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Quantum coherence versus interferometric visibility in a biased Mach–Zehnder interferometer

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Abstract

The double-slit interferometer and the Mach–Zehnder interferometer (MZI) with balanced beam splitters are prototypical setups for investigating the quantum wave-particle duality. These setups induced a quantitative association of interferometric visibility (IVI) with the wave aspect of a single quantum system (WAQ). Recently, it was realized that quantum coherence (QC) can be better suited than IVI for quantifying the WAQ in complementarity relations. In this article, we investigate a MZI with biased beam splitters both in the input and in the output, and we show that in some cases the IVI is not adequate to quantify the WAQ since it does not reflect the behavior of the quantum coherence, even for a bi-dimensional closed quantum system. Using IBM quantum computers, we experimentally verify our theoretical findings by doing a full quantum simulation of the optical MZI with biased beam splitters.

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Data availability

The Qiskit code used for implementing the simulations and experiments used to obtain the data utilized in this article is available upon request to the authors.

Notes

  1. In the cases where \(\Pr (D_j)_{\min }=0\), we have \({\mathcal {V}}_j=(\Pr (D_j)_{\max }-\Pr (D_j)_{\min })/(\Pr (D_j)_{\max }+\Pr (D_j)_{\min })=1\), for \(j = 0\) or 1, even for \(P(D_j)_{\max }\ll 1\). So, if we have a limited number of quantons to experiment with, we see that \({\mathcal {V}}_j'={\mathcal {V}}_j\Pr (D_{j})_{\max }\) would be a better quantifier for the visibility of the interference fringes contrast. It is worthwhile though noticing that this change would not solve the problems IVI has regarding the quantification of the wave character of a quanton.

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Acknowledgements

This work was supported by the Universidade Federal do ABC (UFABC), process 23006.000123/2018-23, by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), process 88887.649600/2021-00, by the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), process 309862/2021-3, and by the Instituto Nacional de Ciência e Tecnologia de Informação Quântica (INCT-IQ), process 465469/2014-0.

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Authors and Affiliations

  1. Departamento de Física, Centro de Ciências Naturais e Exatas, Universidade Federal de Santa Maria, Avenida Roraima 1000, Santa Maria, Rio Grande do Sul, 97105-900, Brazil

    Diego S. S. Chrysosthemos & Jonas Maziero

  2. Centro de Ciências Naturais e Humanas, Universidade Federal do ABC, Avenida dos Estados 5001 Santo André, São Paulo, 09210-580, Brazil

    Marcos L. W. Basso

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  1. Diego S. S. Chrysosthemos
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Correspondence to Jonas Maziero.

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Chrysosthemos, D.S.S., Basso, M.L.W. & Maziero, J. Quantum coherence versus interferometric visibility in a biased Mach–Zehnder interferometer. Quantum Inf Process 22, 68 (2023). https://doi.org/10.1007/s11128-022-03800-6

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