Operational interpretation of the vacuum and process matrices for identical particles

Ricardo Faleiro1, Nikola Paunkovic1,2, and Marko Vojinovic3

1Instituto de Telecomunicações, Avenida Rovisco Pais 1, 1049-001, Lisboa, Portugal
2Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, Avenida Rovisco Pais 1, 1049-001, Lisboa, Portugal
3Institute of Physics, University of Belgrade, Pregrevica 118, 11080 Belgrade, Serbia

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Abstract

This work overviews the single-particle two-way communication protocol recently introduced by del Santo and Dakić (dSD), and analyses it using the process matrix formalism. We give a detailed account of the importance and the operational meaning of the interaction of an agent with the vacuum – in particular its role in the process matrix description. Our analysis shows that the interaction with the vacuum should be treated as an operation, on equal footing with all other interactions. This raises the issue of counting such operations in an operational manner. Motivated by this analysis, we apply the process matrix formalism to capped Fock spaces using the framework of second quantisation, in order to characterise protocols with an indefinite number of identical particles.

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Cited by

[1] Nick Ormrod, Augustin Vanrietvelde, and Jonathan Barrett, "Causal structure in the presence of sectorial constraints, with application to the quantum switch", Quantum 7, 1028 (2023).

[2] Matthias Salzger, "Connecting indefinite causal order processes to composable quantum protocols in a spacetime", arXiv:2304.06735, (2023).

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