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arXiv:1703.01667 · Frontiers of Physics

Quantum teleportation and information splitting via four-qubit cluster state and a Bell state

Marlon David González Ramírez, B. J. Falaye, Guo-Hua Sun, M. Cruz‐Irisson, Shi‐Hai Dong

Published May 26, 2017• 31 citations

Abstract

Quantum teleportation provides a “bodiless” way of transmitting the quantum state from one object to another, at a distant location, using a classical communication channel and a previously shared entangled state. In this paper, we present a tripartite scheme for probabilistic teleportation of an arbitrary single qubit state, without losing the information of the state being teleported, via a fourqubit cluster state of the form | ϕ > 1234 = α |0000>+ β |1010>+ γ |0101>- η |1111>, as the quantum channel, where the nonzero real numbers α , β , γ , and η satisfy the relation j α j2 + | β | 2 + | γ | 2 + | η | 2 = 1. With the introduction of an auxiliary qubit with state |0>, using a suitable unitary transformation and a positive-operator valued measure (POVM), the receiver can recreate the state of the original qubit. An important advantage of the teleportation scheme demonstrated here is that, if the teleportation fails, it can be repeated without teleporting copies of the unknown quantum state, if the concerned parties share another pair of entangled qubit. We also present a protocol for quantum information splitting of an arbitrary two-particle system via the aforementioned cluster state and a Bell-state as the quantum channel. Problems related to security attacks were examined for both the cases and it was found that this protocol is secure. This protocol is highly efficient and easy to implement.

DOI: 10.1007/s11467-017-0684-8

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Quantum teleportation provides a “bodiless” way of transmitting the quantum state from one object to another, at a distant location, using a classical communication channel and a previously shared entangled state. In this paper, we present a tripartite scheme for probabilistic teleportation of an arbitrary single qubit state, without losing the information of the state being teleported, via a fourqubit cluster state of the form | ϕ > 1234 = α |0000>+ β |1010>+ γ |0101>- η |1111>, as the quantum channel, where the nonzero real numbers α , β , γ , and η satisfy the relation j α j2 + | β | 2 + | γ | 2 + | η | 2 = 1. With the introduction of an auxiliary qubit with state |0>, using a suitable unitary transformation and a positive-operator valued measure (POVM), the receiver can recreate the state of the original qubit. An important advantage of the teleportation scheme demonstrated here is that, if the teleportation fails, it can be repeated without teleporting copies of the unknown quantum state, if the concerned parties share another pair of entangled qubit. We also present a protocol for quantum information splitting of an arbitrary two-particle system via the aforementioned cluster state and a Bell-state as the quantum channel. Problems related to security attacks were examined for both the cases and it was found that this protocol is secure. This protocol is highly efficient and easy to implement.

We propose a tripartite scheme for probabilistically teleporting an arbitrary two-qubit state with a four-qubit cluster-class state and a Bell-class state as the quantum channels. In the scheme, the sender and the controller make Bell-state measurements (BSMs) on their respective qubit pairs. With their measurement results, the receiver can reconstruct the original state probabilistically by introducing two auxiliary particles and making appropriate unitary operations and positive operator-valued measure (POVM) instead of usual projective measurement. Moreover, the total success probability and classical communication cost of the present protocol are also worked out.

We study the quantum controlled and probabilistic teleportation protocol via a four-cluster state (Front. Phys. (2017) 12: 120306). The protocol cannot achieve the goal that if the teleportation fails, it can be repeated without copies of the teleported state. And the reason is that all the information of the teleported state shifts to the receiver's particle after Bell measurement and the information cannot shift back to the sender without other entangled states. To realize the claimed goal, a new quantum controlled and probabilistic teleportation protocol using the same four-cluster state is presented. Because no information of the teleported stated is lost during the whole teleportation process, the teleportation process can be repeated until the teleportation success.

A scheme for teleportation of an arbitrary two-qubit state using a four-qubit linear cluster-class state is proposed.Quantum teleportation can be successfully realized with a certain probability if the receiver can adopt an appropriate collective unitary transformation after receiving the sender's Bell-state measurement information.The scheme is more practical than previous ones using maximally entangled states as the quantum channel.In addition,an important conclusion is obtained from the above scheme that a maximally four-qubit entangled state(cluster state)is extracted from a single copy of the cluster-class state with the same probability as the teleportation.

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.

Teleportation of an arbitrary two-qubit state with a single partially entangled state, a four-qubit linear cluster-class state, is studied. The case is more practical than previous ones using maximally entangled states as the quantum channel. In order to realize teleportation, we first construct a cluster-basis of 16 orthonormal cluster states. We show that quantum teleportation can be successfully implemented with a certain probability if the receiver can adopt appropriate unitary transformations after receiving the sender's cluster-basis measurement information. In addition, an important conclusion can be obtained that a four-qubit maximally entangled state (cluster state) can be extracted from a single copy of the cluster-class state with the same probability as the teleportation in principle.

Two schemes for teleporting an unknown two-particle entangled state via a four-qubit non-maximally entangled cluster state as quantum channel are proposed.In the first scheme,a special bipartite entangled state was teleported,the receiver Bob can reconstruct the original state with a certain probability according to the sender Alice's measurement results,and the successful probability is determined by the smallest two coefficients' absolute values of the cluster state.In the latter scheme an arbitrary two-particle entangled state was teleported.Contrast to the first scheme, Bob should perform a quantum controlled phase gate operation besides the unitary transformation. The considerable advantage is that it employs a non-maximally entangled cluster state as quantum channel in these two schemes.Thus,the schemes can greatly reduce the amount of entanglement resources and need less classical bits.