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This study introduces a new framework for detecting quantum incompatibility, offering optimization-free nonlinear witnesses for quantum steering and measurement incompatibility. These novel tools provide tighter bounds on entanglement and serve as genuine incompatibility monotones.

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Area of Science:

  • Quantum Information Theory
  • Foundations of Quantum Mechanics

Background:

  • Quantum incompatibility, encompassing quantum steering, measurement incompatibility, and instrument incompatibility, is a fundamental concept.
  • Existing methods for detecting incompatibility often rely on linear witnesses and can be computationally intensive.

Purpose of the Study:

  • To develop a general, optimization-free framework for constructing nonlinear incompatibility witnesses.
  • To demonstrate the application of these witnesses in quantifying entanglement and certifying measurement/instrument incompatibility.

Main Methods:

  • Construction of nonlinear incompatibility witnesses based on convex functionals.
  • Analysis of witness non-triviality based on the affine property of functionals on extremal points.
  • Application to pure bipartite states and general quantum instruments.

Main Results:

  • Developed optimization-free nonlinear incompatibility witnesses applicable in arbitrary dimensions.
  • Proved that witnesses are nontrivial when functionals are nonaffine on extremal points.
  • For pure bipartite states, witnesses provide lower bounds on entanglement, outperforming linear steering inequalities.
  • Demonstrated the use of Wigner-Yanase skew information and an ℓ₂-type coherence functional as examples.

Conclusions:

  • The proposed framework offers a versatile and powerful tool for detecting and quantifying various forms of quantum incompatibility.
  • The nonlinear witnesses provide a more sensitive measure of entanglement in certain regimes.
  • The approach generalizes to certify measurement and instrument incompatibility, acting as monotones.