[Paper Review] Thermal quantum correlations and teleportation under PT-symmetric system

J. Ramya Parkavi, R. Muthuganesan+2 more|arXiv (Cornell University)|Mar 10, 2022

Quantum Mechanics and Non-Hermitian Physics4 citations

TL;DR

This paper investigates quantum correlations and teleportation in the Heisenberg XY spin model under PT-symmetric operations. It demonstrates that PT-symmetry enhances quantum correlations—particularly measurement-induced nonlocality—beyond entanglement, enabling stable, periodic teleportation fidelity even at high temperatures where standard protocols fail.

ABSTRACT

In this article, we exploit the different notions of quantumness measure to understand the properties of the Heisenberg XY model with and without PT-symmetric operation. In the absence of PT-symmetry, we study the significance of different measures, namely entanglement and measurement induced nonlocality (MIN), in the detection of the quantumness of the Heisenberg XY model. It is observed that the quantum correlations and teleportation fidelity monotonically decreases with respect to temperature. Furthermore, the intervention of PT-symmetric operation enhances the strengths of quantum correlation. In addition, we highlight the role of the system's parameters and PT-symmetric operation on the teleportation of a quantum state. Our results also emphasize that after the addition of PT-symmetric operation, the considered physical model remains a versatile resource to achieve successful teleportation of the quantum state.

Motivation & Objective

• To analyze quantum correlations in the Heisenberg XY model using multiple measures, including entanglement, measurement-induced nonlocality (MIN), and Bell nonlocality.
• To investigate the impact of PT-symmetric operations on quantum correlations and teleportation fidelity in thermally entangled states.
• To determine whether non-unitary PT-symmetric evolution can protect or revive quantum teleportation beyond the limits of entanglement.
• To compare the resilience of different quantum correlation measures—especially MIN—under non-Hermitian dynamics and thermal noise.
• To explore the role of system parameters (e.g., γ, φ, J, B) in sustaining teleportation fidelity under PT-symmetric evolution.

Proposed method

• Employed the Heisenberg XY spin model as a many-body quantum system with tunable interactions and external fields.
• Applied PT-symmetric operations via non-Hermitian Hamiltonians with gain and loss terms, modeled through complex coupling parameters (γ).
• Calculated quantum correlation measures: entanglement (via concurrence), measurement-induced nonlocality (MIN), and Bell nonlocality.
• Simulated time evolution under non-unitary dynamics using the density matrix formalism and thermal states at various temperatures (T = 1, 4, 6).
• Evaluated teleportation fidelity using the standard protocol with a Bell-state measurement and reconstruction fidelity of the teleported state.
• Systematically varied parameters γ (non-Hermiticity strength), φ (angle in the XY plane), J (exchange coupling), and B (magnetic field) to analyze their effects.

Experimental results

Research questions

• RQ1 How do different quantum correlation measures—entanglement, MIN, and Bell nonlocality—behave in the Heisenberg XY model under thermal noise without PT-symmetry?
• RQ2 To what extent does PT-symmetric operation enhance quantum correlations and stabilize teleportation fidelity in the presence of thermal decoherence?
• RQ3 Can measurement-induced nonlocality serve as a more robust indicator of nonlocality than entanglement in non-Hermitian, thermally mixed systems?
• RQ4 How do the parameters of the PT-symmetric Hamiltonian (e.g., γ, φ) influence the dynamics of teleportation fidelity and correlation revival?
• RQ5 Does non-unitary PT-symmetric evolution prevent the sudden death of entanglement and enable periodic revival of teleportation performance?

Key findings

• In the absence of PT-symmetry, quantum correlations and teleportation fidelity monotonically decrease with increasing temperature, with entanglement showing sudden death at high temperatures.
• PT-symmetric operations significantly enhance all quantum correlation measures, particularly MIN, even when entanglement vanishes, indicating that nonlocality persists beyond entanglement.
• Teleportation fidelity under PT-symmetric evolution transitions from decaying to periodic oscillations, with maximum fidelity preserved and oscillations becoming more frequent as non-Hermiticity (γ) decreases.
• For γ = -0.01, the maximum teleportation fidelity increases compared to γ = 0.05, indicating optimal performance at low negative non-Hermiticity strength.
• At high temperatures (T = 4 and T = 6), PT-symmetric operations maintain periodic fidelity oscillations, demonstrating robustness against thermal decoherence.
• The system remains a viable resource for quantum teleportation even when entanglement is absent, highlighting the superiority of MIN as a nonlocality indicator under non-unitary dynamics.