Improved coherence time of a non-Hermitian qubit in a $\mathcal{PT}$-symmetric Environment

TL;DR

This work investigates decoherence control by embedding a qubit in a non-Hermitian PT-symmetric environment. By mapping the non-Hermitian dynamics to a Hermitian counterpart via a metric-based similarity transformation, the authors derive an exact propagator and a decoherence factor $\Lambda(t)$ that governs off-diagonal decay. They show that coherence is maximally preserved when both system and environment are PT-symmetric, with enhanced protection at $\theta = \tfrac{\pi}{2}$ and near the exceptional point $|\alpha_S| = 1$, and that increasing environmental non-Hermiticity $\tau$ can further slow decoherence. The paper also outlines feasible experimental implementations, notably NV-center–based optomechanical schemes, suggesting practical routes to decoherence suppression in quantum information processing.

Abstract

Quantum computing's potential for exponential speedup is fundamentally limited by decoherence, a phenomenon arising from environmental interactions. Non-Hermitian quantum mechanics, particularly $PT$-symmetric systems, offers a novel framework for extending coherence times. This study examines a qubit's coherence under non-Hermitian $PT$-symmetric dynamics, highlighting significantly enhanced coherence times compared to Hermitian setups. The effect is especially pronounced when both the system and environment exhibit $PT$-symmetry. Interestingly, greater environmental non-Hermiticity correlates with extended coherence, contrary to traditional expectations. These findings point to promising strategies for managing decoherence, which could significantly advance approaches to quantum information processing.

Figures (6)

• Figure 1: (Color online) Temporal variation of decoherence for Hermitian system and environment ($E_1=1, \tau=0$), non-Hermitian system and Hermitian environment ($E_1=0.5, \tau=0$), Hermitian system and non-Hermitian environment ($E_1=1, \tau=2$) and both system and environment non-Hermitian ($E_1=0.5, \tau=2$) for a fixed value of $\theta$\ref{['fig1a']}$\theta=\pi/2$\ref{['fig1b']}$\theta=\pi/3$ and \ref{['fig1c']}$\theta=\pi$.
• Figure 2: (Color online) Variation of decoherence with non-Hermiticity of the environment for different values of $\theta$ for $E_1=1,~ t=10$.
• Figure 3: (Color online) Variation of decoherence with time for different functional forms of environment non-Hermiticity $\zeta~\text{with}~\tau=2$ keeping the system non-Hermiticity fixed, i.e., $E_1=0.5$.
• Figure 4: (Color online) Time evolution of decoherence for different values of non-Hermiticity in the environment, keeping the Hermiticity of the system fixed, i.e., $E_1=1$.
• Figure 5: (Color online) Time evolution of decoherence for different values of non-Hermiticity in the system, keeping the Hermiticity of the environment fixed, i.e., $\tau=0$.