[Paper Review] Wave-particle duality revisited: Neither wave nor particle

Jan Sperling, Syamsundar De+5 more|arXiv (Cornell University)|Jul 23, 2019

Quantum Information and Cryptography34 references4 citations

TL;DR

This paper demonstrates that neither the wave nor particle model can fully explain quantum-optical correlations in a single experiment, using a simple interferometer with beam splitters and photon detectors. By deriving correlation-based criteria for wave and particle behavior, the authors show experimentally that squeezed light and coherent states violate both models simultaneously, proving that quantum systems transcend classical wave-particle duality and revealing their nonclassical nature in both pictures.

ABSTRACT

A textbook interpretation of quantum physics is that quantum objects can be described in a particle or a wave picture, depending on the operations and measurements performed. Beyond this widely held believe, we demonstrate in this contribution that neither the wave nor the particle description is sufficient to predict the outcomes of quantum-optical experiments. To show this, we derive correlation-based criteria that have to be satisfied when either particles or waves are fed into our interferometer. Using squeezed light, it is then confirmed that measured correlations are incompatible with either picture. Thus, within one single experiment, it is proven that neither a wave nor a particle model explains the observed phenomena. Moreover, we formulate a relation of wave and particle representations to two incompatible notions of quantum coherence, a recently discovered resource for quantum information processing.For such an information-theoretic interpretation of our method, we certify the nonclassicality of coherent states - the quantum counterpart to classical waves - in the particle picture, complementing the known fact that photon states are nonclassical in the typically applied wave picture.

Motivation & Objective

• To challenge the widely held belief that quantum systems can be described either as waves or particles depending on context.
• To identify experimental conditions where both wave and particle models fail to predict quantum-optical correlations.
• To develop robust, data-driven criteria that test the validity of wave and particle descriptions without postselection or corrections.
• To demonstrate the nonclassicality of coherent states in the particle picture, complementing known nonclassicality in the wave picture.
• To establish a connection between wave-particle duality and two incompatible notions of quantum coherence as a resource for quantum information.

Proposed method

• Design a simple interferometer using 50:50 beam splitters (wave-based) and photon detectors (particle-based), ensuring each component is classically interpretable.
• Define a covariance matrix C from measured detection statistics, decomposed into conditional variance (B) and conditional mean covariance (C') using statistical laws of total variance and covariance.
• Derive a criterion based on the minimal eigenvalue e of (C - B), where e ≥ 0 must hold for any classical model; negative e indicates failure of both wave and particle descriptions.
• Apply this criterion to experimental data from coherent states and squeezed states, evaluating e_wave and e_part. for wave and particle models respectively.
• Use statistical error margins to assess significance, confirming that e_part. < 0 for coherent states across multiple photon numbers.
• Extend the method to higher-order and multimode systems via multivariate and higher-order conditional cumulants, ensuring robustness against losses and uncertainties.

Experimental results

Research questions

• RQ1 Can a single experiment demonstrate that both wave and particle models fail to explain quantum-optical correlations?
• RQ2 Are coherent states nonclassical when assessed in the particle picture, despite being the quantum analog of classical waves?
• RQ3 Can wave-particle duality be reinterpreted as a resource for quantum information by linking it to two incompatible notions of quantum coherence?
• RQ4 Is the proposed criterion robust against experimental noise, losses, and systematic errors without postselection or data correction?
• RQ5 Can the method be generalized to higher-order and multimode quantum systems?

Key findings

• For coherent states with mean photon numbers ranging from 0.395×10⁻² to 4.482×10⁻², the particle model fails with high statistical significance, as e_part. < 0 within error margins.
• The wave model is consistent with data, as e_wave = 0 within error margins for all tested coherent states, confirming their classical wave-like behavior.
• Squeezed states violate both wave and particle models simultaneously, with e_part. < 0 and e_wave < 0, proving that neither classical picture explains the observed correlations.
• The nonclassicality of coherent states in the particle picture is certified with p-values below 0.01 for all tested amplitudes, indicating strong statistical significance.
• The method is robust against losses and systematic errors, as shown by careful uncertainty estimates and lack of data correction or postselection.
• The framework extends naturally to higher-order and multimode systems using multivariate and higher-order conditional cumulants, enabling broader application in quantum information science.