The existence of fundamentally identical particles represents a foundational distinction between classical and quantum mechanics. Due to their exchange symmetry, identical particles can appear to be entangled -- another uniquely quantum phenomenon with far-reaching practical implications. However, a long-standing debate has questioned whether identical particle entanglement is physical or merely a mathematical artefact. In this work, we provide such particle entanglement with a consistent theoretical description as a quantum resource in processes frequently encountered in optical and cold atomic systems. This leads to a plethora of applications of immediate practical impact. On one hand, we show that the metrological advantage for estimating phase shifts in systems of identical bosons amounts to a measure of their particle entanglement, with a clearcut operational meaning. On the other hand, we demonstrate in general terms that particle entanglement is the property resulting in directly usable mode entanglement when distributed to separated parties, with particle conservation laws in play. Application of our tools to an experimental implementation with Bose-Einstein condensates leads to the first quantitative estimation of identical particle entanglement. Further connections are revealed between particle entanglement and other resources such as optical nonclassicality and quantum coherence. Overall, this work marks a resolutive step in the ongoing debate by delivering a unifying conceptual and practical understanding of entanglement between identical particles.

Entanglement between identical particles is a useful and consistent resource

The classical Gibbs paradox concerns the change in entropy upon mixing two gases. Whether or not an observer assigns an entropy increase to the process depends on their ability to distinguish the gases. A resolution is provided by realising that an ``ignorant'' observer, who cannot distinguish the gases with devices in their lab, has no way of extracting work by mixing them. Moving the thought experiment into the quantum realm, we reveal new and surprising behaviour. We show that the ignorant observer can in fact extract work from mixing different gases, even if the gases could not be directly distinguished. Moreover, in a macroscopic limit that classically recovers the ideal gas from statistical mechanics, there is a marked divergence in the quantum case: as much work can be extracted as if the gases had been fully distinguishable. Our analysis reveals that the ignorant observer assigns more microstates to the system than are found by naive state-counting in semiclassical statistical mechanics. This effect demonstrates the importance of carefully accounting for the level of knowledge of an observer, and its implications for genuinely quantum modifications to thermodynamics.

Extracting work from mixing indistinguishable systems: A quantum Gibbs "paradox''

QIT-1: Quantum information theory, software and algorithms

technical paper

The Institute of Physics and IOP Publishing, in partnership with the Chinese Physical Society (CPS) and the University of Science and Technology of China (USTC) are proud to have brought together the international quantum science community online for this inaugural conference.


Early career and leading researchers from universities, industry and government worldwide came together to share, learn and collaborate on the latest research and emerging areas of high interest across quantum science and technology. The broad themes covered by Quantum 2020 included:

Quantum communication;
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Quantum sensing, metrology and imaging;
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Quantum technology in industry.
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Quantum 2020

The Institute of Physics and IOP Publishing, in partnership with the Chinese Physical Society (CPS) and the University of Science and Technology of China (USTC) are proud to have brought together the international quantum science community online for this inaugural conference.

Early career and leading researchers from universities, industry and government worldwide came together to share, learn and collaborate on the latest research and emerging areas of high interest across quantum science and technology. 

Benjamin Morris

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Entanglement between identical particles is a useful and consistent resource

Extracting work from mixing indistinguishable systems: A quantum Gibbs "paradox''

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