What is the Quantum Teleportation Algorithm?
Quantum Teleportation is a protocol that enables the transfer of quantum information from one quantum system to another, even if they are physically separated. This algorithm is crucial for quantum communication and quantum networking protocols. It is a technique that transfers quantum information from one location to another without physically moving the particle. It uses entangled states, which allow for the instantaneous transfer of information, to transport quantum information.
Below is a short video showing how the circuit looks for the 3-Qubit Selection with the option to set the parameters α and β with the condition α + β = 1 to be satisfied.
Process of Teleportation?
In quantum teleportation, entanglement in the Bell state (EPR pair) is utilized to transfer an arbitrary quantum state between two distant observers, often referred to as Alice and Bob. Quantum teleportation does not involve physically transferring information; instead, it involves transferring the state of the information. This concept is crucial in quantum networking and provides a means of transporting information that is otherwise very difficult to transport between two extremely distant locations, whether on Earth or across the universe.
The process of quantum teleportation starts with an entangled pair of particles shared between two parties, usually called Alice and Bob. Alice aims to teleport the state of a qubit to Bob. She performs specific measurements on her particles and sends the results to Bob through classical communication. Bob can then use this information to apply certain operations to his entangled particle, recreating the exact state that Alice intended to teleport.
The simplest quantum teleportation circuit requires only three qubits. Alice puts her qubit into a quantum superposition using what is known as a Hadamard gate, and then she entangles her qubit with Bob’s qubit using what is called a controlled-NOT gate. Alice then takes a third qubit, which has the quantum state to be teleported, and she entangles that qubit with her qubit. She then measures her two qubits in two different bases, which destroys her quantum information but gives her the classical information she needs to provide to Bob. Upon receipt, Bob uses the classical information to perform operations on his qubit that then allows him to use the teleported quantum state for whatever purposes. Because Bob had to wait for the classical information to arrive, no physics laws were violated.
Quantum teleportation allows transferring the unknown quantum state of a qubit (sender, Alice) to another qubit (receiver, Bob) at a distant location. While it doesn’t involve physically transmitting the qubit itself, it leverages the power of entanglement and classical communication to achieve this feat.
1. Initial State:
Alice has a qubit in an unknown state represented by:
|ψ⟩_A = α |0⟩_A + β |1⟩_A
where α and β are complex coefficients determining the state’s superposition.
Alice and Bob share a pre-established entangled pair of qubits:
|Φ⟩_AB = (|00⟩_AB + |11⟩_AB) / √2
This Bell state represents the entanglement between Alice’s qubit (A) and Bob’s qubit (B).
2. Bell State Measurement (BSM):
Alice performs a Bell state measurement (BSM) on her qubit (A) and one qubit from the entangled pair (B). This can be represented by a set of projectors onto the Bell states:
P(Φ+) = |Φ+⟩_AB ⟨Φ+|
P(Φ-) = |Φ-⟩_AB ⟨Φ-|
P(Ψ+) = |Ψ+⟩_AB ⟨Ψ+|
P(Ψ-) = |Ψ-⟩_AB ⟨Ψ-|
The specific outcome of the BSM determines the joint state of Alice’s remaining qubit and Bob’s qubit.
3. Classical Communication:
Alice transmits the outcome of the BSM (which Bell state was measured) to Bob via classical communication (e.g., phone call). This communication doesn’t transmit any quantum information itself, but it’s crucial for Bob to perform the correct operation on his qubit.
4. Bob’s Operation (Pauli Corrections):
Based on the classical information received from Alice, Bob applies one of the Pauli X (σ_x), Y (σ_y), or Z (σ_z) operators to his qubit to recover the original state:
- If Alice measured |Φ+⟩, Bob does nothing (identity operation).
- If Alice measured |Φ-⟩, Bob applies the Z-gate (σ_z).
- If Alice measured |Ψ+⟩, Bob applies the X-gate (σ_x).
- If Alice measured |Ψ-⟩, Bob applies both X (σ_x) and Z (σ_z) gates sequentially.
These Pauli corrections manipulate Bob’s qubit to match the original state Alice was trying to teleport.
5. Final State:
After Bob applies the correction based on the BSM outcome, the final state ideally becomes:
|ψ⟩_B = α |0⟩_B + β |1⟩_B
This represents successful teleportation, where the unknown state of Alice’s qubit has been transferred to Bob’s qubit at a distance.
Potential Usage/Applications of Quantum Teleportation:
Although quantum teleportation may seem far-fetched, it has been experimentally demonstrated and holds potential for various practical applications. Several potential uses of quantum teleportation include:
QUANTUM INTERNET:
A quantum internet could be developed through quantum teleportation. This would provide ultra-secure communication and enable the distribution of quantum information worldwide. Consequently, it could result in the connection of quantum computers, creating a network of quantum nodes for secure data transmissions and distributed quantum computation by teleporting quantum states across long distances.
QUANTUM SENSING & METROLOGY:
Quantum teleportation could enhance the precision and sensitivity of quantum sensors and metrology devices. By teleporting quantum states of particles, such as atoms or photons, it may be possible to improve gravimetric, magneto metric, and timekeeping measurements through quantum-enhanced measurements.
QUANTUM COMMUNICATION:
The principle of quantum teleportation can be utilized to create secure communication channels between two individuals. By using photons as quantum carriers, it is feasible to establish secure quantum key distribution (QKD), ensuring eavesdropper-proof encryption keys.