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04:08The Uncertainty Principle
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 mathematically...
02:46Uncertainty in Measurement: Reading Instruments
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...
03:37Uncertainty in Measurement: Accuracy and Precision
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.
00:59Uncertainty: Overview
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.
03:34Uncertainty in Measurement: Significant Figures
All the digits in a measurement, including the uncertain last digit, are called significant figures or significant digits. Note that zero may be a measured value; for example, if a scale that shows weight to the nearest pound reads “140,” then the 1 (hundreds), 4 (tens), and 0 (ones) are all significant (measured) values.
01:24Calculation of First-Law Quantities II
The first law of thermodynamics establishes that the change in internal energy of a system is given by ΔU = q + w, where q is the heat exchanged, and w is the work performed. For a perfect gas, both internal energy (U) and enthalpy (H) depend solely on temperature. Consequently, for any change of state, whether reversible or irreversible, the internal energy change is determined by integrating the heat capacity at constant volume, and the enthalpy change by integrating the heat capacity at...
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12:19
Measurement of Quantum Interference in a Silicon Ring Resonator Photon Source
Published on: April 4, 2017
Quantum measurement bounds beyond the uncertainty relations.
Vittorio Giovannetti1, Seth Lloyd, Lorenzo Maccone
1NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, piazza dei Cavalieri 7, I-56126 Pisa, Italy.
Physical Review Letters
|September 26, 2012
Summary
We developed new quantum mechanics relations to bound parameter estimation precision using observable expectation values, not just standard deviations. This resolves key precision limits in quantum optics and interferometry.
Area of Science:
- Quantum Mechanics
- Quantum Optics
- Information Theory
Background:
- Heisenberg uncertainty relations and Cramér-Rao inequalities traditionally limit precision in parameter estimation via standard deviation of conjugate observables.
- Existing bounds do not fully capture precision limits in all quantum measurement scenarios.
Purpose of the Study:
- To extend the Heisenberg uncertainty relations and Cramér-Rao inequalities.
- To establish a new bound for parameter estimation precision using the expectation value of the conjugate observable.
Main Methods:
- Theoretical extension of established quantum mechanical inequalities.
- Analysis of precision bounds in terms of expectation values.
Main Results:
- A novel bound on parameter estimation precision is derived, utilizing the expectation value of the conjugate observable.
- This new bound provides a more complete understanding of precision limits.
Conclusions:
- The extended relations have significant foundational implications for quantum mechanics.
- Practical applications include resolving controversies regarding ultimate precision limits in quantum optics, particularly in interferometry.