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International Journal of Theoretical Physics

Methods of Constructing Quantum Channels for Teleporting a General Two-qubit State

Xiu-Lao Tian, Ming‐Liang Hu, Xiao-Qiang Xi

Published May 27, 2009• 5 citations
Publisher
DOI
10.1007/s10773-009-0048-4

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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
According to the collapse principle of quantum state when being measured, we present a method of directly writing out transformation matrix by looking at the figure of a network-controlled quantum channel. We find the rule of constructing transformation matrix in network-controlled teleportation. Based on this method, we gain transformation matrix of two-qubit state teleportation in which two GHZ state act as controlled quantum channels. We further proposed a scheme of one-qubit teleportation by a series-controlled quantum channel and teleportation of three-qubit via a typical network controlled quantum channel, in which two-qubit state instead of GHZ state act as quantum channel. So, Hadamard operation is not necessary in our scheme.
Teleportation of an arbitrary single-qubit state using two partially entangled states is considered.Firstly,we present a method for realizing probabilistically two-destination teleportation by using two partially entangled pairs as quantum channel.Then,we put forward a scheme for realizing deterministic and exact teleportation by using same quantum channel.In these schemes,the sender's local generalized measurement described by a positive operator valued measurement(POVM) lies at the heart.We construct the required POVM.The methods are applicable to any two partially entangled pairs satisfying the condition that their smaller Schmidt coefficients μ and v are 2μ+2μv-2v-1≥0.