Photonic quantum network transmission assisted by the weak cross-Kerr nonlinearity

Efficient quantum state transmission via perfect quantum network coding

“…Thus, when comparing with the other displayed QNCSs, Thus, it appears that the previous schemes [34,[41][42][43] cost either O(k 3 ) or O(k 2 ) of the classical communication. In contrast, our protocol costs only 2(k + 1)⌈log d⌉ (i.e., O(k)) of the classical communication, which is also less than that of the scheme in [36]. These comparisons show that the amount of the classical communication costs in our protocol is the least among all the listed schemes.…”

“…The same benefit is also evident in some schemes under the k-pair network N listed in Table 2. For the scheme in [36], the pair number of the quantum entanglement is 1, which is the same as that of our scheme. Thus, when comparing with the other displayed QNCSs, Thus, it appears that the previous schemes [34,[41][42][43] cost either O(k 3 ) or O(k 2 ) of the classical communication.…”

“…Now, let us firstly analyze the entanglement resource introduced in the QNCSs used for the comparisons. It can easily been seen that, for the pair number of quantum entanglement, only one pair of the entangled state is pre-shared between the two intermediate nodes in our protocol, which is less than the number of the entangled pairs introduced in the schemes (except for [36]) under the most basic network model-butterfly network listed in Table 1. The same benefit is also evident in some schemes under the k-pair network N listed in Table 2.…”

“…An entanglement resource is a key quantum resource used for various quantum communication tasks such as quantum key distribution [24], quantum correlation generation [25], teleportation [26], remote state preparation [27], and quantum-state sharing [28]. Therefore, it is believed that with the assistance of prior entanglement, new breakthroughs in QNC [29][30][31][32][33][34][35][36][37][38][39] can be achieved. In 2007, Hayashi [29] first introduced prior entanglement into QNC, where two maximal entangled states are pre-shared between two source nodes over the butterfly network.…”

“…Li et al [35] analyzed the solvability of several typical quantum multi-unicast networks using global entangled two-dimensional (2D) and three-dimensional (3D) cluster states. Wang et al [36] achieved nearly perfect quantum k-pair transmission by means of an extended photonic entanglement with multiple degrees of freedom, such that the classical unsolvable network becomes quantum solvable. As can be seen, the pair number and the location of the entangled states play an important role in the network coding solution to a quantum network problem.…”