2021/03/30 by Zhiwei Tao, Yi-Chong Ren, Yichong Ren +3
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Cumulative distribution function #Function (biology) #Limit (mathematics) #Mathematical analysis #Mathematics #Metrology #Phase (matter) #Physics #Pi #Probability density function #Q-function #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum computer #Quantum limit #Quantum mechanics #Quantum metrology #Quantum simulator #Quantum state #State (computer science) #Statistics #Vacuum state #quant-ph
paper · pdf · doi:10.1364/josab.419752
published as J. Opt. Soc. Am. B 38(5), 1662-1668 (2021) · 7 pages, 5 figures
openalex publication_date 2021/03/30 · arxiv created 2021/05/03 · arxiv updated 2021/05/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We predict that the phase-dependent error distribution of locally unentangled quantum states directly affects quantum parameter estimation accuracy. Therefore, we employ the displaced squeezed vacuum (DSV) state as a probe state and investigate an interesting question of the phase-sensitive nonclassical properties in the DSV’s metrology. We found that the accuracy limit of parameter estimation is a function of the phase-sensitive parameter <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>ϕ</mml:mi> <mml:mo>−</mml:mo> <mml:mi>θ</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:math> with a period <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>π</mml:mi> </mml:math> . We show that when <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>ϕ</mml:mi> <mml:mo>−</mml:mo> <mml:mi>θ</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> <mml:mtext> </mml:mtext> <mml:mo>∈</mml:mo> <mml:mo stretchy="false">[</mml:mo> <mml:mi>k</mml:mi> <mml:mi>π</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> <mml:mo>,</mml:mo> <mml:mn>3</mml:mn> <mml:mi>k</mml:mi> <mml:mi>π</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>4</mml:mn> <mml:mo stretchy="false">)</mml:mo> <mml:mo stretchy="false">(</mml:mo> <mml:mi>k</mml:mi> <mml:mo>∈</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">Z</mml:mi> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> </mml:math> , we can obtain the accuracy of parameter estimation approaching the ultimate quantum limit through the use of the DSV state with the larger displacement and squeezing strength, whereas when <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>ϕ</mml:mi> <mml:mo>−</mml:mo> <mml:mi>θ</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> <mml:mtext> </mml:mtext> <mml:mo>∈</mml:mo> <mml:mo stretchy="false">(</mml:mo> <mml:mn>3</mml:mn> <mml:mi>k</mml:mi> <mml:mi>π</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>4</mml:mn> <mml:mo>,</mml:mo> <mml:mi>k</mml:mi> <mml:mi>π</mml:mi> <mml:mo stretchy="false">]</mml:mo> <mml:mo stretchy="false">(</mml:mo> <mml:mi>k</mml:mi> <mml:mo>∈</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">Z</mml:mi> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> </mml:math> , the optimal estimation accuracy can be acquired only when the DSV state degenerates to a squeezed vacuum state.