Generation of Quantum Entanglement in Autonomous Thermal Machines: Effects of Non-Markovianity, Hilbert Space Structure, and Quantum Coherence

TL;DR

The paper addresses how entanglement can be generated in an external quantum system by coupling to a quantum autonomous thermal machine under non-Markovian memory. It develops a two-qubit QATM and a two-qubit external system, defines two cycles A and B through a virtual temperature $T_M$ and energy constraints, and analyzes heat, temperature, and entropy production under a Lindblad framework. Entanglement in the external system appears only in cycle A, where non-Markovian memory and coherence correlations are stronger, while cycle B yields negligible entanglement, despite similar total correlations. The work highlights how Hilbert space structure and quantum coherence act as resources to control entanglement in quantum thermodynamic settings and connects to experimental superconducting-qubit platforms for realization.

Abstract

We present a theoretical investigation of entanglement generation in an external quantum system via interaction with a quantum autonomous thermal machine (QATM) under non-Markovian dynamics. The QATM, composed of two qubits each coupled to independent thermal reservoirs, interacts with an external system of two additional qubits. By analyzing the Hilbert space structure, energy level configurations, and temperature gradients, we define a common interaction between the QATM qubits and the external system qubits, which allows the definition of two thermodynamic cycles (A and B) governed by virtual temperatures and energy-conserving transitions. We demonstrate that the QATM can act as a structured reservoir capable of inducing non-Markovian memory effects, as highlighted by negative entropy production rates. Using mutual information and concurrence, we show that entanglement is generated only under cycle A, which is associated with stronger non-Markovian behavior and higher coherence correlations. Our results demonstrate that temperature differences, Hilbert space structure, and coherence serve as quantum resources for controlling and enhancing entanglement in quantum thermodynamic settings, with parameters consistent with experimental superconducting qubit platforms.

Figures (8)

• Figure 1: Diagram of the QATM $M = M_1 \otimes M_2$ coupled to the external system $S = S_1 \otimes S_2$ via a coupling coefficient $g$. $R_1$ and $R_2$ are the bosonic reservoirs of the QATM qubits $M_1$ and $M_2$, respectively.
• Figure 2: (a) Schematic representation of QATM cycle A: heating of qubit $M_1$ and cooling of qubit $M_2$ with heat transfer from the external system to the machine. (b) Cycle B: heating of qubit $M_2$ and cooling of qubit $M_1$ with heat transfer from the machine to the external system. Arrows indicate the direction of heat flow between the qubits, thermal reservoirs, and the external system.
• Figure 3: Heat dynamics for each qubit in the QATM and in the external system. (a,b) Heat exchanged $Q_{M_1}(t)$ and $Q_{M_2}(t)$ for the QATM qubits. (c,d) Heat exchanged $Q_{S_1}(t)$ and $Q_{S_2}(t)$ for the external system qubits. The two regions separated by the white dashed line correspond to the conditions of cycles A and B according to the ratio $T_{M_1}/T_{M_2}$, we set $T_{M_2}=E_{M_2}$, and $g=0.08 E_{M_2}$.
• Figure 4: Temperature evolution of the QATM qubits over time. (a) Cycle A: gradual increase of $T_{M_1}$ and decrease of $T_{M_2}$ with a negative virtual temperature $T_M < 0$. (b) Cycle B: decrease of $T_{M_1}$ and increase of $T_{M_2}$ with a positive virtual temperature $T_M > 0$. The coupling strength is varied as $g=0.03,\,0.05,\,0.07,$ and $0.09$ (in units of $E_{M_2}$), represented by red (dotted), black (dashed), blue (dot--dashed), and magenta (solid) curves.
• Figure 5: Entropy production $\Sigma(t)$ and entropy production rate $\sigma(t)$ over time. (a) Cycle A: smaller entropy production with more frequent and stronger negative rates, indicating stronger non-Markovianity. (b) Cycle B: larger entropy production with less frequent negative rates, indicating weaker non-Markovianity. The coupling strength is varied as $g=0.03,\,0.05,\,0.07,$ and $0.09$ (in units of $E_{M_2}$), represented by red (dotted), black (dashed), blue (dot--dashed), and magenta (solid) curves.