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arXiv:0707.1227

Quantum Teleportation and Von Neumann Entropy

You Hwan Ju, Eylee Jung, Mi-Ra Hwang, D. K. Park, Hung-Soo Kim, Minsoo Kim, Jin-Woo Son, Sahng-Kyoon Yoo, Sayatnova Tamaryan

Published Jul 9, 2007• 0 citations
arXivHTMLPDF

Abstract

The single qubit quantum teleportation (sender and receiver are Alice and Bob respectively) is analyzed from the aspect of the quantum information theories. The various quantum entropies are computed at each stage, which ensures the emergence of the entangled states in the intermediate step. The mutual information $S(B:C)$ becomes non-zero before performing quantum measurement, which seems to be consistent to the original purpose of the quantum teleportation. It is shown that if the teleported state $|ψ>$ is near the computational basis, the quantum measurement in $C$-system is dominantly responsible for the joint entropy $S(A,C)$ at the final stage. If, however, $|ψ>$ is far from the computational basis, this dominant responsibility is moved into the quantum measurement of system $A$. A possible extension of our results are briefly discussed.

DOI
10.48550/arxiv.0707.1227

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The single qubit quantum teleportation (sender and receiver are Alice and Bob respectively) is analyzed from the aspect of the quantum information theories. The various quantum entropies are computed at each stage, which ensures the emergence of the entangled states in the intermediate step. The mutual information S(B:C)S(B:C)S(B:C) becomes non-zero before performing quantum measurement, which seems to be consistent to the original purpose of the quantum teleportation. It is shown that if the teleported state ∣ψ>|ψ>∣ψ> is near the computational basis, the quantum measurement in CCC-system is dominantly responsible for the joint entropy S(A,C)S(A,C)S(A,C) at the final stage. If, however, ∣ψ>|ψ>∣ψ> is far from the computational basis, this dominant responsibility is moved into the quantum measurement of system AAA. A possible extension of our results are briefly discussed.
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.
In this article, the authors have discussed the Alice and Bob experimental set-up for the quantum teleportation, giving a detailed step-by step mathematical explanation of each unit. Quantum teleportation of a qubit requires the creation of an entangled quantum state between the sender’s (Alice) and the receiver’s (Bob) shared quantum state/s. At the end of this experiment, actual measurements of the Alice’s share of quantum information are to be taken and shared with Bob via a classical communication channel. The teleportation is expected to open up a whole new regime of quantum communication, data encryption to be one of its applications.
In this work, we consider two stages one qubit quantum teleportation protocol via an arbitrary entangled two qubits state. In the first stage, Alice use XOR gate and computational basis measurement, while for the second stage, Alice use Hadamard gate and another computational basis measurement. Alice sent measurement result to Bob via one classical bit each. As the result, we show that this teleportation can has unit fidelity if the channel used has non-zero two terms and maximally entangled. Then the protocol is applicable if the channel is one of four Bell's state.
It is shown that a maximally seven-qubit state can be utilized for perfect teleportation of arbitrary three qubit systems and controlled teleportation of an arbitrary three qubit state. For perfect teleportation, the sender first performs a Von-Neumann measurement on her qubits, then the sender(Alice) tells the measurement result to the receiver(Bob) via a classical channel, the receiver can reconstruct the original state by performing appropriate unitary transformations on his qubits at hand. For controlled teleportation, the sender firstly carries out proper Bell-state measurements and the controller(charlie) needs to operate a single-qubit measurement, the receiver can reconstruct the original state by applying appropriate unitary transformations on his qubits after he knows the measurement results of both the sender and controller. Besides, the two teleportation schemes can be realized with the maximal probability.
Abstract In this study, we propose an encrypted quantum teleportation broadcast scheme using a 6-qubit entangled channel and an encrypted quantum teleportation scheme with a controller via a 7-qubit entangled channel. The quantum state of Alice, to be transmitted, is first encrypted into two distinct states that satisfy certain conditions. As the main sender, Alice designates two agents to transmit encrypted states to two receivers. She shares a 6-qubit entangled state with each party and provides the receivers with a 1-bit classical information containing the chosen encryption. After the agents perform measurements on the corresponding orthogonal bases and send the results to the receivers, each receiver can reconstruct the original state sent by Alice. To enhance security for the receivers, the scheme introduces Alice as a controller. The receivers can reconstruct the original state only if Alice performs a measurement and shares her measurement outcome. The use of encryption ensures that even if an agent’s qubit is intercepted, the actual state remains secure. Alice, as the controller, can also terminate the transmission if a security threat is detected or she change her mind to finish the transmission. The teleportation performance depends on how the qubit is encrypted. For a specific input state used as an example, the protocol obtained a teleportation success probability of 0.9608.
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.