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Journal of Shenyang Normal University

EPR pairs of particles and quantum teleportation

Yue Zhang

Published Jan 1, 2012• 0 citations

Abstract

Teleporting a quantum state,the sender Alice disassembles the entire informations into two parts: one purely classical information and the another purely non-classical information,then sends them to the receiver Bob via two different channels.Firstly,sending the purely non-classical part,the EPR pair which consists of two fermions with the spin of 1 2 here plays the key role in the teleportation,one EPR particle is given to Alice,while the other is given to Bob.Alice performs a complete measurement of the von Neumann type on the joint system consisting of the original particle and her EPR particle,this measurement performed in the four eigenstates of the Bell operator leads to collapse the wave packet of the joint wavefunction into the four correlated Bell bases.Through applying the appropriate unitary transformation to the state of his EPR particle Bob can reconstruct a replica of the original state destroyed in Alice's hand.Moreover,this Bell measurement produces two bits of classical information which is sent to Bob,a quantum teleportation is therefore completed.The paper studies the interior relation between EPR pairs of particles and the quantum teleportation.

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Teleporting a quantum state,the sender Alice disassembles the entire informations into two parts: one purely classical information and the another purely non-classical information,then sends them to the receiver Bob via two different channels.Firstly,sending the purely non-classical part,the EPR pair which consists of two fermions with the spin of 1 2 here plays the key role in the teleportation,one EPR particle is given to Alice,while the other is given to Bob.Alice performs a complete measurement of the von Neumann type on the joint system consisting of the original particle and her EPR particle,this measurement performed in the four eigenstates of the Bell operator leads to collapse the wave packet of the joint wavefunction into the four correlated Bell bases.Through applying the appropriate unitary transformation to the state of his EPR particle Bob can reconstruct a replica of the original state destroyed in Alice's hand.Moreover,this Bell measurement produces two bits of classical information which is sent to Bob,a quantum teleportation is therefore completed.The paper studies the interior relation between EPR pairs of particles and the quantum teleportation.

Quantum mechanics shows superiority than classical mechanics in many aspects and quantum entanglement plays an essential role in information processing and some computational tasks such as quantum teleportation (QT). QT was proposed to transmit the unknown states, in which EPR pairs, the entangled states, can be used as quantum channels. In this paper, we present two simple schemes for teleporting a product state of two arbitrary single-particle and an arbitrary two-particle pure entangled state respectively. Alice and Bob have shared an entangle state. Two Bell states are used as quantum channels. Then after Alice measuring her qubits and informing Bob her measurement results, Bob can perfectly reconstruct the original state by performing corresponding unitary operators on his qubits. It shown that a product state of two arbitrary single-particle and an arbitrary two-particle pure entangled state can be teleported perfectly, i.e. the success probabilities of our schemes are both 1.

A scheme to teleport an unknown two qubit state from Alice (the sender) to Bob (the receiver) using two Einstein Podolsky Rosen (EPR) pairs is presented, each EPR pair being shared by both Alice and Bob. Firstly, Alice combines each of the two particles in the teleported state with an EPR particle and makes Bell state measurement on each combination. Then she transmits the outcomes of her measurements to Bob classically. According to Alice′s measurement results, Bob can perform appropriate unitary operations on his two EPR particles to retrieve the initial state.

Summary form only given. Characterizing the entanglement of a general bipartite quantum system is a difficult problem. Most measures involve difficult extremizations and their physical motivation is not always clear. In this paper we propose an experimental measure of entanglement based on a modified version of the familiar teleportation protocol of Bennett et al. (1993). Briefly, teleportation traditionally involves two parties, Alice and Bob. Initially, Alice has a qubit in an unknown quantum state which she would like to communicate to Bob and Bob has two qubits in an entangled Einstein-Podolsky-Rosen (EPR) pair. To accomplish this transfer, Bob shares one qubit of his EPR pair with Alice. She then performs a joint measurement or Bell measurement on her two qubits and relays this information back to Bob over a classical channel. Bob then uses the outcome of Alice's Bell measurement to transform his qubit, with a local unitary transformation, into the original quantum state, always with a fidelity of one.

The teleportation of an arbitrary n -particle state is proposed if n pairs of identical EPR states are utilized as quantum channels. Independent Bell state measurements are performed for joint measurement. By using a special Latin square of order , explicit expressions of outcomes after the Bell state measurements by Alice (sender) and the corresponding unitary transformations by Bob (receiver) can be derived. It is shown that the teleportation of n -particle state can be implemented by a series of single-qubit teleportation.

The teleportation of an arbitrary n-particle state (n ≥ 1) is proposed if n pairs of identical EPR states are utilized as quantum channels. Independent Bell state measurements are performed for joint measurement. By using a special Latin square of order 2n(n ≥ 1), explicit expressions of outcomes after the Bell state measurements by Alice (sender) and the corresponding unitary transformations by Bob (receiver) can be derived. It is shown that the teleportation of n-particle state can be implemented by a series of single-qubit teleportation.

A scheme for controlled teleportation of an arbitrary two-particle state using a maximally entangled EPR pair and a cluster state as the quantum channel is proposed.After receiving Alice's Bell state measurement results, the controller performs a joint measurement on his particles under a non-maximally entangled Bell-basis.The receiver needs to introduce an auxiliary qubit,and performs a series of appropriate unitary transformations on his particles.The original state can be teleported successfully with the probability 2 cos2 9.