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Chinese Physics

Implementing remotely a single-qubit rotation operation by three-qubit entanglement

Libing Chen, H. Lu, Yuhua Liu

Published Jun 23, 2005• 10 citations
Publisher

Abstract

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.

DOI
10.1088/1009-1963/14/7/010

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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 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 show how a many-to-one and a one-to-many controlled remote quantum rotations (CRQRs) can be implemented deterministically and exactly by using partially entangled quantum channels. Firstly, we present a theoretical scheme for a N -to-1 CRQR, in which the quantum rotations initially distributed in N spatially separated qubits can be exactly and deterministically performed onto a remote single qubit via two partially entangled ( N + M +1)-qubit Greenberger-Horne-Zeilinger (GHZ) states without performing any global operations. The feature of this scheme is that, apart from N senders and a receiver, M agents are included in the process as controllers. Should any one of the M agents not cooperate, the receiver could not gain the original rotations. Then, we design another scheme for implementing a 1-to- N CRIC with unit fidelity and unit probability by employing a partially entangled (2 M + N +1)-qubit Einstein-Podolsky-Rosen (EPR)-GHZ state or K partially entangled ( M +2)-qubit GHZ states, in which a quantum rotation can be divided into N pieces ( N K ) and performed from a sender onto N distant receivers via the control of M agents in a quantum network. In these schemes, the senders (or the receivers, or the controllers) local positive operator valued measurement (POVM) lies at the heart. We construct the required POVMs. The fact that deterministic and exact implementation of a many-to-one or a one-to-many CRQR could be realized using partially entangled quantum channel is notable. These schemes can be used to quantum secret sharing, quantum voting, and so on. They definitely have the strong security.
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.
A quantum rotation can be divided into M pieces and teleported from a sender onto M distant receivers via the control of N agents in a quantum network. We utilize the entanglement property of a (2M + N + 1)-qubit Einstein–Podolsky–Rosen (EPR) — Greenberger–Horne–Zeilinger (GHZ) state to design a theoretical scheme for implementing these rotations remotely with unit fidelity and unit probability. The feature of the scheme is that, apart from a sender and M receivers, N agents are included in the process as controllers. Should any one of the N agents not cooperate, the receivers could not gain the original rotations. This scheme can be used to sender-encoded quantum secret sharing. It definitely has the strong security.
We put forward two novel and perfect protocols for preparing an arbitrary single–particle state and simultaneously implementing a rotation operator or an arbitrary unitary operator on that particle. There are schemes for either only teleporting particles or only remotely controlling quantun particles. If one has to remotely control a prepared quantum, then he/ she has to first do remote state preparation and then executes the remote control on the prepared quantum. Both operations ware done separately on two sets of entanglements. However, this intuitive solution is inefficient because many resources are wasted. Thus, we attempt to complete both operations by sharing one three–particle Greenberger–Horne– Zeilinger (GHZ) state. Comparing our two protocols with the corresponding intuitive solutions, respectively, the results show that our protocols are more efficient than the corresponding intuitive solutions. Only Pauli operators, controlled–NOT gate, Bell–state measurement, single–qubit measurement, Einstein–Podolsky–Rosen (EPR) state and GHZ state are used in our schemes, so these schemes are easily realized in physical experiment.
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.