I am facing a situation where the quantum discord of the bipartite quantum channel is zero and in the quantum-correlated state without concurrence. I took a single qubit quantum state as an unknown state to teleport through this quantum channel, and I have found that average teleportation is one at absolute zero and decreases with the environment temperature, and the Bell non-locality measure is non-zero, the three steering measure is also finite, and the L1 norm of quantum coherence is also maximum at zero temperature. The average fidelity of the state indicates that teleportation is successful.
I want to know if any explicit theorem says teleportation cannot occur without entanglement. Though I have found just one paper in the literature on archive, it is not published somewhere, or maybe I didn't find it.
Yes, I read somewhere that teleportation without entanglement is conceivable and makes sense within the paradigm of quantum information, sometimes known as "entanglement-free teleportation". In your case, even if the quantum discord of the bipartite quantum channel is zero and there is no concurrence, other forms of quantum correlations, such as Bell non-locality, steering measures, and quantum coherence, can still exist. These alternate forms of quantum correlations allow for successful quantum state teleportation without the need for shared entanglement between sender and recipient. The presence of residual other quantum correlations in the quantum channel enables the transmission of quantum information without direct entanglement.
Not very exact but some related materails can be found here:
Article A verifiable framework of entanglement-free quantum secret s...
Here, state transformations are studied in entanglement-free regimes:
Article A Branching Distributed Temporal Logic for Reasoning about E...
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