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Traversability dynamics of minimal Sachdev-Ye-Kitaev Wormhole-inspired teleportation protocol with a parity-time (PT)-symmetric non-Hermitian deformation

Abstract

Holography-inspired teleportation has recently emerged as a significant area of research in quantum many-body systems. In this work, we investigate the effects of PT symmetric non-unitary deformations on the traversability of the wormhole-inspired teleportation protocol modeled by coupled Sachdev-Ye-Kitaev systems prepared in a Thermofield Double state bath. By introducing balanced gain and loss terms to the boundary Hamiltonians, we identify a phase transition driven by spectral exceptional points, where the real energy eigenvalues of the effective Hamiltonian coalesce and bifurcate into complex conjugate pairs. We demonstrate that the PT-broken phase acts as an amplifier, enabling exponential growth in the norm of the teleported signal while preserving the causal time window for the wormhole's traversability. A statistical study of disorder realizations reveals that the critical non-Hermiticity threshold γ_c follows a log-normal distribution, reflecting the sensitivity of the transition to the microscopic level spacing of the chaotic SYK spectrum. Furthermore, we observe a ``Purification" effect deep in the broken phase, where the teleportation channel acts as an entanglement distiller, yielding near-perfect teleportation fidelity for post-selected states. Our results suggest that the non-Hermitian topology can be harnessed to enhance holographic quantum communication, providing a robust mechanism for signal amplification in noisy, minimal quantum many-body systems.

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