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Brazilian Journal of Physics

One-Way Flagged Probabilistic Implementation of a Nonlocal Controlled-NOT Gate

Xiaonan Zhang, Yu-Guang Yang, Guang-Bao Xu, 姜东焕 JIANG Dong-huan

Published Oct 5, 2026• 0 citations
Publisher
DOI
10.1007/s13538-026-02157-w

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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.
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.