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Parametric amplification of continuous variable entangled state for loss-tolerant multi-phase estimation

Sijin Li, Wei Wang

Abstract

Quantum parameter estimation exploits quantum states to achieve estimation sensitivity beyond classical limit. In continuous variable (CV) regime, squeezed state has been exploited to implement deterministic phase estimation. It is however, often restricted by fragility of quantum states. The quantum phase estimation sensitivity of squeezed state is significantly affected by loss or detection inefficiency, which restrict its applications. This issue can be solved by using a method of parametric amplification of squeezed state \cite{OPA}. In this work, we implement multi-phase estimation with optical parametric amplification of entanglement generated from squeezed states. We find multi-phase estimation sensitivity is robust against loss or detection inefficiency, where we use two-mode Einstein-Podolsky-Rosen entangled state and four-mode cluster state for analysis. Our work provides a method for realizing large-scale quantum metrology in real-world applications against loss or detection inefficiency.

Parametric amplification of continuous variable entangled state for loss-tolerant multi-phase estimation

Abstract

Quantum parameter estimation exploits quantum states to achieve estimation sensitivity beyond classical limit. In continuous variable (CV) regime, squeezed state has been exploited to implement deterministic phase estimation. It is however, often restricted by fragility of quantum states. The quantum phase estimation sensitivity of squeezed state is significantly affected by loss or detection inefficiency, which restrict its applications. This issue can be solved by using a method of parametric amplification of squeezed state \cite{OPA}. In this work, we implement multi-phase estimation with optical parametric amplification of entanglement generated from squeezed states. We find multi-phase estimation sensitivity is robust against loss or detection inefficiency, where we use two-mode Einstein-Podolsky-Rosen entangled state and four-mode cluster state for analysis. Our work provides a method for realizing large-scale quantum metrology in real-world applications against loss or detection inefficiency.
Paper Structure (5 sections, 17 equations, 5 figures)

This paper contains 5 sections, 17 equations, 5 figures.

Table of Contents

  1. I. INTRODUCTION
  2. II. Two mode
  3. III. Four mode
  4. IV. CONCLUSION
  5. ACKNOWLEDGEMENTS

Figures (5)

  • Figure 1: Schematic of loss-tolerant phase estimation with two-mode entangled state via OPA. Sq: squeezed state; BS: beam splitter; EPR: Einstein-Podolsky-Rosen two-mode entangled state; BHD: balanced homodyne detection.
  • Figure 2: Average phase estimation sensitivity of two phases as a function of loss. The losses in every beam are set to the same value. $r_{1}=1$, corresponding to initial squeezing of about 8 dB. $r_{1}^{'}=4.6$, corresponding to OPA gain of 100. $\beta_{1}=1$, $\beta_{2}5$, $\theta_{1}=1.5^{\circ}$
  • Figure 3: Schematic of loss-tolerant phase estimation with four-mode entangled state via OPA. Sq: squeezed state; U: unitary matrix for construction of cluster state; BHD: balanced homodyne detection.
  • Figure 4: (a)Estimation sensitivity of phase 1 as a function of loss. (b)Average phase estimation sensitivity of four phases as a function of loss. The losses in every beam are set to the same value. $r_{1}=1$, corresponding to initial squeezing of about 8 dB. $r_{1}^{'}=3$, corresponding to OPA gain of 20. $\beta_{1}=1$, $\beta_{2}=\alpha_{3}=2$, $\theta_{1}=1.5^{\circ}$
  • Figure 5: Average phase estimation sensitivity of 4 phases as a function of losses in: (a)modes 1 and 2, with $\eta_{3}=\eta_{4}=0.5$; (b)modes 2 and 3, with $\eta_{1}=\eta_{4}=0.5$; (c)modes 2 and 4, with $\eta_{3}=\eta_{4}=0.5$; (d)modes 3 and 4, with $\eta_{3}=\eta_{4}=0.5$. Other parameters: $r_{1}=1$, corresponding to initial squeezing of about 8 dB. $r_{1}^{'}=3$, corresponding to OPA gain of 20. $\beta_{1}=1$, $\beta_{2}=\alpha_{3}=2$, $\alpha_{2}=1$, $\beta_{4}=3$, $\theta_{1}=1.5^{\circ}$. (a)