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International Symposium on Computer Network and Multimedia Technology

Probabilistic Teleportation of an Arbitrary d-Level n-Particle (n-Qudit) State

Liying Shangguan, Hongxiang Sun, Qiaoyan Wen, Fu-Chen Zhu

Published Dec 1, 2009• 0 citations
Publisher

Abstract

Utilizing partially entangled states as a shared resource, a protocol for the probabilistic teleportation of an arbitrary n-qudit state is proposed in detail. It's more valuable than the research for the teleportation of any other special states. Meanwhile, we summarize the d2nkinds of states with a very concise formula after performing Bell-state measurements by the sender. All different unitary transformations by the receiver are also generalized with a concise matrix.

DOI
10.1109/cnmt.2009.5374506

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Utilizing partially entangled states as a shared resource, a protocol for the probabilistic teleportation of an arbitrary n-qudit state is proposed in detail. It's more valuable than the research for the teleportation of any other special states. Meanwhile, we summarize the d2nkinds of states with a very concise formula after performing Bell-state measurements by the sender. All different unitary transformations by the receiver are also generalized with a concise matrix.
Utilizing the construction of a diagonal projection transformation matrix, a scheme for probabilistic teleportation of an arbitrary n-qudit state is provided via partially entangled states. In addition, we investigate that the total system of particles can be expanded by Bell bases and transformation operators. Not only are the relations between transformation operators and the unitary matrixes performed by the receiver are generalized with a concise formula, but also the diagonal projection transformations. Taking the teleportation of an unknown three-qutrit state as example, it is discussed in great detail.
A scheme for teleporting an arbitrary and unknown three-particle state from a sender to either one of two receivers is proposed. The quantum channel is composed of a two-particle non-maximally entangled state and two three-particle non-maximally entangled W states. An arbitrary three-particle state can be perfectly teleported probabilistically if the sender performs three generalized Bell-state measurements and sends to the two receivers the classical result of these measurements and either one of the two receivers adopts an appropriate unitary transformation conditioned on the suitable measurement outcomes of the other receiver. All kinds of unitary transformations are given in detail.
Quantum teleportation is a unique quantum information processing method in quantum communication. Researchers have shown considerable interest in hierarchically controlled teleportation by using quantum entangled states as the quantum channel. Protocols for the hierarchically controlled teleportation of an arbitrary single-qubit via a four-qubit χ state and a four-qubit cluster state have been proposed. We present a protocol for the hierarchically controlled teleportation of an arbitrary m-qudit (d-dimensional quantum system) state by using a partially entangled quantum state as the quantum channel. The sender performs m generalized Bell-state measurements on her 2m particles. To reconstruct the original state, the upper-grade receiver only needs to apply a unitary operation in accordance with one of the receivers’ measurement results, and the lower-grade receivers need to perform a unitary operation according to all the other receivers’ measurement results. The receivers can reconstruct the original state probabilistically by introducing an auxiliary qubit and performing a collective unitary transformation. The protocol has the advantage of having high channel capacity by using a high-dimensional entangled state as the quantum channel.
Four partially entangled two-particle states are used as the quantum channel.Two schemes for probabilistic teleportation of an arbitrary four-particle entangled state are presented.The entangled state can be perfectly teleported probabilistically from the sender to the receiver if the sender performs four Bell-state measurements while the receiver introduces auxiliary particles and performing appropriate unitary transformations.Based on transformation operator,the theoretical explanation of two schemes is given by utilizing the relation of the transformation operators.