Intrinsic entanglement (IE) is a quantity which aims at quantifying bipartiteentanglement carried by a quantum state as an optimal amount of the intrinsicinformation that can be extracted from the state by measurement. We investigatein detail the properties of a Gaussian version of IE, the so-called Gaussianintrinsic entanglement (GIE). We show explicitly how GIE simplifies to themutual information of a distribution of outcomes of measurements on aconditional state obtained by a measurement on a purifying subsystem of theanalyzed state, which is first minimized over all measurements on the purifyingsubsystem and then maximized over all measurements on the conditional state. Byconstructing for any separable Gaussian state a purification and a measurementon the purifying subsystem which projects the purification onto a productstate, we prove that GIE vanishes on all Gaussian separable states. Viarealization of quantum operations by teleportation, we further show that GIE isnon-increasing under Gaussian local trace-preserving operations and classicalcommunication. For pure Gaussian states and a reduction of thecontinuous-variable GHZ state, we calculate GIE analytically and we show thatit is always equal to the Gaussian R\'{e}nyi-2 entanglement. We also extend theanalysis of IE to a non-Gaussian case by deriving an analytical lower bound onIE for a particular form of the non-Gaussian continuous-variable Werner state.Our results indicate that mapping of entanglement onto intrinsic information iscapable of transmitting also quantitative properties of entanglement and thatthis property can be used for introduction of a quantifier of Gaussianentanglement which is a compromise between computable and physically meaningfulentanglement quantifiers.
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