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arXiv:quant-ph/0001052 · Physical Review A

Canonical quantum teleportation

Sixia Yu, Chang-Pu Sun

Published Jan 18, 2000• 28 citations
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Abstract

Canonically conjugated observables such as position and momentum and phase and number are found to play a threefold role in quantum teleportation. First, the common eigenstate of two commuting canonical observables like phase difference and number sum provides the quantum channel between two systems. Second, a similar pair of canonical observables from another two systems is measured in the Bell-operator measurements. Finally, two translations generated by the canonically conjugated observables of a single system constitute the local unitary operation to recover the unknown state. In addition, the necessary and sufficient condition is presented for a reliable quantum teleportation of finite-level systems.

DOI
10.1103/physreva.61.022310

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Canonically conjugated observables such as position and momentum and phase and number are found to play a threefold role in quantum teleportation. First, the common eigenstate of two commuting canonical observables like phase difference and number sum provides the quantum channel between two systems. Second, a similar pair of canonical observables from another two systems is measured in the Bell-operator measurements. Finally, two translations generated by the canonically conjugated observables of a single system constitute the local unitary operation to recover the unknown state. In addition, the necessary and sufficient condition is presented for a reliable quantum teleportation of finite-level systems.
Two different teleportation protocols are investigated by using two pairs of canonically conjugated observables such as position-momentum and phase-number. The discrete variable and continuous variable quantum teleportation are unified in the framework of canonical quantum teleportation. Canonically conjugated observables are found to play a 3-fold role in the quantum teleportation. Firstly, the common eigenstate of two commuting canonical observables like phase-difference and number-sum provides the quantum channel between two systems. Secondly, a similar pair of canonical observables from another two systems is measured in the Bell operator measurements. Finally, two translations generated by the canonically conjugated observables of a single system constitute the local unitary operation to recover the unknown state.
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.
Two schemes of teleporting an N-particle arbitrary and unknown state are proposed when N groups of three-particle general W states are utilized as quantum channels. In the first scheme, the quantum channels are shared by the sender and the recipient. After the sender's Bell-state measurements on his (her) particles, the recipient carries out unitary transformations on his (her) particles. And then, the recipient performs computational basis measurements to realize the teleportation. The recipient can recover the state on either of particle sequences with the equal maximal probability of successful teleportation if he (she) performs appropriate unitary transformations. In the second scheme, the quantum channels are shared by the sender, the recipient and the third ones. After the sender's Bell-state measurements and the third ones' computational basis measurements if they agree to cooperate, the recipient will introduce auxiliary particles and carry out appropriate unitary transformations. Finally, the recipient performs computational basis measurements to fulfill the teleportation. The second scheme can be realized if and only if the third ones agree to cooperate with the recipient.