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Indian Journal of Science and Technology

Entanglement identification of arbitrary two-qubit quantum channels and the capabilities to realise quantum teleportation

Lila Yuwana, Agus Purwanto, Endarko Endarko, Dwi Januriyanto

Published Nov 1, 2017• 3 citations
Publisher

Abstract

Objectives: To identify the entanglements of arbitrary two-qubit quantum channels and the capabilities to realise quantum teleportation. Methods: The implementation of Schmidt de composition and measurements of quantum system state are equiped in this research. Findings: By constructing the general form of an arbitrary two qubit and measurement state, we able to determine an entanglement of an arbitrary two qubit by utilising Schmidt decomposition. Next, a capability of an arbitrary two qubit entangled state to realise teleportation can be identified by formulating measurement state and unitary operator. Improvement: The methods used in this paper have relatively simple calculations and very beneficial to be implement before developing quantum teleportation system experimentally. Keywords: Entangled States, Quantum Channels, Qubit (Quantum Bit), Quantum Teleportation

DOI
10.17485/ijst/2017/v10i43/118480

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Objectives: To identify the entanglements of arbitrary two-qubit quantum channels and the capabilities to realise quantum teleportation. Methods: The implementation of Schmidt de composition and measurements of quantum system state are equiped in this research. Findings: By constructing the general form of an arbitrary two qubit and measurement state, we able to determine an entanglement of an arbitrary two qubit by utilising Schmidt decomposition. Next, a capability of an arbitrary two qubit entangled state to realise teleportation can be identified by formulating measurement state and unitary operator. Improvement: The methods used in this paper have relatively simple calculations and very beneficial to be implement before developing quantum teleportation system experimentally. Keywords: Entangled States, Quantum Channels, Qubit (Quantum Bit), Quantum Teleportation
Objectives: To formulate the most elementary requirement to realise quantum teleportation. Methods: By expanding procedure to define the capability of general two qubit quantum states to realise quantum teleportation. Findings: By structuring the general form of two qubit and measurement states, we can exhibit the capabilty both separable two qubit states and entangled two qubit states to realise quantum teleportation. Next, we also show the measurement procedure and the unitary operator required to reconstruct a single qubit delivered into correct state. Application/Improvement: The methods exhibited in this paper have relatively simple procedure and very beneficial to improve our last procedure proposed beforehand. Keywords: Entangled States, Separable States, Quantum Channels, Quantum Teleportation
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.
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.
Quantum information theory is a rapidly growing area of math and physics that combines two independent theories, quantum mechanics and information theory. Quantum entanglement is a concept that was first proposed in the EPR paradox. In quantum mechanics, particles can be in superposition, meaning they are in multiple different states at once. It is not until the particle is measured that it is forced into a single state. However, it is possible that particles can be tied to other particles, meaning that the measurement of one particle will determine the measurement of the other particle. Entanglement is at the very core of quantum information theory. It is one of the core pieces that allows for the massive increase in computing power. For this paper, we decided to focus on demonstrating the mathematical method (the Schmidt decomposition) for determining if a system is entangled, and a demonstration of quantum entanglement's use (quantum teleportation) as well as a quick look at how to extend the uses of the Schmidt decomposition.
Abstract Based on the four-qubit cluster state as quantum channel, we put forward a novel scheme for teleporting a two-qubit arbitrary entangled state. The necessary quantum operations for accomplishing the task are two controlled-not gate operations, one controlled-phase gate operation, four single-qubit measurements and two single-qubit transformed operations. They are easily achievable with current experimental techniques. Besides, the present scheme is deterministic because its probability of success is 100 % .