One of the most important steps in the understanding of quantum many-body systems is due to the intensive studies of their entanglement properties [1,2]. Much less, however, is known about the role of quantum nonlocality [3] in these systems. This is because standard many body observables involve correlations among few particles, while there is no multipartite Bell inequality for this scenario. In my talk I will attempt to connect challenges of quantum metrology with those of detection of quantum nonlocality in many body systems. First, I will discuss an intimate relation between entanglement in many body states and usefulness for metrology [3]. I will focus then on usefulness of random symmetric states for metrology [4]. The second part will be devoted to non-locality.
In the second part, I will first discuss shortly the role of entanglement in many body systems, stressing the difference between the gapped and critical systems. I will then concentrate on the results of Refs. [6], where we provide the first examples of nonlocality detection in many-body systems using two-body correlations. To this aim, we construct families of multipartite Bell inequalities that involve only second order correlations of local observables. We then provide examples of systems, relevant for nuclear and atomic physics, whose ground states violate our Bell inequalities for any number of constituents. We identify inequalities that can be tested by measuring collective spin components, opening the way to the experimental detection of many-body nonlocality, for instance with atomic ensembles [7], systems of trapped ions [8], or atoms trapped close to nano-structured (tapered) fibers and photonic crystals [9]. Interestingly, breaking of many body Bell inequalities witnesses certain kinds of many body entanglement [10]. Most of examples will deal with symmetric states, i.e. will call for metrological applications. If time permits, we discuss non-locality in 1D spin-chains, by employing Jordan-Wigner transformation and relation to integrable and non-integrable fermionic models [11].
References
[1] A. Osterloh et al., Nature 416, 608 (2002); T. J. Osborne et al., Quantum Inf. Proc. 1, 45 (2002); Phys. Rev. A 66, 032110 (2002); G. Vidal et al., Phys. Rev. Lett. 90 227902 (2003).
[2] M. Lewenstein, A. Sanpera, and V. Ahufinger, “Ultracold atoms in Optical Lattices: simulating quantum many body physics”, Oxford University Press, Oxford, 2017, ISBN 978-0-19-878580-4.
[3] J. S. Bell, Physics 1, 195-200 (1964).
[4] R. Augusiak, J. Kolodynski, A. Streltsov, M. N. Bera, A. Acín, M. Lewenstein, Asymptotic role of entanglement in quantum metrology, Phys. Rev. A 94, 012339 (2016).
[5] M. Oszmaniec, R. Augusiak, C. Gogolin, J. Kolodynski, A. Acín, and M. Lewenstein, Random bosonic states for robust quantum metrology, Phys. Rev. X 6, 041044 (2016).
[6] J. Tura et al., Detecting the non-locality of quantum many body states, Science 344, 1256 (2014); J. Tura et al., Nonlocality in many-body quantum systems detected with two-body correlators, Ann. Phys. 362, 370-423 (2015).
[7] K. Hammerer et al., Rev. Mod. Phys. 82, 1041 (2010). K. Eckert et al., Nature Phys. 4, 50 (2008).
[8] T. Graß and M. Lewenstein, Trapped-ion quantum simulation of tunable-range Heisenberg chains, arXiv:1401.6414, EPJ Quantum Technology 2014, 1:8, doi:10.1186/epjqt8.
[9] J. S. Douglas, H. Habibian, C.-L. Hung, A. V. Gorshkov, H. J. Kimble, and D. E. Chang, Quantum many-body models with cold atoms coupled to photonic crystals, Nature Photon. 9, 326-331 (2015)
[10] A. Aloy et al., Device Independent Entanglement Depth Witnesses, in preparation.
[11] J. Tura, G. de las Cuevas, R. Augusiak, M. Lewenstein, A. Acín,, and J. I. Cirac, Energy as a detector of nonlocality of many-body spin systems, Phys. Rev. X7, 021005 (2017)