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Entanglement swapping (ES) based multi-hop quantum information transmission is a fundamental way to realize long-distance quantum communication. However, in the conventional quantum networks, the entanglement in one degree of freedom (DOF) of photon system is usually used as a quantum channel, showing disadvantages of low capacity and susceptibility to noise. In this paper, we present an efficient multi-hop quantum hyperentanglement swapping (HES) method based on hyperentanglement, which utilizes the entangled photos in polarization and spatial-mode DOFs to establish the hyperentangled multi-hop quantum channel. Taking long-distance hyperentanglement based quantum teleportation for example, we first describe a basic hop by hop HES scheme. Then, in order to reduce the end-to-end delay of this scheme, we propose a simultaneous HES (SHES) scheme, in which the intermediate quantum nodes perform hyperentangled Bell state measurements concurrently. On the basis of this scheme, we further put forward a hierarchical SHES (HSHES) scheme that can reduce the classical information cost. Theoretical analysis and simulation results show that the end-to-end delay of HSHES is similar to that of SHES, meanwhile, the classical information cost of HSHES is much lower than that of SHES, showing a better tradeoff between the two performance metrics. Compared with the traditional ES methods, the scheme proposed in this paper is conductive to meeting the requirements for long-distance hyperentanglement based quantum communication, which has positive significance for building more efficient quantum networks in the future.
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B和C的量子态 编码结果 A和D的量子态 Bob的幺正变换 $ \left| {{\phi ^{\text{ + }}}} \right\rangle _{P} \left| {{\phi ^{\text{ + }}}} \right\rangle _{S} $ 0000 $ \left| {{\phi ^{\text{ + }}}} \right\rangle _{P} \left| {{\phi ^{\text{ + }}}} \right\rangle _{S} $ $ {U_1} = \sigma _I^P \otimes \sigma _I^S $ $ \left| {{\phi ^{\text{ + }}}} \right\rangle _{P} \left| {{\phi ^ - }} \right\rangle _{S} $ 0001 $ \left| {{\phi ^{\text{ + }}}} \right\rangle _{P} \left| {{\phi ^ - }} \right\rangle _{S} $ $ {U_2} = \sigma _I^P \otimes \sigma _Z^S $ $ \left| {{\phi ^ - }} \right\rangle _{P} \left| {{\phi ^ + }} \right\rangle _{S} $ 0010 $ \left| {{\phi ^ - }} \right\rangle _{P} \left| {{\phi ^ + }} \right\rangle _{S} $ $ {U_3} = \sigma _Z^P \otimes \sigma _I^S $ $ \left| {{\phi ^ - }} \right\rangle _{P} \left| {{\phi ^ - }} \right\rangle _{S} $ 0011 $ \left| {{\phi ^ - }} \right\rangle _{P} \left| {{\phi ^ - }} \right\rangle _{S} $ $ {U_4} = \sigma _Z^P \otimes \sigma _Z^S $ $ \left| {{\psi ^{\text{ + }}}} \right\rangle _{P} \left| {{\phi ^{\text{ + }}}} \right\rangle _{S} $ 0100 $ \left| {{\psi ^{\text{ + }}}} \right\rangle _{P} \left| {{\phi ^{\text{ + }}}} \right\rangle _{S} $ $ {U_5} = \sigma _X^P \otimes \sigma _I^S $ $ \left| {{\psi ^{\text{ + }}}} \right\rangle _{P} \left| {{\phi ^ - }} \right\rangle _{S} $ 0101 $ \left| {{\psi ^{\text{ + }}}} \right\rangle _{P} \left| {{\phi ^ - }} \right\rangle _{S} $ $ {U_6} = \sigma _X^P \otimes \sigma _Z^S $ $ \left| {{\psi ^ - }} \right\rangle _{P} \left| {{\phi ^ + }} \right\rangle _{S} $ 0110 $ \left| {{\psi ^ - }} \right\rangle _{P} \left| {{\phi ^ + }} \right\rangle _{S} $ ${U_7} = - {{i}}\sigma _Y^P \otimes \sigma _I^S$ $ \left| {{\psi ^ - }} \right\rangle _{P} \left| {{\phi ^ - }} \right\rangle _{S} $ 0111 $ \left| {{\psi ^ - }} \right\rangle _{P} \left| {{\phi ^ - }} \right\rangle _{S} $ ${U_8} = - {{i}}\sigma _Y^P \otimes \sigma _Z^S$ $ \left| {{\phi ^{\text{ + }}}} \right\rangle _{p} \left| {{\psi ^{\text{ + }}}} \right\rangle _{S} $ 1000 $ \left| {{\phi ^{\text{ + }}}} \right\rangle _{p} \left| {{\psi ^{\text{ + }}}} \right\rangle _{S} $ $ {U_9} = \sigma _I^P \otimes \sigma _X^S $ $ \left| {{\phi ^{\text{ + }}}} \right\rangle _{p} \left| {{\psi ^ - }} \right\rangle _{S} $ 1001 $ \left| {{\phi ^{\text{ + }}}} \right\rangle _{p} \left| {{\psi ^ - }} \right\rangle _{S} $ ${U_{10} } = \sigma _I^P \otimes - {{i}}\sigma _Y^S$ $ \left| {{\phi ^ - }} \right\rangle _{p} \left| {{\psi ^ + }} \right\rangle _{S} $ 1010 $ \left| {{\phi ^ - }} \right\rangle _{p} \left| {{\psi ^ + }} \right\rangle _{S} $ $ {U_{11}} = \sigma _Z^P \otimes \sigma _X^S $ $ \left| {{\phi ^ - }} \right\rangle _{p} \left| {{\psi ^ - }} \right\rangle _{S} $ 1011 $ \left| {{\phi ^ - }} \right\rangle _{p} \left| {{\psi ^ - }} \right\rangle _{S} $ ${U_{12} } = \sigma _Z^P \otimes - {{i}}\sigma _Y^S$ $ \left| {{\psi ^ + }} \right\rangle _{P} \left| {{\psi ^ + }} \right\rangle _{S} $ 1100 $ \left| {{\psi ^ + }} \right\rangle _{P} \left| {{\psi ^ + }} \right\rangle _{S} $ $ {U_{13}} = \sigma _X^P \otimes \sigma _X^S $ $ \left| {{\psi ^ + }} \right\rangle _{P} \left| {{\psi ^ - }} \right\rangle _{S} $ 1101 $ \left| {{\psi ^ + }} \right\rangle _{P} \left| {{\psi ^ - }} \right\rangle _{S} $ ${U_{14} } = \sigma _X^P \otimes - {{i}}\sigma _Y^S$ $ \left| {{\psi ^ - }} \right\rangle _{P} \left| {{\psi ^ + }} \right\rangle _{S} $ 1110 $ \left| {{\psi ^ - }} \right\rangle _{P} \left| {{\psi ^ + }} \right\rangle _{S} $ ${U_{15} } = - {{i}}\sigma _Y^P \otimes \sigma _X^S$ $ \left| {{\psi ^ - }} \right\rangle _{P} \left| {{\psi ^ - }} \right\rangle _{S} $ 1111 $ \left| {{\psi ^ - }} \right\rangle _{P} \left| {{\psi ^ - }} \right\rangle _{S} $ ${U_{16} } = - {{i}}\sigma _Y^P \otimes - {\rm{i} }\sigma _Y^S$ 
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N1,N2, ···NN– 1测量结果 Alice的幺正变换 $ \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i1}} \cdot \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i2}} \otimes \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i1}} \cdot \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i2}} = 1 $ $ {U_1} = \sigma _I^P \otimes \sigma _I^S $ $ \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i1}} \cdot \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i2}} \otimes \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i1}} \cdot \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i2} = 1 $ $ {U_2} = \sigma _I^P \otimes \sigma _Z^S $ $ \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i1}} \cdot \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i2}} \otimes \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i1} \cdot \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i2}} = 1 $ $ {U_3} = \sigma _I^P \otimes \sigma _X^S $ $ \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i1}} \cdot \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i2}} \otimes \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i1} \cdot \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i2} = 1 $ $ {U_4} = \sigma _I^P \otimes - i\sigma _Y^S $ $ \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i1}} \cdot \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i2} \otimes \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i1}} \cdot \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i2}} = 1 $ $ {U_5} = \sigma _I^P \otimes \sigma _I^S $ $ \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i1}} \cdot \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i2} \otimes \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i1}} \cdot \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i2} = 1 $ $ {U_6} = \sigma _Z^P \otimes \sigma _Z^S $ $ \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i1}} \cdot \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i2} \otimes \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i1} \cdot \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i2}} = 1 $ $ {U_7} = \sigma _Z^P \otimes \sigma _X^S $ $ \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i1}} \cdot \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i2} \otimes \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i1} \cdot \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i2} = 1 $ $ {U_8} = \sigma _Z^P \otimes - i\sigma _Y^S $ $ \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i1} \cdot \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i2}} \otimes \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i1}} \cdot \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i2}} = 1 $ $ {U_9} = \sigma _X^P \otimes \sigma _I^S $ $ \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i1} \cdot \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i2}} \otimes \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i1}} \cdot \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i2} = 1 $ $ {U_{10}} = \sigma _X^P \otimes \sigma _Z^S $ $ \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i1} \cdot \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i2}} \otimes \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i1} \cdot \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i2}} = 1 $ $ {U_{11}} = \sigma _X^P \otimes \sigma _X^S $ $ \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i1} \cdot \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i2}} \otimes \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i1} \cdot \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i2} = 1 $ $ {U_{12}} = \sigma _X^P \otimes - i\sigma _Y^S $ $ \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i1} \cdot \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i2} \otimes \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i1}} \cdot \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i2}} = 1 $ $ {U_{13}} = - i\sigma _Y^P \otimes \sigma _I^S $ $ \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i1} \cdot \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i2} \otimes \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i1}} \cdot \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i2} = 1 $ $ {U_{14}} = - i\sigma _Y^P \otimes \sigma _Z^S $ $ \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i1} \cdot \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i2} \otimes \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i1} \cdot \overline { \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i2}} = 1 $ $ {U_{15}} = - i\sigma _Y^P \otimes \sigma _X^S $ $ \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i1} \cdot \oplus _{i = 1}^{N - 1}{\text{MN}}_P^{i2} \otimes \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i1} \cdot \oplus _{i = 1}^{N - 1}{\text{MN}}_S^{i2} = 1 $ $ {U_{1{\text{6}}}} = - i\sigma _Y^P \otimes - i\sigma _Y^S $ DownLoad:
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[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41]
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