In quantum teleportation, the goal is not to move matter, but to instantly transfer the quantum state of one qubit to another, seemingly over any distance. This amazing protocol is a cornerstone of quantum information science. Let’s imagine a scenario where Alice on Earth wants to send the quantum state of her qubit, $|\sigma\rangle$, to Bob on Mars. Physically sending the qubit itself would be too slow, so they rely on a quantum trick.
🔗 Shared Entanglement and the Teleportation State
The first step requires that Alice and Bob already share an entangled pair of qubits. Before Bob left for Mars, they created a Bell state with two qubits, let’s call them $a$ and $b$, and Bob took qubit $b$ with him. Now that Alice has created her signal qubit $s$ with state $|\sigma\rangle$, all three qubits form a single, entangled system. The magic of this process lies in creating a special state called the teleportation state, $|\tau\rangle$. This complex, three-qubit state is at the heart of the whole process. By performing specific operations on her two qubits, $s$ and $a$, Alice can set up this state, which holds the information of her original qubit in a new, distributed form.
📐 Alice’s Measurements and Classical Communication
Now, Alice measures her two qubits, $s$ and $a$. According to the laws of quantum mechanics, this measurement instantly collapses the entire three-qubit system. The result of Alice’s measurements will be a two-bit classical number. For example, she might measure 00, 01, 10, or 11. Crucially, the act of measuring her qubits changes their state, destroying the original quantum state $|\sigma\rangle$ from her qubit $s$. So there is no copying involved, only a transfer of information.
Because the original state $|\sigma\rangle$ has been encoded into the entangled system, Bob’s qubit $b$ is now in one of four possible states, but Bob doesn’t know which one! He is now waiting for Alice to tell him her measurement. The only way for her to do this is through classical communication, like sending a radio signal. This communication is limited by the speed of light, which is why quantum teleportation cannot be used for faster-than-light communication.
🔮 Bob’s Recovery
Once Bob receives Alice’s two classical bits, he knows exactly which of the four possible states his qubit is in. Depending on the two bits he receives, he applies either the Identity (I), X, Z, or XZ gate to his qubit $b$. The specific gate he applies undoes the quantum transformation that was applied to his qubit in the previous step. The result is that Bob’s qubit is now in the exact state $|\sigma\rangle$ that Alice’s qubit started with on Earth. The state has been teleported from Alice’s lab to Bob’s lab!
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Glassner, Andrew. Quantum Computing: From Concepts to Code. No Starch Press, 2025.
More Topics
- The Quantum Threat: How Shor’s Algorithm Puts Modern Encryption at Risk
- Cracking the Code: How Quantum Parallelism Solves Deutsch’s Problem in One Step
- The Deutsch-Jozsa Algorithm: An Exponential Leap in Quantum Problem Solving
- The Bernstein-Vazirani Algorithm: Unmasking a Secret With a Single Query
- Simon’s Algorithm: The First Quantum Speedup That Left Classical Computers in the Dust
- Your First Quantum Program: The ‘Hello, World!’ of a Qubit
- Scaling Up: How Quantum Computers Handle Multiple Qubits
