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Back-Action-Evading Measurements and Quantum Non-Demolition Variables via Linear Systems Engineering

Zhiyuan Dong, Weichao Liang, Guofeng Zhang

Abstract

We establish a framework for realizing back-action-evading (BAE) measurements and quantum non-demolition (QND) variables in linear quantum systems. The key condition, a purely imaginary Hamiltonian with a real or imaginary coupling operator, enables BAE measurements of conjugate observables. Symmetric coupling further yields QND variables. For non-compliant systems, coherent feedback can engineer BAE measurements. Crucially, the QND interaction condition simultaneously ensures BAE measurements and promotes the coupling operator to a QND observable. This work provides a unified structural theory for enhancing precision in quantum metrology and sensing.

Back-Action-Evading Measurements and Quantum Non-Demolition Variables via Linear Systems Engineering

Abstract

We establish a framework for realizing back-action-evading (BAE) measurements and quantum non-demolition (QND) variables in linear quantum systems. The key condition, a purely imaginary Hamiltonian with a real or imaginary coupling operator, enables BAE measurements of conjugate observables. Symmetric coupling further yields QND variables. For non-compliant systems, coherent feedback can engineer BAE measurements. Crucially, the QND interaction condition simultaneously ensures BAE measurements and promotes the coupling operator to a QND observable. This work provides a unified structural theory for enhancing precision in quantum metrology and sensing.
Paper Structure (16 sections, 9 theorems, 87 equations, 1 figure)

This paper contains 16 sections, 9 theorems, 87 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Realization of BAE measurements
  4. Bilateral quantum BAE measurements
  5. Unilateral quantum BAE measurement
  6. $\Omega_-$ and $\Omega_+$ share the same real part
  7. $\Omega_-$ and $\Omega_+$ have opposite real parts
  8. A special case
  9. Realization of quantum BAE measurements via coherent feedback control
  10. QND interaction
  11. The SISO case
  12. The MIMO case in the annihilation-creation form
  13. The MIMO case in the quadrature form
  14. The MIMO case in the Kalman canonical form
  15. Realization of QND variables under QND interaction
  16. ...and 1 more sections

Key Result

Proposition 3.1

If $\Omega$ is purely imaginary, both $S$ and $\mathcal{C}$ are real, then the transfer function is of the form where

Figures (1)

  • Figure 1: Coherent feedback network.

Theorems & Definitions (24)

  • Proposition 3.1
  • Remark 3.1
  • Lemma 3.1
  • Lemma 3.2
  • Corollary 3.1
  • Example 3.1
  • Corollary 3.2
  • Theorem 3.1
  • Remark 3.2
  • Example 3.2
  • ...and 14 more