### Abstract

In the context of bipartite bosonic systems, two notions of classicality of correlations can be defined: P-classicality, based on the properties of the Glauber-Sudarshan P-function; and C-classicality, based on the entropic quantum discord. It has been shown that these two notions are maximally inequivalent in a static (metric) sense -- as they coincide only on a set of states of zero measure. We extend and reinforce quantitatively this inequivalence by addressing the dynamical relation between these types of non-classicality in a paradigmatic quantum-optical setting: the linear mixing at a beam splitter of a single-mode Gaussian state with a thermal reference state. Specifically, we show that almost all P-classical input states generate outputs that are not C-classical. Indeed, for the case of zero thermal reference photons, the more P-classical resources at the input the less C-classicality at the output. In addition, we show that the P-classicality at the input -- as quantified by the non-classical depth -- does instead determine quantitatively the potential of generating output entanglement. This endows the non-classical depth with a new operational interpretation: it gives the maximum number of thermal reference photons that can be mixed at a beam splitter without destroying the output entanglement.

Original language | English |
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Article number | 062315 |

Number of pages | 11 |

Journal | Physical Review A (Atomic, Molecular, and Optical Physics) |

Volume | 91 |

Issue number | 6 |

DOIs | |

Publication status | Published - 11 Jun 2015 |

### Keywords

- quant-ph

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## Cite this

Brunelli, M., Benedetti, C., Olivares, S., Ferraro, A., & Paris, M. G. A. (2015). Single- and two-mode quantumness at a beam splitter.

*Physical Review A (Atomic, Molecular, and Optical Physics)*,*91*(6), [062315]. https://doi.org/10.1103/PhysRevA.91.062315