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Entanglement depth

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In quantum physics, entanglement depth characterizes the strength of multiparticle entanglement. An entanglement depth k {\displaystyle k} means that the quantum state of a particle ensemble cannot be described under the assumption that particles interacted with each other only in groups having fewer than k {\displaystyle k} particles. It has been used to characterize the quantum states created in experiments with cold gases.

Definition

Entanglement depth appeared in the context of spin squeezing. It turned out that to achieve larger and larger spin squeezing, and thus larger and larger precision in parameter estimation, a larger and larger entanglement depth is needed.

Later it was formalized in terms of convex sets of quantum states, independent of spin squeezing as follows. Let us consider a pure state that is the tensor product of multi-particle quantum states

| Ψ ⟩ = | ϕ 1 ⟩ ⊗ | ϕ 2 ⟩ ⊗ . . . ⊗ | ϕ n ⟩ . {\displaystyle |\Psi \rangle =|\phi _{1}\rangle \otimes |\phi _{2}\rangle \otimes ...\otimes |\phi _{n}\rangle .}

The pure state | Ψ ⟩ {\displaystyle |\Psi \rangle } is said to be k {\displaystyle k} -producible if all ϕ i {\displaystyle \phi _{i}} are states of at most k {\displaystyle k} particles. A mixed state is called k {\displaystyle k} -producible, if it is a mixture of pure states that are all at most k {\displaystyle k} -producible. The k {\displaystyle k} -producible mixed states form a convex set.

A quantum state contains at least multiparticle entanglement of k + 1 {\displaystyle k+1} particles, if it is not k {\displaystyle k} -producible. A N {\displaystyle N} -particle state with N {\displaystyle N} -entanglement is called genuine multipartite entangled.

Finally, a quantum state has an entanglement depth k {\displaystyle k} , if it is k {\displaystyle k} -producible, but not ( k − 1 ) {\displaystyle (k-1)} -producible.

It was possible to detect the entanglement depth close to states different from spin-squeezed states. Since there is not a general method to detect multipartite entanglement, these methods had to be tailored to experiments with various relevant quantum states.

Thus, entanglement criteria has been developed to detect entanglement close to symmetric Dicke states with ⟨ J z ⟩ = 0. {\displaystyle \langle J_{z}\rangle =0.} They are very different from spin-squeezed states, since they do not have a large spin polarization. They can provide Heisenberg limited metrology, while they are more robust to particle loss than Greenberger-Horne-Zeilinger (GHZ) states.

There are also criteria for detecting the entanglement depth in planar-squeezed states. Planar squeezed states are quantum states that can be used to estimate a rotation angle that is not expected to be small.

Finally, multipartite entanglement can be detected based on the metrological usefulness of the quantum state. The criteria applied are based on bounds on the quantum Fisher information.

Experiments

The entanglement criterion in Ref. has been used in many experiments with cold gases in spin-squeezed states.

There have also been experiments in cold gases for detecting multipartite entanglement in symmetric Dicke states.

There have been also experiments with Dicke states that detected entanglement based on metrological usefulness in cold gases and in photons.

References

  1. ^ Sørensen, Anders S.; Mølmer, Klaus (14 May 2001). "Entanglement and Extreme Spin Squeezing". Physical Review Letters. 86 (20): 4431–4434. arXiv:quant-ph/0011035. Bibcode:2001PhRvL..86.4431S. doi:10.1103/PhysRevLett.86.4431. PMID 11384252. S2CID 206327094.
  2. Gühne, Otfried; Tóth, Géza; Briegel, Hans J (4 November 2005). "Multipartite entanglement in spin chains". New Journal of Physics. 7: 229. arXiv:quant-ph/0502160. doi:10.1088/1367-2630/7/1/229.
  3. Duan, L.-M. (27 October 2011). "Entanglement Detection in the Vicinity of Arbitrary Dicke States". Physical Review Letters. 107 (18). arXiv:1107.5162. doi:10.1103/PhysRevLett.107.180502.
  4. ^ Lücke, Bernd; Peise, Jan; Vitagliano, Giuseppe; Arlt, Jan; Santos, Luis; Tóth, Géza; Klempt, Carsten (17 April 2014). "Detecting Multiparticle Entanglement of Dicke States". Physical Review Letters. 112 (15): 155304. arXiv:1403.4542. Bibcode:2014PhRvL.112o5304L. doi:10.1103/PhysRevLett.112.155304. PMID 24785048.
  5. Vitagliano, Giuseppe; Apellaniz, Iagoba; Kleinmann, Matthias; Lücke, Bernd; Klempt, Carsten; Tóth, Géza (20 January 2017). "Entanglement and extreme spin squeezing of unpolarized states". New Journal of Physics. 19 (1): 013027. arXiv:1605.07202. doi:10.1088/1367-2630/19/1/013027.
  6. Vitagliano, G.; Colangelo, G.; Martin Ciurana, F.; Mitchell, M. W.; Sewell, R. J.; Tóth, G. (15 February 2018). "Entanglement and extreme planar spin squeezing". Physical Review A. 97 (2). arXiv:1705.09090. doi:10.1103/PhysRevA.97.020301.
  7. He, Q. Y.; Peng, Shi-Guo; Drummond, P. D.; Reid, M. D. (11 August 2011). "Planar quantum squeezing and atom interferometry". Physical Review A. 84 (2). arXiv:1101.0448. doi:10.1103/PhysRevA.84.022107.
  8. Hyllus, Philipp (2012). "Fisher information and multiparticle entanglement". Physical Review A. 85 (2): 022321. arXiv:1006.4366. Bibcode:2012PhRvA..85b2321H. doi:10.1103/physreva.85.022321. S2CID 118652590.
  9. Tóth, Géza (2012). "Multipartite entanglement and high-precision metrology". Physical Review A. 85 (2): 022322. arXiv:1006.4368. Bibcode:2012PhRvA..85b2322T. doi:10.1103/physreva.85.022322. S2CID 119110009.
  10. Gross, C.; Zibold, T.; Nicklas, E.; Estève, J.; Oberthaler, M. K. (April 2010). "Nonlinear atom interferometer surpasses classical precision limit". Nature. 464 (7292): 1165–1169. arXiv:1009.2374. Bibcode:2010Natur.464.1165G. doi:10.1038/nature08919. PMID 20357767. S2CID 4419504.
  11. Riedel, Max F.; Böhi, Pascal; Li, Yun; Hänsch, Theodor W.; Sinatra, Alice; Treutlein, Philipp (April 2010). "Atom-chip-based generation of entanglement for quantum metrology". Nature. 464 (7292): 1170–1173. arXiv:1003.1651. Bibcode:2010Natur.464.1170R. doi:10.1038/nature08988. PMID 20357765. S2CID 4302730.
  12. Bohnet, J. G.; Cox, K. C.; Norcia, M. A.; Weiner, J. M.; Chen, Z.; Thompson, J. K. (September 2014). "Reduced spin measurement back-action for a phase sensitivity ten times beyond the standard quantum limit". Nature Photonics. 8 (9): 731–736. arXiv:1310.3177. Bibcode:2014NaPho...8..731B. doi:10.1038/nphoton.2014.151. S2CID 67780562.
  13. Cox, Kevin C.; Greve, Graham P.; Weiner, Joshua M.; Thompson, James K. (4 March 2016). "Deterministic Squeezed States with Collective Measurements and Feedback". Physical Review Letters. 116 (9): 093602. arXiv:1512.02150. Bibcode:2016PhRvL.116i3602C. doi:10.1103/PhysRevLett.116.093602. PMID 26991175.
  14. Mitchell, Morgan W; Beduini, Federica A (17 July 2014). "Extreme spin squeezing for photons". New Journal of Physics. 16 (7): 073027. arXiv:1304.2527. Bibcode:2014NJPh...16g3027M. doi:10.1088/1367-2630/16/7/073027.
  15. Zou, Yi-Quan; Wu, Ling-Na; Liu, Qi; Luo, Xin-Yu; Guo, Shuai-Feng; Cao, Jia-Hao; Tey, Meng Khoon; You, Li (19 June 2018). "Beating the classical precision limit with spin-1 Dicke states of more than 10,000 atoms". Proceedings of the National Academy of Sciences. 115 (25): 6381–6385. arXiv:1802.10288. Bibcode:2018PNAS..115.6381Z. doi:10.1073/pnas.1715105115. PMC 6016791. PMID 29858344.
  16. Lücke, B.; Scherer, M.; Kruse, J.; Pezzé, L.; Deuretzbacher, F.; Hyllus, P.; Topic, O.; Peise, J.; Ertmer, W.; Arlt, J.; Santos, L.; Smerzi, A.; Klempt, C. (11 November 2011). "Twin Matter Waves for Interferometry Beyond the Classical Limit". Science. 334 (6057): 773–776. arXiv:1204.4102. doi:10.1126/science.1208798.
  17. Krischek, Roland; Schwemmer, Christian; Wieczorek, Witlef; Weinfurter, Harald; Hyllus, Philipp; Pezzé, Luca; Smerzi, Augusto (19 August 2011). "Useful Multiparticle Entanglement and Sub-Shot-Noise Sensitivity in Experimental Phase Estimation". Physical Review Letters. 107 (8). arXiv:1108.6002. doi:10.1103/PhysRevLett.107.080504.
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