Nonclassicality Invariant of General Two-Mode Gaussian States.

Ievgen I. Arkhipov,Jiří Svozilík,Jan Peřina,Adam Miranowicz

doi:10.1038/srep26523

Abstract

We introduce a new quantity for describing nonclassicality of an arbitrary optical two-mode Gaussian state which remains invariant under any global photon-number preserving unitary transformation of the covariance matrix of the state. The invariant naturally splits into an entanglement monotone and local-nonclassicality quantifiers applied to the reduced states. This shows how entanglement can be converted into local squeezing and vice versa. Twin beams and their transformations at a beam splitter are analyzed as an example providing squeezed light. An extension of this approach to pure three-mode Gaussian states is given.

Highlights

We introduce a new quantity for describing nonclassicality of an arbitrary optical two-mode Gaussian state which remains invariant under any global photon-number preserving unitary transformation of the covariance matrix of the state
We explicitly reveal the conditions for the transformations of squeezed light into entangled light and vice versa by constructing a suitable global nonclassicality invariant (NI) that is composed of the additive identifiers of entanglement and local nonclassicalities
Motivated by the results for two-mode Gaussian states, we suggest an appropriate form of a three-mode NI relying only on the local nonclassicality invariants (LNI) and pairwise entanglement invariant (EI)

Summary

OPEN Nonclassicality Invariant of General

We introduce a new quantity for describing nonclassicality of an arbitrary optical two-mode Gaussian state which remains invariant under any global photon-number preserving unitary transformation of the covariance matrix of the state. Twin beams and their transformations at a beam splitter are analyzed as an example providing squeezed light An extension of this approach to pure three-mode Gaussian states is given. Considering two-mode Gaussian states, we reveal a nonclassicality invariant resistant against any passive (i.e., photon-number preserving) unitary transformation of their covariance matrix. We show that this invariant naturally decomposes into the expressions giving the local nonclassicality and entanglement quantifiers, which are monotones of the Lee nonclassicality depth and the logarithmic negativity, respectively. Good estimate of the nonclassicality 2Ie(n2t3) is linearly proportional to the of EI

Conclusions

Additional Information