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Chinese Optics Letters

Non-local implementation of single-qubit rotation operation

陈立冰, 路洪

Published Jan 1, 2004• 1 citation
OpenAlex

Abstract

We present two optimal schemes for non-local implementing a single-qubit rotation operation via a maxi-mally entangled quantum channel. We report on the quantitative relations between the quantum action,entangled and classical communication resources required in the implementation. We also put forward twoschemes for conclusive implementing the non-local quantum single-qubit rotation via a partially entangledquantum channel. Both these methods can appropriately be referred to as qubit-assisted processes.

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We present two optimal schemes for non-local implementing a single-qubit rotation operation via a maxi-mally entangled quantum channel. We report on the quantitative relations between the quantum action,entangled and classical communication resources required in the implementation. We also put forward twoschemes for conclusive implementing the non-local quantum single-qubit rotation via a partially entangledquantum channel. Both these methods can appropriately be referred to as qubit-assisted processes.
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 present a systematic simple method for constructing non-local quantum conditional rotation with single target and multiple targets operations. We firstly show how a non-local conditional rotation with single target operation can be implemented with unit fidelity and unit probability by using a maximally entangled pair as quantum channel. We also put forward a scheme for probabilistically implementing the operation with unit fidelity by employing a partially entangled pair as quantum channel. The required physical resources for implementation of the non-local operation in these two cases are discussed. We further consider non-local conditional rotation with multiple targets operations on N spatially distributed systems, and show that the number of possible distinct operations increases here exponentially, with the available number of entangled pairs that are initially distributed between systems. We also point out that the non-local conditional rotation operation can be used to generate multiparticle entanglement between particles belonging to distant users in a communication network and distributed quantum computer.
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.