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Covariant Quantum Error-Correcting Codes with Metrological Entanglement Advantage.

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This study introduces a novel quantum error-correcting code derived from SU(2) rotations. The code demonstrates enhanced protection for quantum states, surpassing the standard quantum limit in sensitive measurements.

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Area of Science:

  • Quantum Information Science
  • Quantum Error Correction
  • Quantum Sensing

Background:

  • Quantum error correction is crucial for robust quantum computation.
  • Previous 'thermodynamic codes' showed promise but required generalization.
  • Understanding SU(2) representations is key to developing new quantum codes.

Purpose of the Study:

  • To develop a covariant approximate quantum error-correcting code using SU(2) representations.
  • To generalize existing codes to arbitrary spin and irreducible representations.
  • To analyze the code's performance under various noise models and its application in quantum sensing.

Main Methods:

  • Utilizing properties of the angular momentum algebra for SU(2) tensor products.
  • Deriving a subset of basis states for irreducible representations.
  • Analyzing code inaccuracy under different noise scenarios (generic, i.i.d., heralded erasures).

Main Results:

  • A covariant approximate quantum error-correcting code with transversal U(1) logical gates was constructed.
  • Bounds on code inaccuracy were derived for various noise models.
  • The code was shown to protect probe states, enhancing quantum Fisher information beyond the standard quantum limit.

Conclusions:

  • The developed family of codes offers a new approach to quantum error correction.
  • These codes are effective in protecting quantum information against various noise types.
  • The codes show potential for improving the precision of quantum sensing.