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International Journal of Theoretical Physics

Probabilistic Controlled Teleportation of Two-Particle Entangled State via the Optimal Quantum State

Yuan-Hong Tao, Juhua Zheng

Published Nov 8, 2012• 6 citations
Publisher
DOI
10.1007/s10773-012-1405-2

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Through a detailed study of nondestructive controlled quantum teleportation (NCQT) with two outputs in three-dimensional and high-dimensional Hilbert spaces, we propose an NCQT scheme that synchronously and probabilistically teleports N arbitrary unknown d-dimensional single-particle states from one sender to N different receivers under the supervision of a controller, by using a d-dimensional partially entangled (2N+1)-particle state as the quantum channel. The protocol succeeds if and only if all receivers recover their respective target states, and the optimal success probability of the N-output NCQT is determined by the minimum superposition coefficient of each product two-qudit state in the partially entangled channel. In our scheme, each receiver introduces an auxiliary qubit to assist in the local recovery test. When the auxiliary-qubit measurement outcome is |0⟩, the receiver can restore the target state; when the outcome is |1⟩, the corresponding unknown original state is retained by the sender. Accordingly, the N-output controlled teleportation process can be repeated as many times as additional quantum channels are available after a failed attempt. The results show that weakly entangled channels can still realize N-output controlled teleportation through sufficiently many repetitions, whereas strongly entangled channels require only a small number of repetitions to achieve the same goal.
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.
By eans of the primitive operations consisting of single-qubit gates.two-qubit controlled-not gates,Von Neuman measurement and classically controlled operations.,we construct efficient quantum logic networks for implementing probabilistic teleportation of a single qubit,a two-particle entangled state,and an N-particle entanglement.Based on the quantum networks,we show that after the partially entangled states are concentrated into maximal entanglement,the above three kinds of probabilistic teleportation are the same as the standard teleportation using the corresponding maximally entangled states as the quantum channels.