Implementation of a Measurement-Device-Independent Entanglement Witness

Entanglement, the essential resource in quantum information processing, should be witnessed in many tasks such as quantum computing and quantum communication. The conventional entanglement witness method, relying on an idealized implementation of measurements, could wrongly conclude a separable state to be entangled due to imperfect detections. Inspired by the idea of a time-shift attack, we construct an attack on the conventional entanglement witness process and demonstrate that a separable state can be falsely identified to be entangled. To close such detection loopholes, based on a recently proposed measurement-device-independent entanglement witness method, we design and experimentally demonstrate a measurement-device-independent entanglement witness for a variety of two-qubit states. By the new scheme, we show that an entanglement witness can be realized without detection loopholes.

Figure 1

(a) Conventional EW setup, where Alice and Bob perform local measurements separately and collect information to decide whether the input state is entangled or not. (b) Measurement-device-independent EW setup, where Alice and Bob each prepare an ancillary state and a third party Eve performs Bell state measurements (BSMs) on the ancillary states and the to-be-witnessed bipartite state. Based on the choices of Alice and Bob’s ancillary states and the BSM results, they can judge whether the input state is entangled or not.

Figure 2

Time-shift attack on the conventional EW. (a) Experimental setup of the time-shift attack. Photon pairs are generated by SPDC using a femtosecond pump laser with a central wavelength of 390 nm and a repetition frequency of 80 MHz. POL, polarizer; HWP, half-wave plate; QWP, quarter-wave plate; IF, interference filter with 780 nm central wavelength; PBS, polarizing beam splitter; SFC, single-mode fiber coupler; SMF, single-mode fiber; SPCM, single-photon-counting module. (b) Synchronization between SPCMs. Built-in delay lines enable Eve to shift the output signals $d_{a1}$ and $d_{b0}$ by $\mathrm{\Delta }t$. (c) Coincidence count versus time delay, where the time window is set to 4 ns. All data points are measured for 2 sec, and the time-shift attack is implemented with $\mathrm{\Delta }t=5.50\pm 0.24\mathrm{ns}$, which corresponds to the gray area.

Figure 3

Experimental setup for the MDIEW. The photon pairs are generated by type-II SPDC in 2-mm $\beta$-barium-borate (BBO) crystals. The pulsed pump laser has a central wavelength of 390 nm and a repetition rate of 76 MHz. To prepare the desired state (3), two 2-mm decoherer BBOs (D BBO) are placed side by side with fast axis setting at 0° (up) and 180° (down) to reduce the spatial walk-off effect. By changing the angle $\theta$ of the selector HWP (S HWP), the desired state (2) is prepared with $v={\text{cos}}^2(2\theta )$. Heralded photons 2 and 5 are triggered by the detections of photon 1 and 6, respectively. Wave plates are used to rotate the polarizations to encode photons 2 and 5 to the desired states ${|{\tau }_s⟩}_2$ and ${|{\omega }_t⟩}_5$. The BSM module is composed of three PBSs and two HWPs at 22.5°. All photons are filtered by narrow-band filters (with ${\lambda }_{\mathrm{FWHM}}=2.8\mathrm{nm}$ for BSM I and ${\lambda }_{\mathrm{FWHM}}=8.0\mathrm{nm}$ for BSM II) and then coupled into single-mode fibers, which connect to SPCMs.

Figure 4

MDIEW values are compared for three cases. The theoretical results ($J_{\text{th}}$, solid line) are calculated for the states ${\rho }_{AB}^v$ with different values of $v$ in Eq. (2). The tomography results ($J_{\text{tom}}$, triangle points) are evaluated for the states ${\rho }_{34}^v$ after performing tomography on the to-be-witnessed bipartite state. Each point of the experimental results ($J_{\exp }$, circular points) is measured from a 16-h experiment. Vertical error bars indicate 1 standard deviation and horizontal error bars of the fitting values $v$ from state tomography are described in the Supplemental Material [12]. The inset shows theoretical and experimental values of tangle for input states ${\rho }_{34}^v$.