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arXiv:2401.01776 · npj Quantum Information

Maximal steady-state entanglement in autonomous quantum thermal machines

Shishir Khandelwal, Björn Annby-Andersson, Giovanni Francesco Diotallevi, A. Wacker, Armin Tavakoli

Published Feb 19, 2025• 7 citations
arXivHTMLPDF

Abstract

Abstract We devise an autonomous quantum thermal machine consisting of three pairwise-interacting qubits, two of which are locally coupled to thermal reservoirs. The machine operates autonomously, as it requires no time-coherent control, external driving or quantum bath engineering, and is instead propelled by a chemical potential bias. Under ideal conditions, we show that this out-of-equilibrium system can deterministically generate a maximally entangled steady-state between two of the qubits, or any desired pure two-qubit entangled state, emerging as a dark state of the system. We study the robustness of entanglement production with respect to several relevant parameters, obtaining nearly-maximally-entangled states well-away from the ideal regime of operation. Furthermore, we show that our machine architecture can be generalised to a configuration with 2n − 1 qubits, in which only a potential bias and two-body interactions are sufficient to generate genuine multipartite maximally entangled steady states in the form of a W state of n qubits.

DOI
10.1038/s41534-025-00981-7

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Abstract We devise an autonomous quantum thermal machine consisting of three pairwise-interacting qubits, two of which are locally coupled to thermal reservoirs. The machine operates autonomously, as it requires no time-coherent control, external driving or quantum bath engineering, and is instead propelled by a chemical potential bias. Under ideal conditions, we show that this out-of-equilibrium system can deterministically generate a maximally entangled steady-state between two of the qubits, or any desired pure two-qubit entangled state, emerging as a dark state of the system. We study the robustness of entanglement production with respect to several relevant parameters, obtaining nearly-maximally-entangled states well-away from the ideal regime of operation. Furthermore, we show that our machine architecture can be generalised to a configuration with 2n − 1 qubits, in which only a potential bias and two-body interactions are sufficient to generate genuine multipartite maximally entangled steady states in the form of a W state of n qubits.
We discuss a simple quantum thermal machine for the generation of steady-state entanglement between two interacting qubits. The machine is autonomous in the sense that it uses only incoherent interactions with thermal baths, but no source of coherence or external control. By weakly coupling the qubits to thermal baths at different temperatures, inducing a heat current through the system, steady-state entanglement is generated far from thermal equilibrium. Finally, we discuss two possible implementations, using superconducting flux qubits or a semiconductor double quantum dot. Experimental prospects for steady-state entanglement are promising in both systems.
Abstract Quantum thermal machines can generate steady-state entanglement by harvesting spontaneous interactions with local environments. However, using minimal resources and control, the entanglement is typically weak. Here, we study entanglement generation in a two-qubit quantum thermal machine in the presence of a continuous feedback protocol. Each qubit is measured continuously and the outcomes are used for real-time feedback to control the local system-environment interactions. We show that there exists an ideal operation regime where the quality of entanglement is significantly improved, to the extent that it can violate standard Bell inequalities and uphold quantum teleportation. In agreement with (Khandelwal et al 2020 New J. Phys. 22 073039), we also find, for ideal operation, that the heat current across the system is proportional to the entanglement concurrence. Finally, we investigate the robustness of entanglement production when the machine operates away from the ideal conditions.
We discuss a simple quantum thermal machine for the generation of steady-state entanglement between two interacting qubits. The machine is autonomous in the sense that it uses only incoherent interactions with thermal baths, but no source of coherence or external control. By weakly coupling the qubits to thermal baths at different temperatures, inducing a heat current through the system, steady-state entanglement is generated far from thermal equilibrium. Finally, we discuss two possible implementations, using superconducting flux qubits or a semiconductor double quantum dot. Experimental prospects for steady-state entanglement are promising in both systems.
A quantum thermal machine is presented that is able to autonomously generate steady-state Bell nonlocality. A Lindblad equation is derived for two qubits that are incoherently coupled to a pair of thermal baths and the resulting Liouvillian is found to have a strong symmetry. This out-of-equilibrium system can generate Bell-nonlocal steady states across a range of parameters and at arbitrarily high temperatures for certain initial conditions. To analyse how the machine operates in a more realistic setting, experimental imperfections are then included via a stochastic perturbation to the system Hamiltonian. This breaks the strong symmetry and results in collective and local dephasing noise. It is found that if the sole source of noise is local noise, then the steady state is Bell local. The co-presence of collective noise is then shown to be advantageous, with the ability to increase the degree of Bell-inequality violation and transform a steady state from Bell local to Bell nonlocal.
The generation of genuine multipartite entangled states is challenging in practice. Here we explore an alternative route to this task, via autonomous entanglement engines which use only incoherent coupling to thermal baths and time-independent interactions. We present a general machine architecture, which allows for the generation of a broad range of multipartite entangled states in a heralded manner. Specifically, given a target multiple-qubit state, we give a sufficient condition ensuring that it can be generated by our machine. We discuss the cases of Greenberger-Horne-Zeilinger, Dicke, and cluster states in detail. These results demonstrate the potential of purely thermal resources for creating multipartite entangled states useful for quantum information processing.
We present a theoretical investigation of entanglement generation in an external quantum system during its 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 able to induce non-Markovian memory effects highlighted by negative entropy production rates. Using mutual information and concurrence, we show that entanglement is generated only using 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.