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A one-way quantum amplifier for long-distance quantum communication

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Abstract

In this paper, a model for single photon amplification based on cluster-state quantum computation is proposed. A rescaling of the probability amplitudes of a deteriorated qubit in favor of the one-photon component will define the amplifier’s gain. Unlike the heralded quantum amplifiers, the probabilistic success of the whole process will not depend on the successful detection of a heralding signal. Instead, the whole procedure will rely upon a single-qubit measurement, which is simpler compared to any two-qubit interaction gate in the heralded quantum amplifiers. The proposed model can be used as a qubit protector against propagation losses in long-distance quantum communication networks.

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Notes

  1. This requirement is specific to our analysis, where in general the transfer matrix is Hermitian.

  2. Where \(\vert {\psi }\rangle \) = \(\alpha \vert {0}\rangle +\beta \vert {1}\rangle \) is an arbitrary qubit state.

  3. The \(\frac{1}{\sqrt{2}}\)factor will be taken care of when normalizing the whole state.

  4. This indistinguishability is crucial to the whole amplification process.

  5. Since the detection of one photon in either \(\hat{d_{+}}\) or \(\hat{d_{-}}\) leads to Eq. 7, the probability to successfully produce that state is given by twice its norm.

  6. All of the probability amplitudes can be adjusted as a function of the linear optical elements that will be used during experimentation. This will be clear in Sect. 3.

  7. \(\vert {+}\rangle \) and \(\vert {-}\rangle \) are the eigenstates of the Pauli-X operator with eigenvalues +1, −1, respectively.

  8. The Pauli group is the group of the famous Pauli \(\sigma \) operators.

  9. Where X is the Pauli \(\sigma _{x}, \sigma _{x} \vert {+}\rangle =\vert {+}\rangle \).

  10. \(\rho ^{\prime }={U}\rho {U^{\dagger }}\).

  11. Where this step to be included in the ‘polarization encoding’ block in our diagrams from now on.

  12. This simple encoder consists of: an input in a general polarization state to be encoded, a PBS and an entanglement resource in the state \(\vert {\phi ^{+}}\rangle \). At the PBS, the general input state will be mixed with one member of the entangled resource, and then the detection of exactly one photon at the output of the PBS means that the other two are exiting the device.

  13. Again this can be put in the standard form by applying a Hadamard to qubits 1 and 4.

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  1. Faculty of Engineering, Ain-Shams University, Cairo, Egypt

    Hany Elemy

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Elemy, H. A one-way quantum amplifier for long-distance quantum communication. Quantum Inf Process 16, 134 (2017). https://doi.org/10.1007/s11128-017-1582-2

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