Fig. 1. Theoretical results of steering distillation with filtering operation CF(κ) and CF(κ′). (a) F1sDI (F2sDI). (b) F1sDIκ−F1sDIκ′ (F2sDIκ−F2sDIκ′). (c) S1sDI. (d) S2sDI. Black lines: no filtering operation is performed. Blue lines: filtering operation CF(κ) is performed. Red lines: filtering operation CF(κ′) is performed.

Fig. 2. Theoretical results of assemblage fidelity F1sDI(Σa|xdist,N,Σa|xGHZ) in N-copy 1sDI distillation scenario with (a) N=5, (b) N=10, and (c) N=50. The blue and red lines represent the results with local filtering operations CF(κ) and CF(κ′), respectively.

Fig. 3. Numerical results of optimal local filtering operation in N-copy 1sDI distillation. (a) Optimal values of κ with N=5 (red circle), 10 (cyan cross), 50 (blue square), and 100 (green diamond). The blue solid line represents the optimal value of κ′=12cos2θ with N=2, while the red solid line represents the optimal value of κ′=tan θ with N→∞. Assemblage fidelity F1sDI with optimal CF(κ) in (b) five-copy distillation, (c) 10-copy distillation, and (d) 50-copy distillation. The black solid lines in (b), (c), and (d) represent the analytic expression of F1sDI=1−12(1−sin 2θ)cosN−12θ with local filtering operation CF(κ′).

Fig. 4. Schematic drawing of experimental setup to investigate the two-copy distillation protocol.

Fig. 5. Experimental results of (a) F1sDI, (b) F2sDI, (c) S1sDI, and (d) S2sDI. Black circles: no filtering operation is performed. Blue triangles: filtering operation CF(κ) is performed. Red squares: filtering operation CF(κ′) is performed. The dashed lines represent the corresponding theoretical predictions. The error bars are too small compared to size of markers.