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Communications in Theoretical Physics

Probabilistically Controlled Teleportation of an Arbitrary Two-Qubit State via Positive Operator-Valued Measure

Haifeng Xu, Lian-Fang Han

Published May 1, 2013• 2 citations
Publisher

Abstract

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.

DOI
10.1088/0253-6102/59/5/06

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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.
An explicit scheme for probabilistically teleporting an arbitrary two-qubit state is proposed by using a one-dimensional four-qubit cluster-class state as the quantum channel. In the scheme, the sender first performs two Bell state measurements (BSMs). Then with the sender's help, the receiver can reconstruct the original state probabilistically by introducing an auxiliary qubit and making appropriate unitary operations. Moreover, the total success probability and classical communication cost of the present scheme are also calculated.
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.
A new scheme for controlled teleportation of an arbitrary two-particle state is proposed in detail,using a four-particle cluster state as quantum channel and EPR state to achieve control.First of all,the sender applies to the controller,and then the controller performs the Bell-based measurement on the two particles of his own.And the controller notifies the sender to achieve entanglement swapping.Then,the sender makes the appropriate unitary transformation and performs a Newman measurements on the four particles of his own.And the results inform the receiver.According to the sender's measurement results,the receiver can reconstruct the arbitrary two-particle state after he makes the appropriate unitary transformation on his own particles.The success probability of the program is 100%.
A scheme for controlled teleportation of an arbitrary two-particle state using a maximally entangled EPR pair and a cluster state as the quantum channel is proposed. After receiving Alice's Bell state measurement results, the controller performs a joint measurement on his particles under a non-maximally entangled Bell-basis. The receiver needs to introduce an auxiliary qubit, and performs a series of appropriate unitary transformations on his particles. The original state can be teleported successfully with the probability 2 cos2 θ.
A scheme for controlled teleportation of an arbitrary two-particle state using a maximally entangled EPR pair and a cluster state as the quantum channel is proposed.After receiving Alice's Bell state measurement results, the controller performs a joint measurement on his particles under a non-maximally entangled Bell-basis.The receiver needs to introduce an auxiliary qubit,and performs a series of appropriate unitary transformations on his particles.The original state can be teleported successfully with the probability 2 cos2 9.
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.