The thermodynamic uncertainty relation of a quantum-mechanically coupled two-qubit system

TL;DR

This paper investigates how quantum coupling in a two-qubit system influences the thermodynamic uncertainty relation, revealing that coupling strength modulates the TUR bound and highlighting quantum effects distinct from classical or noisy oscillator systems.

Contribution

It extends the study of TUR bounds from a single quantum two-level system to a coupled two-qubit system, analyzing the impact of coupling strength on TUR and quantum fluctuations.

Findings

Weakly coupled qubits have TUR bound ≈ 1.25.

Strongly coupled qubits have TUR bound ≈ 1.36.

Quantum coupling affects photon current fluctuations and TUR bounds.

Abstract

The minimal bound of the thermodynamic uncertainty relation (TUR) is modulated from that of the classical counterpart ($\mathcal{Q}_{\rm min}=2$) when a quantumness is present in the dynamical process far from equilibrium. A recent study on a dissipative two-level system (TLS) subject to an external field indicates that quantum coherence can suppress the fluctuations of the irreversible current and loosens the TUR bound to $\mathcal{Q}_{\rm min}^{\rm TLS}\approx 1.25$. Here, we extend on the field-driven single TLS % in a photonic bath to a quantum-mechanically coupled two-qubit system (TQS), and explore how the quantum coupling between the two qubits, an additional complexity introduced to the probem of TLS, affects the photon current, fluctuations, and the TUR bound. We find that the TUR bound of TQS depends on the strength of coupling, such that $\mathcal{Q}_{\rm min}^{\rm TQS}=\mathcal{Q}_{\rm min}^{\rm TLS}\approx 1.25$ when the two qubits are effectively decoupled under weak coupling, whereas another loose bound $\mathcal{Q}_{\rm min}^{\rm TQS}\approx 1.36$ is identified for two strongly coupled qubits under strong fields. By contrasting the TQS against two coupled noisy oscillators, we illuminate the quantumness unique to the TQS and its effect on the TUR. Our findings from the study of TQS form the basis for understanding the TUR of more general $N$-qubit systems.