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Error correcting bell inequalities.

Thomas A Walker1, Fiona A C Polack, Samuel L Braunstein

  • 1Computer Science, University of York, York YO10 5DD, United Kingdom.

Physical Review Letters
|September 4, 2008
PubMed
Summary
This summary is machine-generated.

Quantum error-correcting codes protect quantum states. New Bell inequalities derived from these codes violate local realism even with qubit errors, requiring an 11-qubit entangled state for minimal construction.

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Area of Science:

  • Quantum Information Science
  • Quantum Computing
  • Quantum Cryptography

Background:

  • Quantum error-correcting codes are essential for protecting quantum states from decoherence and noise.
  • Bell inequalities are crucial for testing the foundations of quantum mechanics and demonstrating quantum non-locality.

Purpose of the Study:

  • To construct a family of Bell inequalities that inherit the error-resilience properties of quantum error-correcting codes.
  • To demonstrate the violation of local realism using these inequalities, even in the presence of errors on a limited number of qubits.
  • To explore the minimal requirements for such a demonstration, specifically the number of qubits involved.

Main Methods:

  • Construction of a novel family of Bell inequalities based on the structure of quantum error-correcting codes.
  • Analysis of the violation of local realism exhibited by these inequalities.
  • Investigation of the robustness of the violation against arbitrary errors affecting a subset of qubits.

Main Results:

  • A family of Bell inequalities was successfully constructed, directly benefiting from the properties of quantum error-correcting codes.
  • These inequalities demonstrate a robust violation of local realism, unaffected by errors on a limited number of qubits.
  • The minimal experimental setup for observing this phenomenon requires the preparation of an 11-qubit entangled state.

Conclusions:

  • Quantum error-correcting codes can be leveraged to create Bell inequalities that are inherently robust against certain types of errors.
  • The violation of local realism persists even when quantum states are subjected to errors, highlighting the resilience of quantum entanglement.
  • This work provides a pathway for experimentally verifying quantum non-locality in the presence of realistic noise, with practical implications for quantum technologies.