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Chinese Journal of Quantum Electronics

Implementing a non-local SWAP operation on two entangled pairs by a three-qubit entangled state and a Bell state

H. Lu

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

We propose a theoretical scheme for the implementation of a non-local quantum SWAP operation on two spatially separated entangled pairs by a three-qubit entangled state and a Bell state, and we show that the operation can swap two qubits of these entangled pairs. The feature of the scheme is that a third side is included, who may participate the process of quantum non-local implementation as a supervisor. Furthermore, when the quantum channel is partially entangled, the third one can rectify the state distorted by imperfect quantum channel.

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We propose a theoretical scheme for the implementation of a non-local quantum SWAP operation on two spatially separated entangled pairs by a three-qubit entangled state and a Bell state, and we show that the operation can swap two qubits of these entangled pairs. The feature of the scheme is that a third side is included, who may participate the process of quantum non-local implementation as a supervisor. Furthermore, when the quantum channel is partially entangled, the third one can rectify the state distorted by imperfect quantum channel.
We investigate the controlled implementation of a non-local CNOT operation using a three-qubit entangled state. Firstly, we show how the non-local CNOT operation can be implemented with unit fidelity and unit probability by using a maximally entangled GHZ state as controlled quantum channel. Then, we put forward two schemes for conclusively implementing the non-local operation with unit fidelity by employing a partially entangled pure GHZ state as quantum channel. The feature of these schemes is that a third side is included, who may participate the process of quantum non-local implementation as a supervisor. Furthermore, when the quantum channel is partially entangled, the third one can rectify the state distorted by imperfect quantum channel. In addition to the GHZ class state, the W class state can also be used to implement the same non-local operation probabilistically. The probability of successful implementation using the W class state is always less than that using the GHZ class state.
We propose a scheme for the implementation of nonlocal quantum swap operation on two spatially separated entangled pairs and we show that the operation can swap two qubits of these entangled pairs.We discuss the resources of the entangled qubits and classical communication bits required for the optimal implementation of the nonlocal quantum swap operation.We also put forward a scheme for probabilistic implementation of nonlocal swap operation via a nonmaximally entangled quantum channel.The probability of a successful nonlocal swap operation is obtained by introducing a collective unitary transformation.
We propose a scheme for the implementation of nonlocal quantum swap operation on two spatially separated entangled pairs and we show that the operation can swap two qubits of these entangled pairs. We discuss the resources of the entangled qubits and classical communication bits required for the optimal implementation of the nonlocal quantum swap operation. We also put forward a scheme for probabilistic implementation of nonlocal swap operation via a nonmaximally entangled quantum channel. The probability of a successful nonlocal swap operation is obtained by introducing a collective unitary transformation.
We investigate the problem of quantum remote implementation of a single-qubit rotation operation using three-qubit entangled state. Firstly, we utilize the entanglement property of maximally entangled Greenberger–Horne–Zeilinger (GHZ) state to design a theoretical scheme for implementing the operation remotely with unit fidelity and unit probability. Then, we put forward two schemes for conclusive implementing the non-local single-qubit rotation with unit fidelity by employing a partially entangled pure GHZ state as quantum channel. The features of these schemes are that a third side is included, who may participate the process of quantum remote implementation as a supervisor. Furthermore, when the quantum channel is partially entangled, the third side can rectify the state distorted by imperfect quantum channel. In addition to the GHZ class state, the W class state can also be used to remotely implement the same operation probabilistically. The probability of successful implementation using the W class state is always less than that using the GHZ class state.
We propose a measurement scheme of generalized Bell states in which, although entanglement is destroyed, the nonlocality feature can be preserved and swapped. Here we consider two quantum systems: one consisting of two-party three-level maximal entangled pairs; the other being three-party two-level maximal entangled pairs. It is found that these local immeasurable states can be prepared without any classical communication and local operation. Moreover, nonmaximal entangled states cannot preserve nonlocality.
The basic entanglement-swapping scheme can be seen as a process which allows one to redistribute the Bell states properties between different pairs of a four-qubit system. We analyze a similar scheme by performing a Bell--von Neumann measurement over two local qubits, each one initially correlated through an XXX state with a spatially distant qubit. This process swaps the XXX feature without conditions, whereas the input entanglement is partially distributed in the four possible outcome states under certain conditions. Specifically, we obtain two threshold values for the entanglement of formation of the input XXX states in order for the outcome states to be nonseparable.