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

TL;DR

The paper investigates a PT-symmetric non-Hermitian deformation of the wormhole-inspired teleportation protocol implemented with two coupled SYK clusters in a Thermofield Double state. By adding a balanced gain–loss term $H_{ ext{PT}} = i\gamma (Z_L - Z_R)$, the authors reveal a spectral exceptional point $\gamma_c$ separating a real-spectrum phase from a broken phase with complex eigenvalues, where the teleported signal experiences exponential amplification while the scrambling time $t_*$ is preserved. Disorder renders $\gamma_c$ log-normally distributed, reflecting microscopic spectral sensitivity, and the broken phase exhibits a purification effect that yields near-unity teleportation fidelity for post-selected states. Overall, the work shows that non-Hermitian topology can robustly enhance holographic quantum communication by acting as a causal amplifier and a selective filter in minimal quantum many-body systems.

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 $\mathcal{PT}$ 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 $\mathcal{PT}$-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.

Figures (7)

• Figure 1: Spacetime diagram illustrating Wormhole-inspired teleportation protocol in AdS/CFT framework. The two asymptotic boundaries correspond to the left and the right CFTs, while the interior region represents the AdS bulk. An initially localized excitation evolves backward in time on the left boundary, subjected to controlled boundary coupling that induces a bulk shockwave, and then evolves forward to emerge at the right boundary as the final state, effectively realizing information transfer through the wormhole geometry.
• Figure 2: Evolution of the complex many-body energy spectrum of the non-Hermitian effective Hamiltonian $H_{eff}$ as a function of the drive strength $\gamma$(For $N=6$, single disorder realization). (Top) The real component of the eigenvalues. In the $\mathcal{PT}$-unbroken phase ($\gamma < \gamma_c$), the spectrum remains real, and resonant energy levels exhibit level attraction. (Bottom) The imaginary component. The transition to the broken phase occurs at $\gamma_c \approx 0.077$, marked by the emergence of a "fan" of complex conjugate eigenvalues (gain and loss modes).
• Figure 3: Detailed trajectory of the real energy eigenvalues for a resonant eigenstate pair (State 79 and State 80) across the $\mathcal{PT}$-symmetry breaking transition. As the non-Hermiticity $\gamma$ increases, the levels exhibit level attraction and coalesce at the critical threshold $\gamma_c$. The energy gap closes with a sharp vertical cusp ($\Delta E \sim \sqrt{\gamma_c - \gamma}$), identifying this singularity as a second-order Exceptional Point. Beyond $\gamma_c$, the real energies remain strictly degenerate or "locked" to the mean value. This spectral locking is physically critical: it ensures that the emergent gain and loss modes oscillate with the exact same frequency, preventing dephasing and maintaining the coherence of the quantum state during amplification.
• Figure 4: Statistical distribution of the critical $\mathcal{PT}$-symmetry breaking threshold $\gamma_c$ across 100 independent disorder realizations of the coupled SYK model ($N=6$). The histogram indicates that the protocol's stability varies significantly due to the random nature of the Hamiltonian's level spacings and couplings. The solid curve represents a Log-Normal fit to the data, highlighting the heavy-tailed nature of the distribution. This confirms that while level repulsion prevents $\gamma_c \to 0$ (instability at infinitesimal drive), the specific threshold is highly sensitive to the microscopic spectral gap of the disordered instance.
• Figure 5: Statistical dynamics of the $\mathcal{PT}$-symmetric wormhole protocol averaged over 100 disorder realizations ($N=6$). (Blue Solid Line): The mean fidelity remains near the classical baseline $\bar{\mathcal{F}} \approx 0.5$. This reflects the ensemble average, where realization-specific enhancements are counterbalanced by misaligned instances. (Blue Shaded Region): The fidelity variance exhibits a characteristic "funnel-like" expansion, diverging near the phase transition ($\gamma_c \approx 0.07$). This quantifies the system's hypersensitivity to microscopic disorder in the vicinity of the Exceptional Point. (Red Dashed Line): The logarithm of the signal norm (success probability) scales linearly with $\gamma$, confirming the exponential amplification law $P \propto e^{2\gamma t \delta_{\text{max}}}$ and identifying the $\mathcal{PT}$-broken phase as a robust causal amplifier.