I asked how quantum repeaters work if non-cloning theorem is true.
Answer from Perplexity Pro:
Quantum repeaters are essential for long-distance quantum communication, but they must work within the constraints of the no-cloning theorem, which states that an arbitrary unknown quantum state cannot be perfectly copied. Here’s how quantum repeaters manage to function without violating this fundamental principle:
## **How Quantum Repeaters Work**
Quantum repeaters do not simply copy and retransmit quantum information as classical repeaters do. Instead, they use a process called **entanglement swapping** to extend the range of quantum communication.
### **Entanglement Swapping**
Entanglement swapping involves creating entanglement between distant nodes by connecting shorter entangled links. Here’s a step-by-step breakdown:
1. **Initial Entanglement**: Two pairs of entangled particles are created. Let’s call the pairs (A, B) and (C, D), where A and C are at one location and B and D are at another.
2. **Bell State Measurement**: A Bell state measurement is performed on particles B and C. This measurement entangles A and D, even though they have never interacted directly.
3. **Result Communication**: The result of the Bell state measurement is communicated classically to the locations of particles A and D.
4. **State Adjustment**: Based on the measurement result, appropriate operations are performed on particles A and D to complete the entanglement swapping.
By repeating this process over multiple segments, long-distance entanglement can be achieved without directly transmitting qubits over the entire distance, thus circumventing the exponential loss of photons in long fibers[2][4][5].
### **Quantum Memories**
Quantum repeaters also rely on quantum memories to store entangled states temporarily. This allows the system to wait until all necessary entangled links are established before performing entanglement swapping. Quantum memories are crucial for synchronizing the process and ensuring that the entanglement can be extended over long distances without significant loss[5].
## **No-Cloning Theorem and Quantum Repeaters**
The no-cloning theorem asserts that it is impossible to create an exact copy of an arbitrary unknown quantum state[3][6]. Quantum repeaters respect this theorem by not attempting to copy quantum states. Instead, they use the principles of quantum entanglement and teleportation to extend the communication range:
- **Entanglement Distribution**: Quantum repeaters distribute entanglement rather than copying quantum states. This distribution is achieved through entanglement swapping, which connects shorter entangled segments into a longer one.
- **Quantum Teleportation**: Teleportation protocols allow the transfer of quantum information from one location to another without direct transmission, relying on pre-shared entanglement and classical communication to reconstruct the state at the destination.
By leveraging these techniques, quantum repeaters can facilitate long-distance quantum communication without violating the no-cloning theorem. This approach ensures that the integrity and security of quantum information are maintained, enabling the development of a robust quantum internet[1][2][4].
情報源
[1] How does a quantum repeater work without violating the no cloning … https://physics.stackexchange.com/questions/446817/how-does-a-quantum-repeater-work-without-violating-the-no-cloning-theorem
[2] What are quantum repeaters? https://www.aliroquantum.com/blog/what-are-quantum-repeaters
[3] What is No-Cloning Theorem — QuEra Computing https://www.quera.com/glossary/no-cloning-theorem
[4] Quantum repeaters based on atomic ensembles and linear optics https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.83.33
[5] Quantum Repeaters — Quantum Flagship https://qt.eu/quantum-principles/communication/quantum-repeaters
[6] no-cloning theorem in nLab https://ncatlab.org/nlab/show/no-cloning%2Btheorem
[7] Inside Quantum Repeaters | IEEE Journals & Magazine https://ieeexplore.ieee.org/document/7010905
[8] An Illustrated Introduction to Quantum Networks and … — AWS https://aws.amazon.com/blogs/quantum-computing/an-illustrated-introduction-to-quantum-networks-and-quantum-repeaters/
[9] [PDF] The No-Cloning Theorem, Classical Teleportation and Quantum … https://courses.cs.washington.edu/courses/cse599d/06wi/lecturenotes4.pdf
[10] [PDF] arXiv:1809.09711v6 [physics.hist-ph] 22 Sep 2020 https://arxiv.org/pdf/1809.09711.pdf
[11] How do quantum repeaters work? https://www.aliroquantum.com/blog/how-do-quantum-repeaters-work
[12] Cloning Theorem — an overview | ScienceDirect Topics https://www.sciencedirect.com/topics/engineering/cloning-theorem
[13] Surpassing the no-cloning limit with a heralded hybrid linear amplifier https://ieeexplore.ieee.org/document/8119040
[14] Quantum Repeater Goes the Distance — Physics Magazine https://physics.aps.org/articles/v16/84
[15] What is the no-cloning theorem? — PennyLane https://pennylane.ai/qml/glossary/what-is-the-no-cloning-theorem/
