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Journal of Xinjiang Normal University

Analysis of Hot Sports on High Dimensional Quantum Entangled States as Quantum Channel

Ju Jin

Published Jan 1, 2015• 0 citations
OpenAlex

Abstract

The hot content of quantum teleportation is analyzed,and two schemes are proposed to transmit an unknown single-qubit state by using 4-dimensional entangled state as the quantum channel. In the analysis,the two schemes can be seen if the Alice's measurement and the unitary operation of Bob are appropriate,the teleportation can be successfully realized with the maximal probability.

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The hot content of quantum teleportation is analyzed,and two schemes are proposed to transmit an unknown single-qubit state by using 4-dimensional entangled state as the quantum channel. In the analysis,the two schemes can be seen if the Alice's measurement and the unitary operation of Bob are appropriate,the teleportation can be successfully realized with the maximal probability.
In this paper, we present two different quantum teleportation schemes of an arbitrary single-particle, one is perfect teleportation and the other is probabilistic teleportation.In the first scheme, a four-particle maximally entangled state is used as the quantum channel.Besides, Bob needs to apply appropriate unitary transformations according to Alice's measurement results to recover the unknown state and the success probability is 1.In the latter scheme, the quantum channel is a four-particle non-maximally entangled state, which is a more general state.Furthermore, Bob needs to introduce an auxiliary qubit so that he can reconstruct the unknown state with the success probability of ( ).
We propose a quantum teleportation scheme for transmitting a single qutrit state by adopting a 2-qudit entangled state as the quantum channel. The measurement basis for Alice has been carefully and systematically constructed, which is essential for the successful implementation of the teleportation protocol. Based on Alice's measurement outcomes, we design the corresponding collective unitary transformations to be performed by Bob on an auxiliary qubit and information particle. After implementing the collective unitary transformation, Bob performs a von Neumann measurement on the auxiliary qubit. The single qutrit state is then teleported to the distant receiver Bob with a finite success probability. We obtain the achievable success probabilities of the proposed teleportation scheme for different quantum channels. The obtained results not only enrich the theory of quantum teleportation over high-dimensional entangled channels but also provide a novel and feasible approach to implementing qutrit teleportation.
Abstract The purpose of this article is to explore how to transmit low-dimensional unknown single-particle states in a multi-output manner through a high-dimensional entangled state as a quantum channel under the control of a supervisor. First, we construct a set of complete orthogonal non-symmetric bases in ( d × f ) -dimensional Hilbert space and a ( 2 N + 1 ) -qudit maximally entangled state in d -dimensional Hilbert space, taking a set of ( 3 × 2 ) -dimensional non-symmetric bases and a 3-dimensional 5-qutrit entangled state as their special cases, respectively. We then propose a controlled teleportation scheme, where by using the 3-dimensional 5-qutrit maximally entangled state as a quantum channel and employing the ( 3 × 2 ) -dimensional non-symmetric basis measurement, two 2-dimensional single-qubit states are simultaneously teleported through quantum teleportation technology under the control of a supervisor. Subsequently, the above maximally entangled quantum channel is replaced by a 3-dimensional 5-qutrit non-maximally entangled state, and two unknown single-qubit states are teleported, under the control of a supervisor, in such a way that they can be probabilistically reconstructed by introducing auxiliary qubits and performing appropriate operations. The success probabilities of the above two schemes are given, and the analysis shows that the scheme based on a non-maximally entangled channel is a generalization of the previous scheme. In addition, the above schemes can be extended from the following two perspectives: (a) the quantum channels can be extended from 3-dimensional to arbitrary d -dimensional; (b) the transmitted quantum information can be extended from 2-dimensional to any f -dimensional through d -dimensional entangled quantum channels ( f < d ).
We propose a method to realize the teleportation of an unknown entangled state that consists of many qudits through a partially entangled-qudit quantum channel with the help of 2log 2 d -bit classical communication. The operations used in the teleportation process include a generalized Bell-state measurement and a series of single-qudit π-measurements performed by Alice, a series of generalized qudit-Pauli gates and two-level unitary gates, as well as a qubit measurement performed by Bob. For a maximally entangled quantum channel, the successful probability of the teleportation becomes unit.
A bidirectional quantum controlled teleportation scheme using the entanglement property of six-qubit maximally entangled state was presented.In the theoretical scheme,the sixqubit maximally entangled state was employed as the quantum channel linking three legitimate participants.Users were both sender and receiver.Alice transmitted an arbitrary single qubit state of qubit ato Bob and Bob transmitted an arbitrary single qubit state of qubit bto Alice via the control of the supervisor Charlie.Users carried out the Bell state measurements on their own particles and publicly announced their measurement results via a classical channel.Then they operated proper unitary transformation on their own particles,respectively.The bidirectional quantum controlled teleportation was successfully realized.
Abstract The purpose of this paper is to explore how to teleport a low-dimensional (two-dimensional) arbitrary unknown two-qubit cat-like state through a high-dimensional entangled state constituting the quantum channel. We first present a scheme employing a maximally entangled three-qutrit state as the channel. Within this scheme, the sender performs a single-qubit projective measurement and a non-symmetric basis measurement on their particles. Based on these measurement outcomes, the receiver applies specific unitary operations to reconstruct the original cat-like state. Subsequently, the maximally entangled channel is replaced with a non-maximally entangled three-qutrit state. For this probabilistic teleportation scheme, the target state is reconstructed by introducing an auxiliary qubit and performing appropriate operations; the corresponding success probability is derived. Analysis indicates that the non-maximally entangled scheme generalizes the previous maximally entangled approach. Furthermore, both schemes are shown to be directly extendable to quantum channels formed by arbitrary high-dimensional entangled states.