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arXiv:2204.01714

Quantum teleportation between two quantum spin Hall insulator rings

Thiago Prudêncio

Published Apr 3, 2022• 0 citations
arXivHTMLPDF

Abstract

A quantum teleportation between two quantum spin Hall insulator (QSHI) rings is proposed. A qubit state is generated in the first QSHI ring and the second is used as a quantum channel in entangled QSHI state. In the intersection of outer edges is placed a joint detector, allowing a Bell state analysis. After the Bell state measurement, Alice, that is composed originally of a qubit in the first QSHI ring and one spin state in the second QSHI ring, allows Bob, that is composed of the other spin edge state in the second QSHI ring, to realize the corresponding control of the tunneling amplitudes in the second QSHI ring, what implements a complete quantum teleportation between the QSHI rings. It is also showed that Bob's table, used after the classical communication by Alice, is the same independently the way the qubit is generated in the first QSHI ring. This description indicates that a quantum teleportation can be fully implemented in the context of two-dimensional (2D) topological edge states and opens perspectives in the scenario of quantum information in topological matter, decoherence free systems, as well as for the development of quantum technologies associated to spintronics and quantum computation.

DOI
10.48550/arxiv.2204.01714

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A quantum teleportation between two quantum spin Hall insulator (QSHI) rings is proposed. A qubit state is generated in the first QSHI ring and the second is used as a quantum channel in entangled QSHI state. In the intersection of outer edges is placed a joint detector, allowing a Bell state analysis. After the Bell state measurement, Alice, that is composed originally of a qubit in the first QSHI ring and one spin state in the second QSHI ring, allows Bob, that is composed of the other spin edge state in the second QSHI ring, to realize the corresponding control of the tunneling amplitudes in the second QSHI ring, what implements a complete quantum teleportation between the QSHI rings. It is also showed that Bob's table, used after the classical communication by Alice, is the same independently the way the qubit is generated in the first QSHI ring. This description indicates that a quantum teleportation can be fully implemented in the context of two-dimensional (2D) topological edge states and opens perspectives in the scenario of quantum information in topological matter, decoherence free systems, as well as for the development of quantum technologies associated to spintronics and quantum computation.
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.
A scheme of two-way teleportation was proposed,with GHZ quadripartite entangled state as quantum channel.Two sides of communication(Alice and Bob) shared two pairs of GHZ quadripartite entangled state in advance.After communication,Alice and Bob performed quantum projection measurement on their own qubits respectively,and announced the measured results via classical channel.Then according to the measured results presented by the other party,Alice and Bob can make appropriate unitary transformations that its own party can reconstruct the opposite quantum state information,and thus the whole two-way teleportation was realized.As long as the both sides of communication chose the suitable GHZ entangled state as quantum channel and distributed the entangled partites imparity and properly in advance,two-way teleporting including unknown general one qubit and two qubits entangled Bell state or three qubits entangled GHZ state could be realized respectively.
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.
We consider a scheme for on-demand teleportation of a dual-rail electron qubit state, based on single-electron sources and detectors. The scheme has a maximal efficiency of 25%, which is limited both by the shared entangled state as well as the Bell-state measurement. We consider two experimental implementations, realizable with current technology. The first relies on surface acoustic waves, where all the ingredients are readily available. The second is based on Lorentzian voltage pulses in quantum Hall edge channels. As single-electron detection is not yet experimentally established in these systems, we consider a tomographic detection of teleportation using current correlators up to (and including) third order. For both implementations, we take into account environmental effects.
Quantum teleportation provides a way to transfer unknown quantum states from one system to another via an entangled state as a quantum channel without physical transmission of the object itself. The entangled channel, measurement performed by the sender (Alice), and classical information sent to the receiver (Bob) are three key ingredients in the procedure, which need to cooperate with each other. To study the relationship among the three parts, we propose a scheme for perfect teleportation of a qubit through a high-dimensional quantum channel in a pure state with two equal largest Schmidt coefficients. The scheme requires less entanglement of Alice's measurement but more classical bits than the original scheme via a Bell state. The two quantities increase with the entanglement of the quantum channel when its dimension is fixed and thereby can be regard as Alice's necessary capabilities to use the quantum channel. And the two capabilities appear complementary to each other.
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.