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Related Concept Videos

Uncertainty: Overview00:59

Uncertainty: Overview

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In analytical chemistry, we often perform repetitive measurements to detect and minimize inaccuracies caused by both determinate and indeterminate errors. Despite the cares we take, the presence of random errors means that repeated measurements almost never have exactly the same magnitude. The collective difference between these measurements - observed values - and the estimated or expected value is called uncertainty. Uncertainty is conventionally written after the estimated or expected value.
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Uncertainty in Measurement: Accuracy and Precision03:37

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Scientists typically make repeated measurements of a quantity to ensure the quality of their findings and to evaluate both the precision and the accuracy of their results. Measurements are said to be precise if they yield very similar results when repeated in the same manner. A measurement is considered accurate if it yields a result that is very close to the true or the accepted value. Precise values agree with each other; accurate values agree with a true value. 
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Uncertainty in Measurement: Reading Instruments02:46

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Counting is the type of measurement that is free from uncertainty, provided the number of objects being counted does not change during the process. Such measurements result in exact numbers. By counting the eggs in a carton, for instance, one can determine exactly how many eggs are there in the carton. Similarly, the numbers of defined quantities are also exact. For example, 1 foot is exactly 12 inches, 1 inch is exactly 2.54 centimeters, and 1 gram is exactly 0.001 kilograms. Quantities...
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Propagation of Uncertainty from Random Error00:59

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An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
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Propagation of Uncertainty from Systematic Error01:10

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The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this...
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The Uncertainty Principle04:08

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Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He...
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Uncertainty Relations for Coarse-Grained Measurements: An Overview.

Fabricio Toscano1, Daniel S Tasca2, Łukasz Rudnicki3,4

  • 1Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, Rio de Janeiro 21941-972, Brazil.

Entropy (Basel, Switzerland)
|December 3, 2020
PubMed
Summary
This summary is machine-generated.

Quantum mechanics uncertainty relations are crucial for quantum information tasks. This review covers coarse-grained uncertainty relations in continuous variable systems, highlighting their applications and theoretical/experimental perspectives.

Keywords:
continuous variablesquantum foundationsquantum informationquantum uncertainty

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Area of Science:

  • Quantum Physics
  • Quantum Information Science

Background:

  • Uncertainty relations are fundamental to quantum mechanics and essential for quantum cryptography and correlation detection.
  • In continuous variable systems, coarse-graining measurements is necessary due to continuous spectra.
  • Coarse-grained observables may not follow standard uncertainty relations, potentially leading to inaccuracies in applications.

Purpose of the Study:

  • To review the state-of-the-art in coarse-grained uncertainty relations for continuous variable quantum systems.
  • To discuss the applications of these relations in fundamental quantum physics and quantum information tasks.
  • To provide a balanced perspective encompassing both theoretical and experimental viewpoints.

Main Methods:

  • Review of existing literature on coarse-grained uncertainty relations.
  • Analysis of theoretical frameworks for these relations.
  • Discussion of experimental implementations and perspectives.

Main Results:

  • Several specialized uncertainty relations for coarse-grained observables have been developed.
  • These relations are crucial for accurate analysis in continuous variable quantum systems.
  • The review synthesizes theoretical advancements and experimental progress.

Conclusions:

  • Coarse-grained uncertainty relations are vital for reliable quantum information processing.
  • Accurate application requires specific relations tailored for coarse-grained measurements.
  • The field benefits from integrated theoretical and experimental research.