The balance of quantum correlations for a class of feasible tripartite continuous variable states

TL;DR

This paper investigates the conservation laws of quantum correlations in tripartite continuous variable states, demonstrating explicit relations for pure states and their evolution into inequalities under noise.

Contribution

It explicitly proves Koashi-Winter-like conservation laws for Gaussian entanglement, discord, and entropy in tripartite CV states, including noisy mixed states.

Findings

Conservation laws hold for pure tripartite CV states.

Noise causes the equalities to become inequalities.

Theoretical framework for quantum correlation dynamics in CV systems.

Abstract

We address the balance of quantum correlations for continuous variable (CV) states. In particular, we consider a class of feasible tripartite CV pure states and explicitly prove two Koashi-Winter-like conservation laws involving Gaussian entanglement of formation, Gaussian quantum discord and sub-system Von Neumann entropies. We also address the class of tripartite CV mixed states resulting from the propagation in a noisy environment, and discuss how the previous equalities evolve into inequalities.