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arXiv:2212.13309 · Physical Review A

Impossibility of bosonic autonomous entanglement engines in the weak-coupling limit

Bradley Longstaff, Michael G. Jabbour, Jonatan Bohr Brask

Published Sep 13, 2023• 3 citations
arXivHTMLPDF

Abstract

Entanglement is a fundamental feature of quantum physics and a key resource for quantum communication, computing, and sensing. Entangled states are fragile and maintaining coherence is a central challenge in quantum information processing. Nevertheless, entanglement can be generated and stabilized through dissipative processes. In fact, entanglement has been shown to exist in the steady state of certain interacting quantum systems subject solely to incoherent coupling to thermal baths. This has been demonstrated in a range of bi- and multipartite settings using systems of finite dimension. Here we focus on the steady state of infinite-dimensional bosonic systems. Specifically, we consider any set of bosonic modes undergoing excitation-number-preserving interactions of arbitrary strength and divided between an arbitrary number of parties that each couple weakly to thermal baths at different temperatures. We show that a unique steady state is always separable.

DOI
10.1103/physreva.108.032209

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Entanglement is a fundamental feature of quantum physics and a key resource for quantum communication, computing, and sensing. Entangled states are fragile and maintaining coherence is a central challenge in quantum information processing. Nevertheless, entanglement can be generated and stabilized through dissipative processes. In fact, entanglement has been shown to exist in the steady state of certain interacting quantum systems subject solely to incoherent coupling to thermal baths. This has been demonstrated in a range of bi- and multipartite settings using systems of finite dimension. Here we focus on the steady state of infinite-dimensional bosonic systems. Specifically, we consider any set of bosonic modes undergoing excitation-number-preserving interactions of arbitrary strength and divided between an arbitrary number of parties that each couple weakly to thermal baths at different temperatures. We show that a unique steady state is always separable.
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 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.
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.
This is the second of a series of three papers examining how viable it is for entanglement to be sustained at high temperatures for quantum systems in thermal equilibrium (Case A), in nonequilibrium (Case B) and in nonequilibrium steady state (NESS) conditions (Case C). The system we analyze here consists of two coupled quantum harmonic oscillators each interacting with its own bath described by a scalar field, set at temperatures T 1 > T 2. For constant bilinear inter-oscillator coupling studied here (Case C1) owing to the Gaussian nature, the problem can be solved exactly at arbitrary temperatures even for strong coupling. We find that the valid entanglement criterion in general is not a function of the bath temperature difference, in contrast to thermal transport in the same NESS setting [1]. Thus lowering the temperature of one of the thermal baths does not necessarily help to safeguard the entanglement between the oscillators. Indeed, quantum entanglement will disappear if any one of the thermal baths has a temperature higher than the critical temperature T c, defined as the temperature above which quantum entanglement vanishes. With the Langevin equations derived we give a full display of how entanglement dynamics in this system depends on T 1, T 2, the inter-oscillator coupling and the system-bath coupling strengths. For weak oscillator-bath coupling the critical temperature T c is about the order of the inverse oscillator frequency, but for strong oscillator-bath coupling it will depend on the bath cutoff frequency. We conclude that in most realistic circumstances, for bosonic systems in NESS with constant bilinear coupling, ‘hot entanglement’ is largely a fiction.
In 2015 Jonatan Bohr Brask et al. showed that steady-state entanglement could be generated in two interacting qubits incoherently coupled to thermal baths of different temperatures [1]. This thesis is an attempt to re-evaluate their findings with the hope that a slightly different approach and system can help further our understanding of this not yet well understood phenomena. A Lindblad master equation approach is taken to study a two-qubit thermal machine interacting with bosonic thermal reservoirs. It is found that the steady-state entanglement behaves similarly using the Lindblad approach, the main difference being that a larger amount of entanglement can be generated than initially found in Ref. [1].
We present a short overview of quantum entanglement generation and preservation in a steady state. In addition to the focus on quantum entanglement stabilization, we briefly discuss the same objective for steady-state quantum coherence. The overview classifies the approaches into two main categories: hybrid drive and dissipation methods and purely dissipative schemes. Furthermore, purely dissipative schemes are discussed under two subclasses of equilibrium and nonequilibrium environments. The significance of the dissipative route to sustained quantum entanglement and challenges against it are pointed out. Besides the value of steady-state entanglement for existing quantum technologies, quantum computation, communication, sensing, and simulation, its unique opportunities for emerging and future quantum technology applications, particularly quantum heat engines and quantum energy processing, are discussed.