Fig. 1. Schematic of the experimental setup. (a) Arrangement of the optical components used to generate and measure the entangled photon pairs between two multicore fibers. (b) Imaging configuration for the pump beam and photons coupled to the fiber cores (L=250  mm, f1=50  mm, f2=75  mm, and f3=15  mm). Inset: phase patterns on SLM0. SLM, spatial light modulator; L, lens; MCF, multicore fiber; Q, quarter-wave plate; H, half-wave plate; PBS, polarizing beam splitter; IF, interference filter; FC, fiber coupler; SMF, single-mode fiber.

Fig. 2. Reconstructed density matrices by quantum state tomography: (a) d=2, (b) d=3, and (c) d=4.

Fig. 3. Quantum correlations between the two-core superposition states, while changing the relative phase of the pump beam spots. Photon 1 in MCF1 is projected onto the state (|j⟩+|k⟩)/2. Photon 2 in MCF2 is projected onto (|j⟩+|k⟩)/2 (red circles) or (|j⟩+i|k⟩)/2 (black squares). The phase ϕ of the two-photon state component |k⟩|k⟩ is scanned from 0 to 2π by a relative phase of the relevant subsection pattern on SLM0. The coincidence counting period was 60 s. (a) j=0, k=1. (b) j=1, k=2. (c) j=2, k=3. (d) j=3, k=0.

Fig. 4. Measured Bell-type parameter Sd (squares), compared with the limit by the local variable theories (triangles) and the theoretical values for the maximally entangled states (circles).

Fig. 5. Relative amounts of the core-mode components and the Bell parameter S4 in entangled states (|0⟩|0⟩+γ|1⟩|1⟩+γ|2⟩|2⟩+|3⟩|3⟩)/2(1+γ2). Dashed lines denote the design values. (a) γ≈1.35. (b) γ≈1.00. (c) γ≈0.74. (d) γ≈0.32.