The remote implementation of all possible generalized quantum measurement on single atomic qubit in a quantum network

To implement generalized quantum measurement (GQM) one has to extend the original Hilbert space. Generally speaking, the additional dimensions of the ancilla space increase as the number of the operators of the GQM n increases. This paper presents a scheme for deterministically implementing all possible n-operator GQMs on a single atomic qubit by using only one 2-dimensional ancillary atomic qubit repeatedly, which remarkably reduces the complexity of the realistic physical system. Here the qubit is encoded in the internal states of an atom trapped in an optical cavity and single-photon pulses are employed to provide the interaction between qubits. It shows that the scheme can be performed remotely, and thus it is suitable for implementing GQM in a quantum network. What is more, the number of the total ancilla dimensions in our scheme achieves the theoretic low bound.