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Related Concept Videos

The Uncertainty Principle04:08

The 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...
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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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When one or more data points appear far from the rest of the data, there is a need to determine whether they are outliers and whether they should be eliminated from the data set to ensure an accurate representation of the measured value. In many cases, outliers arise from gross errors (or human errors) and do not accurately reflect the underlying phenomenon. In some cases, however, these apparent outliers reflect true phenomenological differences. In these cases, we can use statistical methods...
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Measurement of Quantum Interference in a Silicon Ring Resonator Photon Source
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Quantum measurement occurrence is undecidable.

J Eisert1, M P Müller, C Gogolin

  • 1Qmio Group, Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany.

Physical Review Letters
|September 26, 2012
PubMed
Summary
This summary is machine-generated.

Quantum measurement problems can be undecidable, unlike their classical counterparts. This genuine quantum property, demonstrated with Stern-Gerlach devices, has implications for quantum computing and many-body physics.

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Area of Science:

  • Quantum Physics
  • Theoretical Computer Science
  • Quantum Information Theory

Background:

  • Classical decision problems are generally decidable with algorithms.
  • Quantum measurement theory presents complex theoretical challenges.
  • Undecidability in formal systems means no algorithm can solve all instances.

Purpose of the Study:

  • To investigate undecidability in quantum measurement theory.
  • To determine if undecidability is an inherent quantum property.
  • To explore the implications of quantum undecidability.

Main Methods:

  • Analyzing decision problems related to sequential Stern-Gerlach measurements.
  • Comparing quantum measurement problems with their classical analogues.
  • Formal definition of undecidability applied to quantum systems.

Main Results:

  • Certain natural quantum measurement problems are undecidable.
  • This undecidability is shown to be a genuine quantum phenomenon.
  • Classical analogues of these problems are decidable.

Conclusions:

  • Undecidability is a fundamental property unique to quantum mechanics.
  • Implications for measurement-based quantum computing and quantum many-body models.
  • Suggests a wide range of potentially undecidable problems in quantum physics.