Measurement-Device-Independent Entanglement Detection for Continuous-Variable Systems

We study the detection of continuous-variable entanglement, for which most of the existing methods designed so far require a full specification of the devices, and we present protocols for entanglement detection in a scenario where the measurement devices are completely uncharacterized. We first generalize, to the continuous variable regime, the seminal results by Buscemi [Phys. Rev. Lett. 108, 200401 (2012)] and Branciard et al. [Phys. Rev. Lett. 110, 060405 (2013)], showing that all entangled states can be detected in this scenario. Most importantly, we then describe a practical protocol that allows for the measurement-device-independent certification of entanglement of all two-mode entangled Gaussian states. This protocol is feasible with current technology as it makes use only of standard optical setups such as coherent states and homodyne measurements.

Figure 1

Experimental setup for the MDI entanglement detection of a two-mode state. Fiduciary coherent states are prepared by the parties and measured together with the corresponding subsystems of the unknown state ${\rho }_{AB}$. To compute the bound of the entanglement witness (13), measurements should be seen as uncharacterized black boxes producing the outputs. To obtain a violation, the following specific measurements are implemented: the coherent states are mixed with the respective modes of ${\rho }_{AB}$ in a $50:50$ beam splitter and homodyne measurements of $\widehat{x}$ and $\widehat{p}$ are performed on the two outputs.

Figure 2

Contour plot of the obtainable value (19) of $⟨{\mathrm{MDIEW}}_{\kappa =1}⟩$, for a two-mode squeezed vacuum state with squeezing parameter $r$, under the presence of losses with parameter ${\eta }_A={\eta }_B\equiv \eta$ [cf. (23)]. The contours are chosen to match the separable bound (13) for different values of $\sigma$, which corresponds to the width of the Gaussian prior used in the experiment. Therefore the area under each $\sigma$ contour defines the range of parameters for which MDI entanglement is certified.