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Journal of Physics B Atomic Molecular and Optical Physics

Economical and feasible controlled teleportation of an arbitrary unknownN-qubit entangled state

Zhong‐Xiao Man, Yun‐Jie Xia, Nguyen Ba An

Published Apr 30, 2007• 29 citations
Publisher

Abstract

We propose a new quantum protocol to teleport an arbitrary unknown N-qubit entangled state from a sender to a fixed receiver under the control of M (M < N) controllers. In comparison with other existing protocols, ours is more economical and more feasible. The quantum resource required is just M Greenberger–Horne–Zeilinger trios plus (N − M) Einstein–Podolsky–Rosen pairs. The techniques required are only N Bell measurements by the sender, a von Neumann measurement by a controller and N single-qubit transformations by the receiver. The rule for the receiver to reconstruct the desired state is derived explicitly in the most general case.

DOI
10.1088/0953-4075/40/10/011

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We propose a new quantum protocol to teleport an arbitrary unknown N-qubit entangled state from a sender to a fixed receiver under the control of M (M < N) controllers. In comparison with other existing protocols, ours is more economical and more feasible. The quantum resource required is just M Greenberger–Horne–Zeilinger trios plus (N − M) Einstein–Podolsky–Rosen pairs. The techniques required are only N Bell measurements by the sender, a von Neumann measurement by a controller and N single-qubit transformations by the receiver. The rule for the receiver to reconstruct the desired state is derived explicitly in the most general case.
We present a (t, n) threshold multiparty controlled quantum teleportation protocol of an arbitrary m-qubit quantum state between two remote parties. The unknown m-qubit quantum state can be recovered by the receiver under control of a subset of the n controllers if the number of the subset is larger than or equal to a threshold, say, t, but not for any t – 1 or fewer controllers. Our scheme seems to be more practical and more flexible than other existing protocols. The quantum resource required is just m Einstein–Podolsky–Rosen (EPR) pairs plus some single photons. The techniques required are only Bell state measurement, single-qubit unitary operation and von Neumann measurement. So our scheme is also feasible with present-day technique.
A general scheme for controlled teleportation of an arbitrary multi-qudit state with d -dimensional Greenberger–Horne–Zeilinger (GHZ) states is proposed. For an arbitrary m -qudit state, the sender Alice performs m generalized Bell-state projective measurements on her 2 m qudits and the controllers need only take some single-particle measurements. The receiver Charlie can reconstruct the unknown m -qudit state by performing some single-qudit unitary operations on her particles if she cooperates with all the controllers. As the quantum channel is a sequence of maximally entangled GHZ states, the intrinsic efficiency for qudits in this scheme approaches 100% in principle.
A scheme of M -party controlled teleportation for one N -qubit entangled W state via ( N -1) Einstein–Podolsky–Rosen (EPR) pairs and one ( M +2)-qubit Greenberger–Horne–Zeilinger (GHZ) state is proposed. We achieve the teleportation in such a way that M agents can execute the Hadamard transformation, perform the measurement on their qubits and inform the receiver of their measurements. Then we discuss that the receiver cannot fully recover the state from the sender if one agent does not co-operate with him.
A general scheme for controlled teleportation of an arbitrary single-qubit state with four-qubit asymmetric state is proposed.In this scheme, the sender performs Bell measurement on his particle, the two controllers and the receiver perform joint unitary operation on the rest particles.Finally, the receiver can reconstruct the single particle by introducing an auxiliary particle, he first does unitary transformation on his particle and the auxiliary particle, then performs a Von Neumann measurement on the auxiliary particle.Thus the scheme can be realized in certain probability.
Recently, there is much interest in the study of quantum teleportation. Its marvelous security property makes it particularly attractive as potential means for future communication. Uncertain principal and no-cloning theories of quantum mechanics forbid exact copy of quantum states. To solve the problem, quantum teleportation devides message state into two parts: classical message and quantum message which are transmitted through relevant classical and quantum channels from a sender Alice to a distant receiver Bob, respectively. According to both message states, Bob can recover the original message state with certain possibility. Utilizing the general quantum teleportation protocol, in this scheme, a new method is presented by which multi-qubit quantum information can be teleported in a much easier way. It has been extended to teleportation of an arbitrary N-qubit state via entanglement swapping and probabilistic teleportation is investigated as well, which has a more general meaning. N non-maximally entangled triplet GHZ states (Greenberger-Home-Zeilinger), taking the place of the previous EPR states (Einstein-Podolsky-Rosen), serve as quantum channels, which avoids introducing extra auxiliary qubit. In order to complete the teleportation, Alice has to devide all qubits into N parts and make Bell-State measurement on qubit pair (i, x(subscript i)) and tell Bob the measurement result through classical channel, then Bob perform some simple local operations on qubits (y(subscript i), z(subscript i)) to finish teleporting the i-th qubit. Conditioned on N-times similar repeat, Bob can faithfully reconstruct the initial state. Results show that, in this method, the identification difficulty of entangled states is considerably reduced, the new method is more feasible in technique. And the total possibility of successful teleportation is (The equation is abbreviated). As a special case, teleportation of an arbitrary two-qubit state is proposed.