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Weak values and the Leggett-Garg inequality in solid-state qubits.

Nathan S Williams1, Andrew N Jordan

  • 1Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA.

Physical Review Letters
|February 1, 2008
PubMed
Summary

Weak values in solid-state qubits are nonclassical only when Leggett-Garg inequalities are violated. This study explores generalized weak values and their connection to quantum measurement in qubits.

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Area of Science:

  • Quantum mechanics
  • Solid-state physics
  • Quantum information science

Background:

  • Weak values offer a unique perspective on quantum measurements.
  • Investigating nonclassical behavior in solid-state qubits is crucial for quantum technologies.
  • Leggett-Garg inequalities provide a test for classicality in quantum systems.

Purpose of the Study:

  • To implement and investigate weak values in solid-state qubits.
  • To establish the relationship between nonclassical weak values and Leggett-Garg inequality violations.
  • To explore generalized weak values with post-selection on a range of measurement outcomes.

Main Methods:

  • Analysis of weak values in the context of solid-state qubits.
  • Demonstration of conditions for nonclassical weak values.
  • Derivation of Leggett-Garg inequalities for bounded operators using classical weak values.
  • Application to kicked quantum nondemolition measurements on a quantum double-dot charge qubit.

Main Results:

  • A weak value is nonclassical if and only if a Leggett-Garg inequality is violated.
  • Generalized weak values are defined for a range of post-selected measurement results.
  • Classical weak values allow for the derivation of Leggett-Garg inequalities for bounded operators.

Conclusions:

  • The nonclassicality of weak values is intrinsically linked to the violation of Leggett-Garg inequalities.
  • The framework provides a method to test for quantum behavior in solid-state systems.
  • The study offers insights into quantum measurement and nonclassicality in qubits.