Experimental distillation of bipartite polarization entanglement using polarizing Mach-Zehnder interferometers

Entanglement distillation is the process of concentrating entanglement from a given quantum state. We present a technique for distillation of bipartite polarization entanglement using interferometry. This technique can be optimized to extract maximal entanglement from any pure or mixed entangled state. A model for this method is presented, and, in particular, we present experimental results for pure states when using polarizing Mach-Zehnder interferometers. These experimentally distilled states always demonstrate an increased violation of Bell's inequality.

Figure 1

Experimental schematic for performing bipartite entanglement distillation using two polarizing Mach-Zehnder interferometers. Entangled photon pairs from a source are separated; each photon in the pair traverses an interferometer. By appropriately setting the half-wave plates, unwanted photons are discarded, leaving maximally entangled photons to exit the interferometer in the desired output port.

Figure 2

Theoretical plots for the CHSH values that are attainable for bipartite states before [Eq. (3)] and after [Eq. (4)] the distillation. This CHSH test is used as an indicator of the nonlocal quantum correlation between the two particles. The green line indicates the boundary between entangled and separable states. (a) The initial CHSH value for all the states before distillation. The red dashed line is the boundary where the CHSH value is $\ge 2$. (b) The CHSH values after distillation. The black dashed line shows the region whose CHSH value exceeded 2 after distillation. (c) Taking the difference between panels (a) and (b) reveals that distillation improves the bipartite correlation best for states that were initially heavily imbalanced as expected. There exists a region where the distilled states show worse CHSH values, but states with these starting values are typically of no interest in quantum communications.

Figure 3

(a) Experimental setup for the distillation using a folded Mach-Zehnder interferometer. A photon pair source ($S$) capable of producing nonmaximally entangled photons with different $\epsilon$'s is used. The dotted lines are the untangled photons filtered out by the interferometer. Two polarizers ($P$) are used to measure the polarization correlations that contribute to the CHSH parameter. A quarter-wave plate oriented at $0^{\circ }$ introduces a phase between horizontal and vertical components depending upon its tilt angle. This phase can be used to compensate any phase offset created either by the source or by the interferometer. A dichroic mirror (DM) separates the distilled signal and idler photons. (b) and (c) show the stability of the constructive and destructive interferences created by the folded Mach-Zehnder interferometer. The small drift in the constructive interference output (approximately 1%) is attributed to the shift in the input laser power. However, there is no phase instability as the constructive and destructive interference contrasts remain the same over the course of the experiment.

Figure 4

(a) Two-photon polarization correlation for a nonmaximally entangled state with $\epsilon =0.11$. $V,D,H$, and $A$ correspond to the vertical, diagonal, horizontal, and antidiagonal polarization projections on the signal photon. (b) Polarization correlation curves for the distilled state. The visibilities of the curves are unchanged during the distillation. The diagonal basis visibility is observed to be 94%. (c) CHSH value for different nonmaximally entangled states before and after distillation when measured in mutually unbiased bases. The blue dotted line is the upper bound ($2\sqrt{2}$) for the CHSH value. The imbalance $\epsilon ={cos}^2\left(2\theta \right)$, where $\theta$ corresponds to the angle of the HWP that rotated the pump polarization. When the imbalance parameters have extreme values, the distillation procedure filters out most of the photons from the source resulting in a low signal-to-noise ratio, increasing the standard deviation of the measured CHSH values.