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Quantum Metrology with Indefinite Causal Order.

Xiaobin Zhao1,2, Yuxiang Yang3, Giulio Chiribella1,2,4,5

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Quantum metrology using indefinite causal order provides a quadratic advantage for estimating average displacements. This novel approach surpasses the Heisenberg limit, offering enhanced precision in quantum measurements.

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Area of Science:

  • Quantum physics
  • Quantum information science
  • Quantum metrology

Background:

  • Quantum metrology traditionally relies on fixed causal orders for measurements.
  • The Heisenberg limit dictates the best achievable precision in parameter estimation.

Purpose of the Study:

  • To investigate quantum metrology enhanced by indefinite causal order.
  • To demonstrate a quadratic advantage in estimating the product of two average displacements.
  • To compare the precision scaling against fixed-order and Heisenberg limits.

Main Methods:

  • Utilizing continuous variable systems.
  • Implementing a quantum system that probes displacements in a superposition of two alternative orders.
  • Proving the optimality of the super-Heisenberg scaling.

Main Results:

  • A quadratic advantage (1/N^2 scaling) in precision was achieved using indefinite causal order.
  • This super-Heisenberg scaling surpasses the conventional Heisenberg limit (1/N).
  • The demonstrated scaling is optimal for superpositions of definite causal order setups.

Conclusions:

  • Indefinite causal order offers significant enhancements for quantum metrology.
  • This opens new avenues for designing quantum measurement setups.
  • Potential applications include enhanced tests of canonical commutation relations and quantum gravity research.