Are Quantum Measurements Truly Special Cases of Unitary Operators?

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SUMMARY

Quantum measurements are indeed special cases of quantum channels, specifically characterized as Completely Positive Trace-Preserving (CPTP) maps. The Stinespring dilation theorem confirms that any quantum channel can be represented by a unitary operator acting on an extended Hilbert space. This means that measurements can be understood through the lens of unitary evolution, despite their seemingly random nature. Examples of such unitary operators can be derived from the application of CPTP maps in quantum computing.

PREREQUISITES
  • Understanding of quantum channels and CPTP maps.
  • Familiarity with the Stinespring dilation theorem.
  • Knowledge of unitary operators in quantum mechanics.
  • Basic concepts of Hilbert spaces in quantum theory.
NEXT STEPS
  • Study the Stinespring dilation theorem in detail.
  • Explore examples of unitary operators in quantum mechanics.
  • Learn about the implications of CPTP maps in quantum computing.
  • Investigate the relationship between quantum measurements and unitary evolution.
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Quantum physicists, quantum computing researchers, and students seeking to deepen their understanding of the relationship between quantum measurements and unitary operators.

Heidi
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Hi Pfs

I read this answer in
https://quantumcomputing.stackexcha...-gates-must-be-unitary-what-about-measurement

Quantum measurements are special cases of quantum channels (CPTP cards). Stinespring dilation states that any quantum channel is realized by partially tracing a unitary operator acting on a possibly larger Hilbert space.

I wonder if it is true. and in this case is it possible to give an example of such unitary operator? i suppose that the evolution process is random.

[I translated the French part. Please use English only.]
 
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