Heralded generation of maximal entanglement in any dimension via incoherent coupling to thermal baths

Armin Tavakoli1, Géraldine Haack1, Marcus Huber2, Nicolas Brunner1, and Jonatan Bohr Brask1

1Department of Applied Physics, University of Geneva, 1211 Geneva, Switzerland
2Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria

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We present a scheme for dissipatively generating maximal entanglement in a heralded manner. Our setup requires incoherent interactions with two thermal baths at different temperatures, but no source of work or control. A pair of $(d+1)$-dimensional quantum systems is first driven to an entangled steady state by the temperature gradient, and maximal entanglement in dimension $d$ can then be heralded via local filters. We discuss experimental prospects considering an implementation in superconducting systems.

In this work, we show how a thermal machine can be used to create quantum entanglement by coupling to baths at different temperatures and exploiting the heat flows between them.

In the classical, everyday world, thermal machines do a lot of useful tasks for us. Power plants turn heat into electricity. Refrigerators keep our beers cold. Steam locomotives pull trains (OK, at least they used to). In general, they are machines which move heat around, or transform it. Often by connecting different points of the machine to different temperatures and exploiting the resulting heat flows.

Classical thermal machines are big, and generally one does not need to worry about quantum physics to understand what is going on. But what happens if make such a machine smaller and smaller, to the point where quantum effects become important? Say we take a locomotive and scale it down, down, down, until the boiler and gears and so on consist of just a few atoms? Of course, it won't really be a locomotive any more - but maybe we can learn something interesting?

Indeed, we can. And the machine can still be useful.

In recent years, physicists have learned a lot about thermodynamics on the quantum scale by studying such tiny thermal machines. Looking at how fundamental concepts from classical thermodynamics, such as the 2nd law or Carnot efficiency, behave in the quantum regime, we gain new insights into the differences between the classical and quantum worlds.

We can also think about whether there are new tasks that such quantum thermal machines could do.

Entanglement is an essential quantum phenomena. Objects which are entangled behave as if they are a single entity even when separated and manipulated independently. This enables new, powerful applications such as quantum computing and quantum metrology, and is at the heart of the foundations of quantum physics. So creating and studying entanglement is very interesting from both fundamental and applied points of view. Might a thermal machine be used to generate entanglement then?

Entanglement is generally very fragile, and thermal noise tends to wash it out quickly. In fact, a lot of effort in quantum physics experiments goes into keeping the systems cold and isolated, so as to be able to observe the genuinely quantum effects. So it is not at all obvious that using a thermal machine for entanglement generation would work. However, it turns out that connecting with noisy environments can indeed help to create and keep entanglement stable, in certain systems.

This has been studied for a variety of systems and settings. In this paper, we focus on very simple machines which require no external control or driving and use just a temperature difference between hot and cold baths. It was found previously that entanglement can indeed be generated in this setting. However, the amount of entanglement was rather limited. Here, we present a new quantum thermal machine which generates maximal entanglement. It can do this for the simplest possible case of just two quantum bits, but also for two quantum trits, and in fact for two quantum systems of any dimension. The new machine again uses just two different temperatures and two quantum systems. One system is connected to a cold bath, one to a hot bath, and they interact with each other. When heat flows from hot to cold through the two systems, they become entangled. Local filters allow the extraction of maximal entanglement.

Our work opens a path towards thermal generation of larger entangled states useful for building quantum computers or sensitive quantum sensors.

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