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Quantum Teleportation: Difference between revisions
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This [https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.70.1895 example protocol] performs the task of | This [https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.70.1895 example protocol] performs the task of quantum teleportation by which a quantum state (or information stored in a quantum state) can be transmitted physically from one location (or one party) to another. This protocol requires sharing an [[entangled state]] like an [[EPR pair]] between two parties and also allowing the parties to communicate classically (sending bits of information). Quantum Teleportation can be treated as a send/receive scheme for qubits. Quantum teleportation provides a mechanism of sending an unknown qubit from one location to another, without physically moving the particle. This task can be done due to the existence of long-range correlations between entangled pairs. The quantum teleportation is used widely as a basic protocol in many other quantum communication and quantum cryptography protocols. | ||
</br></br> | </br></br> | ||
'''Tags:''' [[:Category: Building Blocks|Building Blocks]], teleportation, quantum communication, sending quantum information, send/receive in the quantum network, [[:Category: Quantum Functionality|Quantum Functionality]], [[:Category: Specific Task|Specific Task]] | '''Tags:''' [[:Category: Building Blocks|Building Blocks]], teleportation, quantum communication, sending quantum information, send/receive in the quantum network, [[:Category: Quantum Functionality|Quantum Functionality]], [[:Category: Specific Task|Specific Task]] | ||
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* There is no transfer of matter or energy involved. Sender's particle has not been physically moved to Receiver; only the particle's state has been transferred | * There is no transfer of matter or energy involved. Sender's particle has not been physically moved to Receiver; only the particle's state has been transferred | ||
==Outline== | ==Outline== | ||
The quantum teleportation protocol begins with a quantum state or qubit, in the possession of the first party ( | The quantum teleportation protocol begins with a quantum state or qubit, in the possession of the first party (the sender). We need this quantum state to be transferred to the second party (the receiver). This state is unknown to both parties meaning that the Sender does not know the representation of the qubit on any basis. Before starting the protocol the two parties must share an entangled state (for example an [[EPR pair]]). The entangled state here is a two-qubit state where each party has one share of these qubits which have a special [[quantum correlation]]. After sharing the entangled state, the parties can take an arbitrary distance (In theory, without any noise and by assuming that the entanglement can be held for an arbitrary distance which is not the case in the real experiments). After this preparation stage, the two parties will perform the protocol as follows:</br> | ||
* At Sender's location, a Bell measurement of the EPR pair qubit and the qubit to be teleported is performed, yielding one of four measurement outcomes, which can be encoded in two classical bits of information. Both qubits at Sender's location are then discarded. | * At Sender's location, a Bell measurement of the EPR pair qubit and the qubit to be teleported is performed, yielding one of four measurement outcomes, which can be encoded in two classical bits of information. Both qubits at Sender's location are then discarded. | ||
* Using the classical channel, the two bits are sent from Sender to Receiver. | * Using the classical channel, the two bits are sent from Sender to Receiver. | ||
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* The teleportation protocol uses entanglement (or entangled EPR states) as a resource. | * The teleportation protocol uses entanglement (or entangled EPR states) as a resource. | ||
* The teleportation protocol is secure against cloning attacks, as a result of [[no-cloning theorem]] in quantum mechanics i.e. any of the involved states in the protocol cannot perfectly be copied. Also, any other interference will affect the shared state between the two parties and the attack will be discovered. | * The teleportation protocol is secure against cloning attacks, as a result of [[no-cloning theorem]] in quantum mechanics i.e. any of the involved states in the protocol cannot perfectly be copied. Also, any other interference will affect the shared state between the two parties and the attack will be discovered. | ||
* The teleportation protocol is secure against entanglement attacks because of the [[ | * The teleportation protocol is secure against entanglement attacks because of the [[monogamy of entanglement]] in quantum mechanics. It means that if an adversary tries to entangle her state with the shared EPR pair, the amount of the entanglement of the shared state between two parties will change and the attacker will be discovered. | ||
* The size of the classical information sent by the Sender to the Receiver is infinitely smaller than the information required to give a classical description of the teleported quantum state. | * The size of the classical information sent by the Sender to the Receiver is infinitely smaller than the information required to give a classical description of the teleported quantum state. | ||
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# The sender(A) performs a local measurement on two qubits that she has (the original state and her share of the EPR pair) in the Bell basis. | # The sender(A) performs a local measurement on two qubits that she has (the original state and her share of the EPR pair) in the Bell basis. | ||
# The output of this measurement will be one of the four Bell states: | # The output of this measurement will be one of the four Bell states: <math>|\Phi^+\rangle</math>, <math>|\Phi^-\rangle</math>, <math>|\Psi^+\rangle</math> and <math>|\Psi^-\rangle</math></br></br> | ||
'''<u>Stage 3</u>''' Send classical information | '''<u>Stage 3</u>''' Send classical information | ||
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# '''if''' the result is <math>|\Psi^+\rangle \rightarrow</math> Receiver's state will be: <math>\beta |0\rangle + \alpha |1\rangle</math> | # '''if''' the result is <math>|\Psi^+\rangle \rightarrow</math> Receiver's state will be: <math>\beta |0\rangle + \alpha |1\rangle</math> | ||
# '''if''' the result is <math>|\Psi^-\rangle \rightarrow</math> Receiver's state will be: <math>\beta |0\rangle - \alpha |1\rangle</math> | # '''if''' the result is <math>|\Psi^-\rangle \rightarrow</math> Receiver's state will be: <math>\beta |0\rangle - \alpha |1\rangle</math> | ||
* The receiver will perform following | * The receiver will perform following operators on the above states: | ||
# '''if''' he receives <math>00 \rightarrow</math> he performs <math>I</math> (does nothing) | # '''if''' he receives <math>00 \rightarrow</math> he performs <math>I</math> (does nothing) | ||
# '''if''' he receives <math>01 \rightarrow</math> he performs <math>Z</math>([[Pauli Z]]) | # '''if''' he receives <math>01 \rightarrow</math> he performs <math>Z</math> ([[Pauli Z]]) | ||
# '''if''' he receives <math>10 \rightarrow</math> he performs <math>X</math>([[Pauli X]]) | # '''if''' he receives <math>10 \rightarrow</math> he performs <math>X</math> ([[Pauli X]]) | ||
# '''if''' he receives <math>11 \rightarrow</math> he performs <math>ZX</math> (Pauli X then a Pauli Z) | # '''if''' he receives <math>11 \rightarrow</math> he performs <math>ZX</math> (Pauli X then a Pauli Z) | ||
*As a result, the state of the receiver will be: <math>|\psi\rangle_B = \alpha|0\rangle + \beta |1\rangle</math> | *As a result, the state of the receiver will be: <math>|\psi\rangle_B = \alpha|0\rangle + \beta |1\rangle</math> | ||