
outcomes over many experimental runs. We propose a dynamical evolution equation
for the projective collapse of the quantum state in individual experimental
runs, which is consistent with the well-established framework of quantum
mechanics. In case of gradual weak measurements, its predictions for ensemble
evolution are different from those of the Born rule. It is an open question
whether or not suitably designed experiments can observe this alternate
evolution.Comment: 6 pages. Talk presented at the Discussion Meeting on Quantum
Measurements, IISc, Bangalore, 22-24 October 2014. Comments welcome. (v2)
Version to be published in the Proceedings. Notation generalised for
multi-dimensional projection operators. Tests for 1- and 2-qubit systems
described. Usefulness for error correction pointed ou
Weak Measurements, Quantum State Collapse and the Born Rule
Projective measurement is used as a fundamental axiom in quantum mechanics,
even though it is discontinuous and cannot predict which measured operator
eigenstate will be observed in which experimental run. The probabilistic Born
rule gives it an ensemble interpretation, predicting proportions of various
outcomes over many experimental runs. Understanding gradual weak measurements
requires replacing this scenario with a dynamical evolution equation for the
collapse of the quantum state in individual experimental runs. We revisit the
quantum trajectory framework that models quantum measurement as a continuous
nonlinear stochastic process. We describe the ensemble of quantum trajectories
as noise fluctuations on top of geodesics that attract the quantum state
towards the measured operator eigenstates. Investigation of the restrictions
needed on the ensemble of quantum trajectories, so as to reproduce projective
measurement in the appropriate limit, shows that the Born rule follows when the
magnitudes of the noise and the attraction are precisely related, in a manner
reminiscent of the fluctuation-dissipation relation. That implies that both the
noise and the attraction have a common origin in the measurement interaction
between the system and the apparatus. We analyse the quantum trajectory
ensemble for the scenarios of quantum diffusion and binary quantum jump, and
show that the ensemble distribution is completely determined in terms of a
single evolution parameter. This trajectory ensemble distribution can be tested
in weak measurement experiments. We also comment on how the required noise may
arise in the measuring apparatus.Comment: Revtex, 11 pages, 4 figures. Some text overlap with arXiv:1412.1312
(v2) Substantially revised, duly acknowledging similar results obtained by
Nicolas Gisin thirty years ago. (v3) Expanded and rewritten to include
analysis of shot noise and fluctuation-dissipation relation (v4) Final
versio
FP-tree and COFI Based Approach for Mining of Multiple Level Association Rules in Large Databases
In recent years, discovery of association rules among itemsets in a large
database has been described as an important database-mining problem. The
problem of discovering association rules has received considerable research
attention and several algorithms for mining frequent itemsets have been
developed. Many algorithms have been proposed to discover rules at single
concept level. However, mining association rules at multiple concept levels may
lead to the discovery of more specific and concrete knowledge from data. The
discovery of multiple level association rules is very much useful in many
applications. In most of the studies for multiple level association rule
mining, the database is scanned repeatedly which affects the efficiency of
mining process. In this research paper, a new method for discovering multilevel
association rules is proposed. It is based on FP-tree structure and uses
cooccurrence frequent item tree to find frequent items in multilevel concept
hierarchy.Comment: Pages IEEE format, International Journal of Computer Science and
Information Security, IJCSIS, Vol. 7 No. 2, February 2010, USA. ISSN 1947
5500, http://sites.google.com/site/ijcsis
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