Resource-Efficient Measurement-Device-Independent Entanglement Witness

Imperfections in experimental measurement schemes can lead to falsely identifying, or over estimating, entanglement in a quantum system. A recent solution to this is to define schemes that are robust to measurement imperfections—measurement-device-independent entanglement witness (MDI-EW). This approach can be adapted to witness all entangled qubit states for a wide range of physical systems and does not depend on detection efficiencies or classical communication between devices. Here we extend the theory to remove the necessity of prior knowledge about the two-qubit states to be witnessed. Moreover, we tested this model via a novel experimental implementation for MDI-EW that significantly reduces the experimental complexity. By applying it to a bipartite Werner state, we demonstrate the robustness of this approach against noise by witnessing entanglement down to an entangled state fraction close to 0.4.

Figure 1

Measurement-device-independent entanglement witness concept. Top: An entangled state is probed with locally prepared quantum inputs prepared by trusted linear optic circuits (LOC) and the (2 possible) results of the Bell state measurements (BSM) are used to compute the witness. Bottom: The simplified scheme uses trusted quantum states encoded on an extra degree of freedom of the initial entangled state using LOCs and the (4 possible) BSM outcomes are used to compute the witness.

Figure 2

Experimental setup. Polarization entangled photon pairs are produced by first pumping a type-II periodically poled lithium niobate (PPLN) nonlinear crystal with a continuous laser, then by deterministically separating the degenerate photons using a single channel dense wavelength division multiplexer (DWDM). The input qubits ${\tau }_x$ and ${\tau }_y$ are encoded directly onto the path of the corresponding photon via a trusted linear optical circuit (LOC). Alice and Bob perform Bell state measurements (BSM) using a half-wave plate (HWP) in the lower arm of the interferometers, and polarizing beam splitters (PBS) on each output arms followed by single photon detectors. L, lens; PMF, polarization maintaining fiber; SB, Soleil-Babinet; BS, beam splitter; S, shutter; QWP, quarter-wave plate; PZT, piezoelectric transducer.

Figure 3

Witness values for two-qubit Werner states with different weights $\lambda$. The data points ${\beta }^{\lambda }$ and ${\beta }^{\lambda =0.94}$ correspond to the results obtained when $\beta$ are calculated for each points and only for the first point, respectively. The uncertainty associated with each point has been calculated using Monte Carlo algorithm and a Poissonian noise on the detection rate.