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04:08The Uncertainty Principle
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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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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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03:37Uncertainty in Measurement: Accuracy and Precision
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00:59Uncertainty: Overview
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01:10Propagation of Uncertainty from Systematic Error
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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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00:59Propagation of Uncertainty from Random Error
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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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Quantum Uncertainty Principles for Measurements with Interventions.
Yunlong Xiao1,2, Yuxiang Yang3,4, Ximing Wang2
1Institute of High Performance Computing (IHPC), Agency for Science Technology and Research (A*STAR), 1 Fusionopolis Way, No. 16-16 Connexis, Singapore 138632, Republic of Singapore.
Physical Review Letters
|June 30, 2023
Summary
Heisenberg's uncertainty principle now applies to interactive experiments with multiple interventions. This reveals fundamental trade-offs between learning different causal relationships in quantum systems.
Area of Science:
- Quantum mechanics
- Information theory
- Causal inference
Background:
- Heisenberg's uncertainty principle traditionally limits simultaneous measurement of quantum properties at a single time point.
- Inferring causality in complex systems often necessitates adaptive, multi-round experimental interventions.
Purpose of the Study:
- To establish universal uncertainty principles for general interactive measurements.
- To explore the implications of these principles for causal inference in quantum systems.
Main Methods:
- Development of a theoretical framework for universal uncertainty principles.
- Analysis of interactive measurement protocols involving arbitrary rounds of interventions.
- Application to case studies demonstrating trade-offs in causal dependency measurements.
Main Results:
- Demonstration of universal uncertainty principles applicable to interactive measurements.
- Identification of fundamental uncertainty trade-offs between measurements supporting different causal dependencies.
- Extension of uncertainty principle concepts beyond single-time measurements.
Conclusions:
- Interactive measurements are subject to fundamental uncertainty constraints, analogous to traditional quantum measurements.
- These constraints impose trade-offs on the ability to simultaneously infer distinct causal relationships.
- The findings have implications for designing experiments in quantum information and causal inference.