Hybrid entanglement swapping of photons: Creating the orbital angular momentum Bell states and Greenberger-Horne-Zeilinger states

Entanglement Swapping for Distant Bose-Einstein Condensates

“…These schemes all avoid the direct interaction, either rely on the entanglement transfer, i.e., entanglement of the driving fields can be transferred to the other pair of particles, or by means of the interaction with a common bus. [14][15][16][17][18][19][20] is another method to create entanglement between remote independent particles that have never interacted in the past. For example, we consider two pairs of particles 1, 2 and 3, 4, particles 1 and 2 are entangled and similarly for particles 3 and 4, however, neither 1 and 4 nor 2 and 3 are entangled.…”

High-efficient quantum secret sharing based on the Chinese remainder theorem via the orbital angular momentum entanglement analysis

“…In an OAM analyzer, the interaction of the SMF and polarizer sustains the fundamental Gaussian mode [14,37]. Therefore, it projects the incoming photons onto the hyper-entanglement state…”

“…The key procedure in the above transformation is due to the relations of the horizontal and circular polarizations [14,15,43], i.e.,…”

“…(3), one can create the OAM entanglement channel, i.e., |Θ ± or |Ω ± for given shadows (a, b) embedded in Eq. (14), which corresponds to the secret X on finite field.…”

“…Spin angular momentum (SAM) is associated with the polarization state that produces a qubit in two-dimensional Hilbert space [12], while orbital angular momentum (OAM) is associated with the helical phase front e ilφ , utilizing an additional degree of freedom to allow for encoding information in qudit (state in multidimensional OAM Hilbert space) [13]. Currently, entanglement swapping based on the SAM or OAM entanglement has been developed in the theory or practice [12][13][14][15].…”