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Transport Measurements of Majorization Order for Wave Coherence.

Cheng Guo1, David A B Miller1, Shanhui Fan1

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We introduce the majorization order to compare wave coherence, showing it governs transport measurements like absorption and transmission. Lower coherence waves, as defined by this order, lead to more limited measurement outcomes.

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Area of Science:

  • Quantum mechanics
  • Wave phenomena
  • Information theory

Background:

  • Wave coherence is crucial for understanding quantum transport.
  • Majorization order provides a mathematical framework for comparing probability distributions.
  • Previous studies have not fully explored the link between majorization order and wave coherence in transport.

Purpose of the Study:

  • To investigate the majorization order for comparing wave coherence.
  • To reveal the fundamental consequences of this order in transport measurements.
  • To establish a method for experimental characterization of wave coherence.

Main Methods:

  • Utilizing the mathematical framework of majorization order.
  • Analyzing transport phenomena including power distribution, absorption, transmission, and reflection.
  • Proving the preservation of the majorization order under unitary control.

Main Results:

  • Majorization order successfully compares wave coherence.
  • Transport measurements (power distribution, absorption, transmission, reflection) preserve the majorization order under unitary control.
  • Waves with lower coherence exhibit restricted ranges of achievable measurement values.

Conclusions:

  • The majorization order offers a powerful tool for characterizing wave coherence.
  • Experimental verification of the majorization order in transport measurements is feasible.
  • This work deepens the understanding of coherence's role in quantum transport phenomena.