物理学报2026，Vol.75Issue(12)：248-254,7.DOI:10.7498/aps.75.20260152
非对称Mach-Zehnder干涉计中条纹可见度和量子纠缠满足的互补性关系
Complementary relationship between fringe visibility and quantum entanglement in an asymmetric Mach-Zehnder interferometer
摘要
Abstract
Bohr's complementarity principle is one of the fundamental principles in quantum mechanics.The wave-particle duality is often used to reflect Bohr's complementarity principle,so the wave-particle duality has also attracted considerable attention.As research progresses,it has been revealed that the fundamental reason for a particle's particle-like property lies in its quantum entanglement with the which-path detector.However,current research on complementarity based on the entanglement perspective is limited to the symmetric Mach-Zehnder interferometer model with a balanced beam splitter splitting ratio.To overcome the limitation of fixed splitting ratios in conventional balanced beam splitters,this work achieves continuous modulation of both fringe visibility and quantum entanglement by employing an asymmetric Mach-Zehnder interferometer with a continuously tunable beam-splitting ratio.This design provides an additional degree of freedom for manipulation,thus enabling a more comprehensive exploration of the complementary relationship between fringe visibility and quantum entanglement. In this work,the wave-particle duality of a particle is investigated with an asymmetric Mach-Zehnder interferometer.Fringe visibility and quantum entanglement are employed to quantify the wave-like and particle-like properties of the particle,respectively.In order to detect the particle passing through the apparatus,a particle detector is placed at one of the output ports of the interferometer.Subsequently,the probability of detecting the particle can be obtained,and the fringe visibility V of the quantized wave-like property can be calculated.A which-path detector is placed on one of the paths of the asymmetric Mach-Zehnder interferometer.When the particle passes through the path with the which-path detector,it will be entangled with the which-path detector.The quantum entanglement,represented by the concurrence C,is used to quantify the particle-like property. In conclusion,we find that the concurrence depends on both the input state of the particle governed by the Bloch vector S={Sx,Sy,Sz} and the second asymmetric beam splitter characterized by parameter β.Here,Sx represents the component of the particle's initial state on the σx,and β determines the reflection or transmission coefficient of the second beam splitter.When β=π/2,the reflection and transmission coefficients of the second beam splitter are equal.It is found that the concurrence reaches the upper bound when Sx=-cos β.This demonstrates that the quantum entanglement between the particle and the which-path detector is maximized when the parameter β of the asymmetric beam splitter is adjusted to achieve a specific matching relationship with the particle's initial state parameter Sx,thereby achieving effective modulation of the particle-like and wave-like properties.This paper also presents the complementary relation between fringe visibility and concurrence,which is expressed as V2+C2 ≤ 1.The equals sign holds when the particle is initially in the pure state and Sx=-cos β.This work provides a theoretical basis for researchers to further explore the wave-like and particle-like properties of quantum systems flexibly.关键词
非对称Mach-Zehnder干涉计/条纹可见度/量子纠缠/并发度Key words
asymmetrical Mach-Zehnder Interferometer/fringe visibility/quantum entanglement/concurrence引用本文复制引用
刘彦军,王美亚,相忠诚,刘迎娣,朱雪刚,纪登辉,吴海滨..非对称Mach-Zehnder干涉计中条纹可见度和量子纠缠满足的互补性关系[J].物理学报,2026,75(12):248-254,7.基金项目
国家自然科学基金(批准号:12574540)、河北省自然科学基金(批准号:A2022106001)、河北省教育厅科学研究项目(批准号:QN2025176)和石家庄学院重点培育项目(批准号:24PY004)资助的课题. Project supported by the National Natural Science Foundation of China(Grant No.12574540),the Natural Science Foundation of Hebei Province,China(Grant No.A2022106001),the Science Research Project of Hebei Education Department,China(Grant No.QN2025176),and the Key Cultivation Project of Shijiazhuang University,China(Grant No.24PY004). （批准号:12574540）
