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Acta Physica Sinica

Controlled implementation of a nonlocal and open-target destination quantum controlled-Not （CNOT） gate using partially entangled pairs

Libing Chen, Tan Peng, Dong Shao-Guang, Lu Hong, 佛山科学技术学院光电子与物理学系，佛山 528000

Published Jan 1, 2009• 1 citation
Publisher

Abstract

We show how a nonlocal and open-target destination quantum controlled-Not （CNOT） gate can be probabilistically implemented by using partially entangled pairs of particles. We first investigate the controlled implementation of a nonlocal and three-target destination CNOT gate using three partially entangled pairs, and then generalize the scheme to the case of N-target destination. In this scheme, Alice’s local generalized measurement described by a positive operator valued measurement （POVM） plays a key role. We construct the required POVM. It is worth noting that deterministic and exact implementation of a nonlocal CNOT gate can be realized using partially entangled pairs.

DOI
10.7498/aps.58.6772

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We present a systematic simple method to implement a generalized quantum control-NOT (CNOT) gate on two d -dimensional distributed systems. First, we show how the nonlocal generalized quantum CNOT gate can be implemented with unity fidelity and unity probability by using a maximally entangled pair of qudits as a quantum channel. We also put forward a scheme for probabilistically implementing the nonlocal operation with unity fidelity by employing a partially entangled qudit pair as a quantum channel. Analysis of the scheme indicates that the use of partially entangled quantum channel for implementing the nonlocal generalized quantum CNOT gate leads to the problem of 'the general optimal information extraction'. We also point out that the nonlocal generalized quantum CNOT gate can be used in the entanglement swapping between particles belonging to distant users in a communication network and distributed quantum computer.
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Teleportation of an arbitrary single-qubit state using two partially entangled states is considered.Firstly,we present a method for realizing probabilistically two-destination teleportation by using two partially entangled pairs as quantum channel.Then,we put forward a scheme for realizing deterministic and exact teleportation by using same quantum channel.In these schemes,the sender's local generalized measurement described by a positive operator valued measurement(POVM) lies at the heart.We construct the required POVM.The methods are applicable to any two partially entangled pairs satisfying the condition that their smaller Schmidt coefficients μ and v are 2μ+2μv-2v-1≥0.