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Entanglement between Identical Particles Is a Useful and Consistent Resource

Benjamin Morris1,*,†, Benjamin Yadin1,2,*,‡, Matteo Fadel3,4, Tilman Zibold3, Philipp Treutlein3, and Gerardo Adesso1,§

  • 1School of Mathematical Sciences and Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
  • 2Wolfson College, University of Oxford, Linton Road, Oxford OX2 6UD, United Kingdom
  • 3Department of Physics and Swiss Nanoscience Institute, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
  • 4State Key Laboratory for Mesoscopic Physics, School of Physics and Collaborative Innovation Center of Quantum Matter, Peking University, 100871 Beijing, China

  • *These authors contributed equally to this work.
  • †benjamin.morris@nottingham.ac.uk
  • ‡benjamin.yadin@nottingham.ac.uk
  • §gerardo.adesso@nottingham.ac.uk
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Phys. Rev. X 10, 041012 – Published 16 October, 2020

DOI: https://doi.org/10.1103/PhysRevX.10.041012

Abstract

The existence of fundamentally identical particles represents a foundational distinction between classical and quantum mechanics. Because of 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 artifact. 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 the 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 clear-cut 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.

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Popular Summary

Quantum theory tells us that some particles, such as two photons of the same frequency or two atoms of the same isotope, are fundamentally indistinguishable. When these particles are grouped together, one cannot tell them apart. Nevertheless, the theory also suggests that identical particles can be entangled with each other—described by Einstein as “spooky action at a distance.” Identical particle entanglement is now known to play an essential part in quantum computation and communication, and yet it is often dismissed as meaningless and a quirk of the mathematical formalism. Challenging that perspective, we show that identical particle entanglement can be understood rigorously as a valuable resource in the right setting.

Our first result explains that identical particle entanglement is hard to create using the experimental operations typically available in systems of optics or cold atoms. Thus, the presence of identical particle entanglement signals the potential for a state to be useful in quantum information processing. One significant example is a quantitative connection between the amount of entanglement in a system and its usefulness for making precision measurements.

We also prove that identical particle entanglement is precisely the resource required for distributing usable entanglement to separated parties. Using this result, we analyze a recent Bose-Einstein condensate experiment, evaluating a quantitative measure of entanglement. Finally, we study the counterintuitive emergence of identical particle entanglement when one creates several copies of a system.

Our work demonstrates a consistent and physically meaningful theoretical description of identical particle entanglement. This conceptual advance points the way to developing new theoretical and practical characterizations of the quantum properties of bosonic many-body systems.

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Phys. Rev. X 10, 041012– Published 16 October, 2020
  • Received 14 October 2019
  • Revised 20 April 2020
  • Accepted 21 August 2020
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