Coherence and contextuality in a Mach-Zehnder interferometer

Rafael Wagner1,2, Anita Camillini1,2, and Ernesto F. Galvão1,3

1International Iberian Nanotechnology Laboratory (INL), Av. Mestre José Veiga, 4715-330 Braga, Portugal
2Centro de Física, Universidade do Minho, Braga 4710-057, Portugal
3Instituto de Física, Universidade Federal Fluminense, Av. Gal. Milton Tavares de Souza s/n, Niterói, RJ, 24210-340, Brazil

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Abstract

We analyse nonclassical resources in interference phenomena using generalized noncontextuality inequalities and basis-independent coherence witnesses. We use recently proposed inequalities that witness both resources within the same framework. We also propose, in view of previous contextual advantage results, a systematic way of applying these tools to characterize advantage provided by coherence and contextuality in quantum information protocols. We instantiate this methodology for the task of quantum interrogation, famously introduced by the paradigmatic bomb-testing interferometric experiment, showing contextual quantum advantage for such a task.

In this paper, we explore nonclassical resources in interference phenomena by analyzing generalized noncontextuality inequalities and basis-independent coherence witnesses. We apply recently proposed inequalities to characterize coherence and contextuality in quantum information protocols, focusing on Mach-Zehnder interferometers (MZIs). Our study reveals that basis-independent quantum coherence within MZIs can be witnessed and quantified using coherence-free inequalities, providing experimentally accessible methods for assessing coherence. Using novel techniques, we show a quantifiable advantage provided by quantum contextuality to the task of quantum interrogation. Our contributions range from novel inequalities, analytical results, and proposed experimental protocols, shedding light on the relationship between coherence and contextuality in MZIs and offering a general approach for proving quantum advantages in interferometric experiments.

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[1] Vinicius P. Rossi, David Schmid, John H. Selby, and Ana Belén Sainz, "Contextuality with vanishing coherence and maximal robustness to dephasing", Physical Review A 108 3, 032213 (2023).

[2] Rafael Wagner, Zohar Schwartzman-Nowik, Ismael L. Paiva, Amit Te'eni, Antonio Ruiz-Molero, Rui Soares Barbosa, Eliahu Cohen, and Ernesto F. Galvão, "Quantum circuits for measuring weak values, Kirkwood-Dirac quasiprobability distributions, and state spectra", Quantum Science and Technology 9 1, 015030 (2024).

[3] Lorenzo Catani, Matthew Leifer, David Schmid, and Robert W. Spekkens, "Why interference phenomena do not capture the essence of quantum theory", Quantum 7, 1119 (2023).

[4] Lorenzo Catani, Matthew Leifer, Giovanni Scala, David Schmid, and Robert W. Spekkens, "Aspects of the phenomenology of interference that are genuinely nonclassical", Physical Review A 108 2, 022207 (2023).

[5] Rafael Wagner, Rui Soares Barbosa, and Ernesto F. Galvão, "Inequalities witnessing coherence, nonlocality, and contextuality", arXiv:2209.02670, (2022).

[6] Rafael Wagner, Roberto D. Baldijão, Alisson Tezzin, and Bárbara Amaral, "Using a resource theoretic perspective to witness and engineer quantum generalized contextuality for prepare-and-measure scenarios", Journal of Physics A Mathematical General 56 50, 505303 (2023).

[7] Taira Giordani, Rafael Wagner, Chiara Esposito, Anita Camillini, Francesco Hoch, Gonzalo Carvacho, Ciro Pentangelo, Francesco Ceccarelli, Simone Piacentini, Andrea Crespi, Nicolò Spagnolo, Roberto Osellame, Ernesto F. Galvão, and Fabio Sciarrino, "Experimental certification of contextuality, coherence, and dimension in a programmable universal photonic processor", Science Advances 9 44, eadj4249 (2023).

[8] Rafael Wagner and Ernesto F. Galvão, "Simple proof that anomalous weak values require coherence", Physical Review A 108 4, L040202 (2023).

[9] Massy Khoshbin, Lorenzo Catani, and Matthew Leifer, "Alternative robust ways of witnessing nonclassicality in the simplest scenario", arXiv:2311.13474, (2023).

[10] Holger F. Hofmann, "Sequential propagation of a single photon through five measurement contexts in a three-path interferometer", arXiv:2308.02086, (2023).

[11] Marcos L. W. Basso, Ismael L. Paiva, and Pedro R. Dieguez, "Unveiling quantum complementarity trade-offs in relativistic scenarios", arXiv:2306.08136, (2023).

The above citations are from SAO/NASA ADS (last updated successfully 2024-02-26 15:34:33). The list may be incomplete as not all publishers provide suitable and complete citation data.

On Crossref's cited-by service no data on citing works was found (last attempt 2024-02-26 15:34:32).