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This study introduces an optimal Greenberger-Horne-Zeilinger (GHZ) paradox for mixed quantum states. It reveals how quantum nonlocality can be maximized even with state impurities, resisting up to 50% noise.

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Area of Science:

  • Quantum Information Science
  • Quantum Foundations

Background:

  • Quantum nonlocality is a key resource in quantum information processing.
  • Characterizing nonlocality in mixed states remains less explored than in pure states.

Purpose of the Study:

  • To prove the existence of an optimal Greenberger-Horne-Zeilinger (GHZ) paradox for mixed states.
  • To establish a method for extracting states that maximize quantum nonlocality for a given purity.

Main Methods:

  • Development of a novel and simple method to identify optimal states.
  • Formulation of a logical inequality based on GHZ-typed event probabilities.
  • Analysis of the tradeoff between quantum nonlocality and state purity.

Main Results:

  • Demonstration of an optimal GHZ paradox that maximally violates a logical inequality for any fixed purity.
  • Identification of the optimal state as a GHZ state with flipped color noise.
  • Determination that the optimal state can tolerate up to 50% noise.

Conclusions:

  • The findings provide a deeper understanding of quantum nonlocality as a physical resource in mixed states.
  • The developed method offers a way to saturate the tradeoff relation between nonlocality and purity.
  • This work contributes to characterizing the resilience of quantum nonlocality against noise.