Bound entangled states fit for robust experimental verification

Gael Sentís1,2, Johannes N. Greiner3, Jiangwei Shang4,1, Jens Siewert5,6, and Matthias Kleinmann1,2

1Naturwissenschaftlich-Technische Fakultät, Universität Siegen, 57068 Siegen, Germany
2Departamento de Física Teórica e Historia de la Ciencia, Universidad del País Vasco UPV/EHU, E-48080 Bilbao, Spain
33rd Institute of Physics, University of Stuttgart and Institute for Quantum Science and Technology, IQST, Pfaffenwaldring 57, D-70569 Stuttgart, Germany
4Beijing Key Laboratory of Nanophotonics and Ultrafine Optoelectronic Systems, School of Physics, Beijing Institute of Technology, Beijing 100081, China
5Departamento de Química Física, Universidad del País Vasco UPV/EHU, E-48080 Bilbao, Spain
6IKERBASQUE Basque Foundation for Science, E-48013 Bilbao, Spain

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Preparing and certifying bound entangled states in the laboratory is an intrinsically hard task, due to both the fact that they typically form narrow regions in state space, and that a certificate requires a tomographic reconstruction of the density matrix. Indeed, the previous experiments that have reported the preparation of a bound entangled state relied on such tomographic reconstruction techniques. However, the reliability of these results crucially depends on the extra assumption of an unbiased reconstruction. We propose an alternative method for certifying the bound entangled character of a quantum state that leads to a rigorous claim within a desired statistical significance, while bypassing a full reconstruction of the state. The method is comprised by a search for bound entangled states that are robust for experimental verification, and a hypothesis test tailored for the detection of bound entanglement that is naturally equipped with a measure of statistical significance. We apply our method to families of states of $3\times 3$ and $4\times 4$ systems, and find that the experimental certification of bound entangled states is well within reach.

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[1] M. Horodecki, P. Horodecki, and R. Horodecki, Mixed-State Entanglement and Distillation: Is there a “Bound” Entanglement in Nature?, Physical Review Letters 80, 5239 (1998), 10.1103/​PhysRevLett.80.5239.

[2] K. Horodecki, M. Horodecki, P. Horodecki, and J. Oppenheim, Secure Key from Bound Entanglement, Physical Review Letters 94, 160502 (2005), 10.1103/​PhysRevLett.94.160502.

[3] P. Horodecki, M. Horodecki, and R. Horodecki, Bound Entanglement Can Be Activated, Physical Review Letters 82, 1056 (1999), 10.1103/​PhysRevLett.82.1056.

[4] L. Masanes, All Bipartite Entangled States Are Useful for Information Processing, Physical Review Letters 96, 150501 (2006), 10.1103/​PhysRevLett.96.150501.

[5] Ł. Czekaj, A. Przysiȩżna, M. Horodecki, and P. Horodecki, Quantum metrology: Heisenberg limit with bound entanglement, Physical Review A 92, 062303 (2015), 10.1103/​PhysRevA.92.062303.

[6] G. Tóth and T. Vértesi, Quantum States with a Positive Partial Transpose are Useful for Metrology, Physical Review Letters 120, 020506 (2018), 10.1103/​PhysRevLett.120.020506.

[7] T. Moroder, O. Gittsovich, M. Huber, and O. Gühne, Steering Bound Entangled States: A Counterexample to the Stronger Peres Conjecture, Physical Review Letters 113, 050404 (2014), 10.1103/​PhysRevLett.113.050404.

[8] T. Vértesi and N. Brunner, Disproving the Peres conjecture by showing Bell nonlocality from bound entanglement, Nature Communications 5, 5297 (2014), 10.1038/​ncomms6297.

[9] M. Horodecki, J. Oppenheim, and R. Horodecki, Are the Laws of Entanglement Theory Thermodynamical?, Physical Review Letters 89, 240403 (2002), 10.1103/​PhysRevLett.89.240403.

[10] F. G. S. L. Brandao and M. B. Plenio, Entanglement theory and the second law of thermodynamics, Nature Physics 4, 873 (2008), 10.1038/​nphys1100.

[11] E. Amselem and M. Bourennane, Experimental four-qubit bound entanglement, Nature Physics 5, 748 (2009), 10.1038/​nphys1372.

[12] J. Lavoie, R. Kaltenbaek, M. Piani, and K. J. Resch, Experimental bound entanglement?, Nature Physics 6, 827 (2010), 10.1038/​nphys1832.

[13] J. Lavoie, R. Kaltenbaek, M. Piani, and K. J. Resch, Experimental Bound Entanglement in a Four-Photon State, Physical Review Letters 105, 130501 (2010), 10.1103/​PhysRevLett.105.130501.

[14] J. A. Smolin, Four-party unlockable bound entangled state, Physical Review A 63, 032306 (2001), 10.1103/​PhysRevA.63.032306.

[15] J. T. Barreiro, P. Schindler, O. Gühne, T. Monz, M. Chwalla, C. F. Roos, M. Hennrich, and R. Blatt, Experimental multiparticle entanglement dynamics induced by decoherence, Nature Physics 6, 943 (2010), 10.1038/​nphys1781.

[16] H. Kampermann, D. Bruß, X. Peng, and D. Suter, Experimental generation of pseudo-bound-entanglement, Physical Review A 81, 040304 (2010), 10.1103/​PhysRevA.81.040304.

[17] K. Dobek, M. Karpiński, R. Demkowicz-Dobrzański, K. Banaszek, and P. Horodecki, Experimental Extraction of Secure Correlations from a Noisy Private State, Physical Review Letters 106, 030501 (2011), 10.1103/​PhysRevLett.106.030501.

[18] F. Kaneda, R. Shimizu, S. Ishizaka, Y. Mitsumori, H. Kosaka, and K. Edamatsu, Experimental Activation of Bound Entanglement, Physical Review Letters 109, 040501 (2012), 10.1103/​PhysRevLett.109.040501.

[19] E. Amselem, M. Sadiq, and M. Bourennane, Experimental bound entanglement through a Pauli channel, Scientific Reports 3, 1966 (2013), 10.1038/​srep01966.

[20] K. Dobek, M. Karpiński, R. Demkowicz-Dobrzański, K. Banaszek, and P. Horodecki, Experimental generation of complex noisy photonic entanglement, Laser Physics 23, 025204 (2013), 10.1088/​1054-660X/​23/​2/​025204.

[21] J. DiGuglielmo, A. Samblowski, B. Hage, C. Pineda, J. Eisert, and R. Schnabel, Experimental Unconditional Preparation and Detection of a Continuous Bound Entangled State of Light, Physical Review Letters 107, 240503 (2011), 10.1103/​PhysRevLett.107.240503.

[22] B. C. Hiesmayr and W. Löffler, Complementarity reveals bound entanglement of two twisted photons, New Journal of Physics 15, 083036 (2013), 10.1088/​1367-2630/​15/​8/​083036.

[23] M. Paris and J. Řeháček (eds.), Quantum State Estimation, vol. 649 of Lecture Notes in Physics (Springer Berlin Heidelberg, Berlin, Heidelberg) (2004), ISBN 978-3-540-22329-0, 10.1007/​b98673.

[24] Z. Hradil, Quantum-state estimation, Physical Review A 55, R1561 (1997), 10.1103/​PhysRevA.55.R1561.

[25] D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, Measurement of qubits, Physical Review A 64, 052312 (2001), 10.1103/​PhysRevA.64.052312.

[26] T. Sugiyama, P. S. Turner, and M. Murao, Effect of non-negativity on estimation errors in one-qubit state tomography with finite data, New Journal of Physics 14, 085005 (2012), 10.1088/​1367-2630/​14/​8/​085005.

[27] C. Schwemmer, L. Knips, D. Richart, H. Weinfurter, T. Moroder, M. Kleinmann, and O. Gühne, Systematic Errors in Current Quantum State Tomography Tools, Physical Review Letters 114, 080403 (2015), 10.1103/​PhysRevLett.114.080403.

[28] B. Efron and R. J. Tibshirani, An introduction to the bootstrap (Chapman & Hall/​CRC) (1994), ISBN 0-412-04231-2.

[29] J. Shang, H. K. Ng, A. Sehrawat, X. Li, and B.-G. Englert, Optimal error regions for quantum state estimation, New Journal of Physics 15, 123026 (2013), 10.1088/​1367-2630/​15/​12/​123026.

[30] M. Christandl and R. Renner, Reliable Quantum State Tomography, Physical Review Letters 109, 120403 (2012), 10.1103/​PhysRevLett.109.120403.

[31] R. Blume-Kohout, Robust error bars for quantum tomography, arXiv:1202.5270 [quant-ph] (2012).

[32] L. Knips, C. Schwemmer, N. Klein, J. Reuter, G. Tóth, and H. Weinfurter, How long does it take to obtain a physical density matrix?, arXiv:1512.06866 [quant-ph] (2015).

[33] D. Suess, Ł. Rudnicki, T. O. Maciel, and D. Gross, Error regions in quantum state tomography: computational complexity caused by geometry of quantum states, New Journal of Physics 19, 093013 (2017), 10.1088/​1367-2630/​aa7ce9.

[34] K. Życzkowski, Volume of the set of separable states. II, Physical Review A 60, 3496 (1999), 10.1103/​PhysRevA.60.3496.

[35] S. Bandyopadhyay, S. Ghosh, and V. Roychowdhury, Robustness of entangled states that are positive under partial transposition, Physical Review A 77, 032318 (2008), 10.1103/​PhysRevA.77.032318.

[36] O. Gühne and G. Tóth, Entanglement detection, Physics Reports 474, 1 (2009), 10.1016/​j.physrep.2009.02.004.

[37] B. Baumgartner, B. C. Hiesmayr, and H. Narnhofer, State space for two qutrits has a phase space structure in its core, Physical Review A 74, 032327 (2006), 10.1103/​PhysRevA.74.032327.

[38] R. A. Bertlmann and P. Krammer, Bloch vectors for qudits, Journal of Physics A: Mathematical and Theoretical 41, 235303 (2008), 10.1088/​1751-8113/​41/​23/​235303.

[39] R. A. Bertlmann and P. Krammer, Bound entanglement in the set of Bell-state mixtures of two-qutrits, Physical Review A 78, 014303 (2008), 10.1103/​PhysRevA.78.014303.

[40] R. A. Bertlmann and P. Krammer, Geometric entanglement witnesses and bound entanglement, Physical Review A 77, 024303 (2008), 10.1103/​PhysRevA.77.024303.

[41] R. A. Bertlmann and P. Krammer, Entanglement witnesses and geometry of entanglement of two-qutrit states, Annals of Physics 324, 1388 (2009), 10.1016/​j.aop.2009.01.008.

[42] G. Sentís, C. Eltschka, and J. Siewert, Quantitative bound entanglement in two-qutrit states, Physical Review A 94, 020302(R) (2016), 10.1103/​PhysRevA.94.020302.

[43] T. Moroder and O. Gittsovich, Calibration-robust entanglement detection beyond Bell inequalities, Physical Review A 85, 032301 (2012), 10.1103/​PhysRevA.85.032301.

[44] N. L. Johnson, S. Kotz, and N. Balakrishnan, Continuous Univariate Distributions, 2nd ed. (John Wiley & Sons, New York) (1994), ISBN 978-0-471-58495-7.

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[9] Paul B. Slater, "Jagged Islands of Bound Entanglement and Witness-Parameterized Probabilities", arXiv:1905.09228.

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