Photon loss effects on light-mediated non-Gaussian entangled Bose–Einstein condensates projecting with different counts

Abstract The theory of quantum information processing for macroscopic qubits is based on the fact that every macroscopic qubit has a conserved number of particles. However, from an experimental point of view, every such qubit experiences decoherence that impacts the possibilities for entanglement generation between such qubits to be used in quantum information processing efficiently. One of the most prospective methods for generating entanglement between distant atomic BECs is quantum nondemolition measurements. Here, we study how the effects of photon measurement impact the entanglement when photon loss decoherence is included. We employ the thermally entangled state representation (TESR) and integral within the ordered operator (IWOP) approach to obtain the accurate density matrix in a photon loss channel. We demonstrate that varying outcomes of photon number measurements lead to the generation of distinct entangled states, each exhibiting unique characteristics. In the scenario where two photoelectric detectors detect the same number of photons n c = n d , we observe that the entangled state demonstrates greater robustness compared to cases with unequal photon counts, providing a reliable resource for better performance with post-processing. We have used Hofmann-Takeuchi and Duan-Giedke-Cirac-Zoller criteria to detect entanglement and find that these methods offer significant benefits in detecting entanglement compared to the Wineland squeezing and EPR steering criteria, when evaluating the regions of detectable entanglement time in these contexts.