Wave-Particle Duality Relation with a Quantum Which-Path Detector

Abstract

According to the relevant theories on duality relation, the summation of the extractable information of a quanton’s wave and particle properties, which are characterized by interference visibility V and path distinguishability D, respectively, is limited. However, this relation is violated upon quantum superposition between the wave-state and particle-state of the quanton, which is caused by the quantum beamsplitter (QBS). Along another line, recent studies have considered quantum coherence C in the l1-norm measure as a candidate for the wave property. In this study, we propose an interferometer with a quantum which-path detector (QWPD) and examine the generalized duality relation based on C. We find that this relationship still holds under such a circumstance, but the interference between these two properties causes the full-particle property to be observed when the QWPD system is partially present. Using a pair of polarization-entangled photons, we experimentally verify our analysis in the two-path case. This study extends the duality relation between coherence and path information to the quantum case and reveals the effect of quantum superposition on the duality relation.

Wave–particle duality relation with a quantum N-path beamsplitter*

“…4.3. Wave-particle duality with a quantum WPD [47] As a supplementary analysis, we consider waveparticle duality in a symmetric N-path interferometer, with a quantum WPD. Similar to a QBS N , when a quantum WPD's position degree of freedom is initially in (1/ √ 2)|absence c + (1/ √ 2)|presence c , and finally collapses on sin α|presence c + cos α|absence c , the combined system is in the state of wave-particle superposition cos α|p sd + sin α|w sd , where…”

Fringe visibility and correlation in Mach–Zehnder interferometer with an asymmetric beam splitter

“…Yoon et al [7] have proved that the experimental scheme using two stimulated parametric down-conversion processes is an ideal tool for investigating and understanding wave-particle duality and Bohr's complementarity quantitatively. Wang et al [8] experimentally verified the duality relation between coherence and path information to the quantum case and revealed the effect of quantum superposition on the duality relation. Pozzobom et al [9] performed experimental tests of these complementarity relations applied to a particular class of one-qubit quantum states and also for random quantum states of one, two, and three qubits.…”