JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2024, Vol. 59 ›› Issue (8): 103-112.doi: 10.6040/j.issn.1671-9352.0.2023.007

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Multi-particle short-distance teleportation in noisy environment with weak measurement

Miao LIU1,2(),Jiayin PENG1,2,3,*(),Jiangang TANG1,2   

  1. 1. School of Mathematics and Statistics, Yili Normal University, Yining 835000, Xinjiang, China
    2. Institute of Applied Mathematics, Yili Normal University, Yining 835000, Xinjiang, China
    3. School of Mathematics and Information Science, Neijiang Normal University, Neijiang 641100, Sichuan, China
  • Received:2023-01-05 Online:2024-08-20 Published:2024-07-31
  • Contact: Jiayin PENG E-mail:lium76@163.com;pengjiayin62226@163.com

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Abstract:

Using a three-particle maximally entangled state and an auxiliary particle in the ground state |0? as the quantum channel, a new deterministic scheme for transmitting an unknown three-particle GHZ (Greenberger-Horne-Zeilinger) state is proposing. In this scheme, the sender and the receiver share the auxiliary particle at the same time, and both parties need to perform quantum gate operation on the shared auxiliary particle. The results show that the scheme saves quantum entanglement resources but shortens the teleportation distance, and can be extended to the teleportation of multi-particle GHZ state. Furthermore, taking the amplitude damping channel as an example, the influence of quantum noise on the scheme is discussed, and the fidelity of teleportation is obtained. The influence of weak measurement and its reversal measurement on the noise scheme is analyzed. It is found that for a specific GHZ state, the weak measurement and its reversal measurement will suppress or deteriorate the degradation of the fidelity of its teleportation caused by noise.

Key words: short-distance teleportation, GHZ state, amplitude damping, weak measurement

CLC Number: 

  • O431.2

Table 1

Relationship between Alice's measurement result, collapse state, and Bob's recovery unitary transformation"

测量结果 塌陷态 恢复酉变换
|0001?或者|1101? α|000?+β|111? σ0⊗σ0⊗σ0
|0101?或者|1001? α|000?-β|111? σ0⊗σ0⊗σz
|0011?或者|1111? α|001?+β|110? σ0⊗σ0⊗σx
|0111?或者|1011? α|001?-β|110? σ0⊗σ0⊗iσy
|0000?或者|1100? α|001?+β|001? σx⊗σx⊗σ0
|0100?或者|1000? α|001?-β|001? σx⊗σx⊗σz
|0010?或者|1110? α|111?+β|000? σx⊗σx⊗σx
|0110?或者|1010? α|111?+β|000? σx⊗σx⊗iσy

Fig.1

Fidelity of short-distance teleportation based onAD channel"

Fig.2

Comparison of fidelity of short-distance teleportation with and without weak measurements"

Fig.3

3D comparison of fidelity of short-distance teleportation with and without weak measurements"

Fig.4

Total success probability of short distance teleportation under weak and reverse measurements"

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