Operational interpretation of the vacuum and process matrices for identical particles

TL;DR

This paper analyzes the interaction with the vacuum in quantum communication protocols using process matrices, emphasizing its operational role and extending the formalism to systems with indefinite particle numbers.

Contribution

It provides an operational interpretation of vacuum interactions within process matrices and applies this to second quantization frameworks for identical particles.

Findings

Vacuum interactions are operationally significant in quantum protocols.

Process matrix formalism can be extended to systems with indefinite particle numbers.

The analysis clarifies the role of vacuum in quantum communication scenarios.

Abstract

This work overviews the single-particle two-way communication protocol recently introduced by del Santo and Daki\'c (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.