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This study shows a quantum sensor network using entangled states achieves optimal sensitivity for phase shift estimation. This entangled sensor network offers a significant gain over independent sensors, using fewer nonclassical states.

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Area of Science:

  • Quantum optics
  • Quantum metrology
  • Interferometry

Background:

  • Mach-Zehnder interferometers (MZIs) are key quantum sensors.
  • Achieving high sensitivity in multiparameter estimation is crucial.
  • Nonclassical states can enhance quantum sensor performance.

Purpose of the Study:

  • To investigate the multiparameter sensitivity bounds of a network of d Mach-Zehnder interferometers (MZIs).
  • To determine if local measurements on MZIs can achieve the quantum Cramér-Rao bound.
  • To compare the sensitivity of an entangled sensor network with independent MZIs.

Main Methods:

  • Creating a d-mode entangled state by mixing a nonclassical state with vacuum states.
  • Probing each MZI with a mode of the entangled state and a coherent state.
  • Analyzing sensitivity bounds using local measurements and comparing with independent MZIs.

Main Results:

  • Local measurements on the MZI network saturate the quantum Cramér-Rao bound.
  • The sensor network overcomes the shot noise limit for estimating linear combinations of phase shifts.
  • An entangled sensor network provides a sensitivity scaling of 1/n[over ¯]_{T}^{2}, offering a gain factor d over separable sensors.

Conclusions:

  • A single nonclassical state in an entangled network achieves the same sensitivity as d nonclassical states in independent MZIs.
  • The entangled protocol demonstrates a significant sensitivity advantage, especially for larger networks.
  • This work highlights the power of entanglement for enhanced quantum sensing capabilities.