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Communications in Theoretical Physics

Controlled Probabilistic Teleportation of an Unknown Multi-Particle High-Dimensional Entangled State

Shi Jin, You-Bang Zhan

Published Jun 1, 2009• 7 citations
Publisher

Abstract

We propose a protocol for controlled probabilistic teleportation of an unknown tripartite qutrit entangled state with two partial tripartite qutrit entangled states as the quantum channel. It is found that teleportation associated with the generalized qutrit Bell-basis measurement, the generalized qutrit π-state measurement and the generalized Hadamard operator in three-dimensional Hilbert space. We generalize the protocol for controlled probabilistic teleportation of an unknown k-particle qudit entangled state with a multi-particle qudit entangled state and a tripartite qudit entangled state as the quantum channel. We also calculate the classical communication cost required in both cases.

DOI
10.1088/0253-6102/51/6/13

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We propose a protocol for controlled probabilistic teleportation of an unknown tripartite qutrit entangled state with two partial tripartite qutrit entangled states as the quantum channel. It is found that teleportation associated with the generalized qutrit Bell-basis measurement, the generalized qutrit π-state measurement and the generalized Hadamard operator in three-dimensional Hilbert space. We generalize the protocol for controlled probabilistic teleportation of an unknown k-particle qudit entangled state with a multi-particle qudit entangled state and a tripartite qudit entangled state as the quantum channel. We also calculate the classical communication cost required in both cases.
In this paper a scheme for controlled teleportation of arbitrary high-dimensional unknown quantum states is proposed by using the generalized Bell-basis measurement and the generalized Hadamard transformation. As two special cases, two schemes of controlled teleportation of an unknown single-qutrit state and an unknown two-qutrit state are investigated in detail. In the first scheme, a maximally entangled three-qutrit state is used as the quantum channel, while in the second scheme, an entangled two-qutrit state and an entangled three-qutrit state are employed as the quantum channels. In these schemes, an unknown qutrit state can be teleported to either one of two receivers, but only one of them can reconstruct the qutrit state with the help of the other. Based on the case of qutrits, a scheme of controlled teleportation of an unknown qudit state is presented.
In this paper,a protocol which can realize probabilistic quantum teleportation of an unknown classical tripartite W entangled state is proposed.Controlled probabilistic quantum teleportation of an unknown generic tripartite W entangled state with a non-maximal tripartite GHZ entangled state and a pair of non-maximal EPR entangled particles as the quantum channels can be realized too.The teleportation associates with the generalized Bell-basis measurement and the C-Not operate,respectively.After the base vector transformation,an auxiliary qubit which the initial state is in the zero state and the corresponding unitary transformation are included in this protocol.
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 present a scheme to teleport an unknown three-particle entangled state from a sender to either one of two receivers. The partial three-particle entangled state and the three-particle entangled W state are considered as the quantum channels. An unknown three-particle entangled state can be perfectly teleported probabilistically by performing two generalized Bell measurements and the Hadamard operation at the sender's side and introducing an appropriate unitary transformation in each receiver's laboratory conditioned on the simple measurement outcome of the other. All kinds of unitary transformations are given in details. This scheme can be directly generalized to teleport an unknown three-particle entangled state from a sender to any one of N receivers by the partial three-particle entangled state and the ( N + 1)-particle entangled W state.