Quantum teleportation under non-Hermitian operations

We investigate the standard quantum teleportation protocol for a single-qubit state, focusing on the scenario where the qubit undergoes a class of non-unitary evolution governed by parity-time ( \mathcal{PT} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mstyle mathvariant="script"> <mml:mi>𝒫</mml:mi> <mml:mi>𝒯</mml:mi> </mml:mstyle> </mml:math> )-symmetric non-Hermitian Hamiltonians. Additionally, we examine the case where the entangled pair shared by Alice and Bob is exposed to a noise channel. In the \mathcal{PT} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mstyle mathvariant="script"> <mml:mi>𝒫</mml:mi> <mml:mi>𝒯</mml:mi> </mml:mstyle> </mml:math> -symmetric regime, the teleportation fidelity exhibits time-dependent oscillations. Compared to the conventional case without non-Hermitian operations, periodic enhancements in fidelity are observed, and we analytically derive their dependence on the parameters of both the non-Hermitian Hamiltonian and noise channel. When the \mathcal{PT} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mstyle mathvariant="script"> <mml:mi>𝒫</mml:mi> <mml:mi>𝒯</mml:mi> </mml:mstyle> </mml:math> symmetry is broken, the fidelity ceases to oscillate and instead decays to a steady value. Notably, even in this regime, non-Hermitian operations can yield fidelity improvements over conventional schemes. We further investigate the teleportation of quantum Fisher information (QFI) and find that its evolutionary behavior differs from that of fidelity. Analytical results reveal that QFIs corresponding to different estimated parameters exhibit distinct outcomes at Bob’s receiving end during teleportation. Furthermore, we derive a trade-off inequality between fidelity and QFI, offering a theoretical tool to coordinately optimize these two quantities in the teleportation process.