Impact of dephased entangled states and varying measurement orientations on the reliability of cryptographic keys generated via the quantum protocol E91: A quantum simulation approach

Abstract

One of the main requirements to achieve reliable quantum communications are on-demand sources of highly entangled photon pairs, and semiconductor quantum dots have emerged as prominent candidates to satisfy the necessary conditions of brightness and entanglement fidelity. However, in most cases the biexciton-exciton-vacuum cascade produces a pair of maximally polarization-entangled photons with a dephasing, due to a non-negligible exciton fine structure splitting in the emitting nanostructure. This work focuses on the performance of the E91 quantum key distribution protocol under the variation of two elements: first, the phase in the input state when the protocol is implemented using entangled photons generated via the radiative cascade, and second, the relative directions of the polarization analyzers. We use a quantum computational approach by means of the IBM's API Qiskit to simulate the optical implementation of the studied cryptographic protocol and thus to validate analytical expressions derived for the secret key rate and the Bell's parameter. Our results show that the performance of the quantum transmission is highly impacted by the product between the exciton lifetime and the quantum dot's fine structure splitting and that such an impact may be modulated through the orientation of the polarizers. Under some specific conditions, the studied E91 protocol is shown to turn into the BBM92 protocol, to which the results can be extended. These findings provide important insight for the scalable implementation of quantum key distribution protocols with realistic entanglement sources. Furthermore, this study constitutes an illustrative example of how quantum computation can be used as a tool for simulating physical processes whose experimental realization can be substituted by short algorithms run on quantum software.