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The absolute value is a mathematical tool that represents the distance of a number from zero on the number line, regardless of its sign. In the context of inequalities, absolute value expressions help define a range of permissible values or boundaries for a variable. These inequalities are commonly used in scientific modeling and data interpretation, where variability within or beyond a certain threshold must be captured precisely.An absolute value inequality of the form ∣x∣ ≤...
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Maximal Randomness Generation from Steering Inequality Violations Using Qudits.

Paul Skrzypczyk1, Daniel Cavalcanti2

  • 1H. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol, BS8 1TL, United Kingdom.

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This summary is machine-generated.

We demonstrate how violating Einstein-Podolsky-Rosen (EPR) steering inequalities can generate maximal randomness. This one-sided device-independent randomness generation is achievable with specific quantum states in various dimensions.

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Area of Science:

  • Quantum Information Theory
  • Foundations of Quantum Mechanics

Background:

  • Quantum entanglement and non-locality are key features of quantum mechanics.
  • Einstein-Podolsky-Rosen (EPR) steering is a quantum phenomenon demonstrating non-locality.
  • Device-independent protocols offer enhanced security by minimizing assumptions about devices.

Purpose of the Study:

  • To investigate the generation of randomness through the violation of EPR steering inequalities.
  • To explore one-sided device-independent randomness generation in a simplified scenario.
  • To determine the conditions for maximal randomness generation.

Main Methods:

  • Analysis of EPR steering inequalities in a two-party scenario with a two-measurement uncharacterized party.
  • Utilizing semidefinite programming to quantify randomness generation.
  • Characterizing quantum states that achieve maximal violation.

Main Results:

  • Identified EPR steering inequalities whose maximal violation guarantees maximal randomness generation (log(d) bits).
  • Showed that pure, partially entangled, full-Schmidt-rank states in all dimensions can achieve this maximal violation.
  • Developed a semidefinite program to calculate randomness for non-maximal violations.

Conclusions:

  • Maximal violation of specific EPR steering inequalities is a robust method for one-sided device-independent randomness generation.
  • A broad class of quantum states can be used to achieve this maximal randomness.
  • The framework provides a quantitative tool to assess randomness generation from steering inequality violations.