• Photonics Research
  • Vol. 10, Issue 9, 2047 (2022)
Gaoyan Zhu1, Chengjie Zhang2、3, Kunkun Wang1, Lei Xiao1, and Peng Xue1、*
Author Affiliations
  • 1Beijing Computational Science Research Center, Beijing 100084, China
  • 2School of Physical Science and Technology, Ningbo University, Ningbo 315211, China
  • 3State Key Laboratory of Precision Spectroscopy, School of Physics and Electronic Science, East China Normal University, Shanghai 200241, China
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    DOI: 10.1364/PRJ.462212 Cite this Article Set citation alerts
    Gaoyan Zhu, Chengjie Zhang, Kunkun Wang, Lei Xiao, Peng Xue. Experimental witnessing for entangled states with limited local measurements[J]. Photonics Research, 2022, 10(9): 2047 Copy Citation Text show less
    References

    [1] P. Xue, Y.-F. Xiao. Universal quantum computation in decoherence-free subspace with neutral atoms. Phys. Rev. Lett., 97, 140501(2006).

    [2] Z. Bian, J. Li, H. Qin, X. Zhan, R. Zhang, B. C. Sanders, P. Xue. Realization of single-qubit positive-operator-valued measurement via a one-dimensional photonic quantum walk. Phys. Rev. Lett., 114, 203602(2015).

    [3] R. F. Werner. Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model. Phys. Rev. A, 40, 4277-4281(1989).

    [4] A. Peres. Separability criterion for density matrices. Phys. Rev. Lett., 77, 1413-1415(1996).

    [5] O. Rudolph. On the cross norm criterion for separability. J. Phys. A, 36, 5825(2003).

    [6] K. Chen, L.-A. Wu. A matrix realignment method for recognizing entanglement(2002).

    [7] P. Wocjan, M. Horodecki. Characterization of combinatorially independent permutation separability criteria. Open Syst. Inf. Dyn., 12, 331-345(2005).

    [8] M. Horodecki, P. Horodecki, R. Horodecki. Separability of mixed quantum states: linear contractions and permutation criteria. Open Syst. Inf. Dyn., 13, 103-111(2006).

    [9] M. Horodecki, P. Horodecki, R. Horodecki. Separability of mixed states: necessary and sufficient conditions. Phys. Lett. A, 223, 1-8(1996).

    [10] B. M. Terhal. Bell inequalities and the separability criterion. Phys. Lett. A, 271, 319-326(2000).

    [11] B. M. Terhal. A family of indecomposable positive linear maps based on entangled quantum states. Linear Algebra Appl., 323, 61-73(2001).

    [12] B. M. Terhal. Detecting quantum entanglement. Theor. Comput. Sci., 287, 313-335(2002).

    [13] G. Tóth, O. Gühne. Detecting genuine multipartite entanglement with two local measurements. Phys. Rev. Lett., 94, 060501(2005).

    [14] F. A. Bovino, G. Castagnoli, A. Ekert, P. Horodecki, C. M. Alves, A. V. Sergienko. Direct measurement of nonlinear properties of bipartite quantum states. Phys. Rev. Lett., 95, 240407(2005).

    [15] O. Gühne, N. Lütkenhaus. Nonlinear entanglement witnesses. Phys. Rev. Lett., 96, 170502(2006).

    [16] R. Augusiak, M. Demianowicz, P. Horodecki. Universal observable detecting all two-qubit entanglement and determinant-based separability tests. Phys. Rev. A, 77, 030301(2008).

    [17] O. Gühne, G. Tóth. Entanglement detection. Phys. Rep., 474, 1-75(2009).

    [18] O. Gühne, P. Hyllus, D. Bruß, A. Ekert, M. Lewenstein, C. Macchiavello, A. Sanpera. Detection of entanglement with few local measurements. Phys. Rev. A, 66, 062305(2002).

    [19] O. Gühne, P. Hyllus. Investigating three qubit entanglement with local measurements. Int. J. Theor. Phys., 42, 1001-1013(2003).

    [20] O. Gühne, P. Hyllus, D. Bruss, A. Ekert, M. Lewenstein, C. Macchiavello, A. Sanpera. Experimental detection of entanglement via witness operators and local measurements. J. Mod. Opt., 50, 1079-1102(2003).

    [21] C.-J. Zhang, Y.-S. Zhang, S. Zhang, G.-C. Guo. Optimal entanglement witnesses based on local orthogonal observables. Phys. Rev. A, 76, 012334(2007).

    [22] B. Jungnitsch, T. Moroder, O. Gühne. Taming multiparticle entanglement. Phys. Rev. Lett., 106, 190502(2011).

    [23] M. Mozrzymas, A. Rutkowski, M. Studziński. Using non-positive maps to characterize entanglement witnesses. J. Phys. A: Math. Theor., 48, 395302(2015).

    [24] F. Shahandeh, M. Ringbauer, J. C. Loredo, T. C. Ralph. Ultrafine entanglement witnessing. Phys. Rev. Lett., 118, 110502(2017).

    [25] M. Gachechiladze, N. Wyderka, O. Gühne. The structure of ultrafine entanglement witnesses. J. Phys. A: Math. Theor., 51, 365307(2018).

    [26] S. Gerke, W. Vogel, J. Sperling. Numerical construction of multipartite entanglement witnesses. Phys. Rev. X, 8, 031047(2018).

    [27] D. Chruściński, G. Sarbicki, F. Wudarski. Entanglement witnesses from mutually unbiased bases. Phys. Rev. A, 97, 032318(2018).

    [28] S.-Q. Shen, T.-R. Xu, S.-M. Fei, X. Li-Jost, M. Li. Optimization of ultrafine entanglement witnesses. Phys. Rev. A, 97, 032343(2018).

    [29] T. Simnacher, N. Wyderka, R. Schwonnek, O. Gühne. Entanglement detection with scrambled data. Phys. Rev. A, 99, 062339(2019).

    [30] J. Bae, D. Chruściński, B. C. Hiesmayr. Mirrored entanglement witnesses. npj Quantum Inf., 6, 15(2020).

    [31] S.-Q. Shen, J.-M. Liang, M. Li, J. Yu, S.-M. Fei. Nonlinear improvement of qubit-qudit entanglement witnesses. Phys. Rev. A, 101, 012312(2020).

    [32] T. Li, L.-M. Lai, D.-F. Liang, S.-M. Fei, Z.-X. Wang. Entanglement witnesses based on symmetric informationally complete measurements. Int. J. Theor. Phys., 59, 3549-3557(2020).

    [33] M. Barbieri, F. De Martini, G. Di Nepi, P. Mataloni, G. M. D’Ariano, C. Macchiavello. Detection of entanglement with polarized photons: experimental realization of an entanglement witness. Phys. Rev. Lett., 91, 227901(2003).

    [34] G. Lima, E. S. Gómez, A. Vargas, R. O. Vianna, C. Saavedra. Fast entanglement detection for unknown states of two spatial qutrits. Phys. Rev. A, 82, 012302(2010).

    [35] J. Dai, Y. L. Len, Y. S. Teo, B.-G. Englert, L. A. Krivitsky. Experimental detection of entanglement with optimal-witness families. Phys. Rev. Lett., 113, 170402(2014).

    [36] F. Brange, O. Malkoc, P. Samuelsson. Minimal entanglement witness from electrical current correlations. Phys. Rev. Lett., 118, 036804(2017).

    [37] N. Friis, G. Vitagliano, M. Malik, M. Huber. Entanglement certification from theory to experiment. Nat. Rev. Phys., 1, 72-87(2019).

    [38] B. Dirkse, M. Pompili, R. Hanson, M. Walter, S. Wehner. Witnessing entanglement in experiments with correlated noise. Quantum Sci. Technol., 5, 035007(2020).

    [39] G. Zhu, D. Dilley, K. Wang, L. Xiao, E. Chitambar, P. Xue. Less entanglement exhibiting more nonlocality with noisy measurements. npj Quantum Inf., 7, 166(2021).

    [40] R. Horodecki, P. Horodecki, M. Horodecki, K. Horodecki. Quantum entanglement. Rev. Mod. Phys., 81, 865-942(2009).

    [41] M. Lewenstein, B. Kraus, J. I. Cirac, P. Horodecki. Optimization of entanglement witnesses. Phys. Rev. A, 62, 052310(2000).

    [42] A. Riccardi, D. Chruściński, C. Macchiavello. Optimal entanglement witnesses from limited local measurements. Phys. Rev. A, 101, 062319(2020).

    [43] R. Jozsa. Fidelity for mixed quantum states. J. Mod. Opt., 41, 2315-2323(1994).

    [44] J. Fiurášek. Maximum-likelihood estimation of quantum measurement. Phys. Rev. A, 64, 024102(2001).

    [45] A. Chiuri, V. Rosati, G. Vallone, S. Pádua, H. Imai, S. Giacomini, C. Macchiavello, P. Mataloni. Experimental realization of optimal noise estimation for a general Pauli channel. Phys. Rev. Lett., 107, 253602(2011).

    [46] A. Orieux, L. Sansoni, M. Persechino, P. Mataloni, M. Rossi, C. Macchiavello. Experimental detection of quantum channels. Phys. Rev. Lett., 111, 220501(2013).

    [47] K. Życzkowski, P. Horodecki, A. Sanpera, M. Lewenstein. Volume of the set of separable states. Phys. Rev. A, 58, 883-892(1998).

    [48] G. Vidal, R. F. Werner. Computable measure of entanglement. Phys. Rev. A, 65, 032314(2002).

    [49] G. Zhu, O. Kálmán, K. Wang, L. Xiao, D. Qu, X. Zhan, Z. Bian, T. Kiss, P. Xue. Experimental orthogonalization of highly overlapping quantum states with single photons. Phys. Rev. A, 100, 052307(2019).

    [50] Z. Bian, L. Xiao, K. Wang, F. A. Onanga, F. Ruzicka, W. Yi, Y. N. Joglekar, P. Xue. Quantum information dynamics in a high-dimensional parity-time-symmetric system. Phys. Rev. A, 102, 030201(2020).

    [51] X. Zhan, X. Zhang, J. Li, Y. Zhang, B. C. Sanders, P. Xue. Realization of the contextuality-nonlocality tradeoff with a qubit-qutrit photon pair. Phys. Rev. Lett., 116, 090401(2016).

    [52] D. Chruściński, G. Sarbicki. Entanglement witnesses: construction, analysis and classification. J. Phys. A, 47, 483001(2014).

    [53] K.-C. Ha. Atomic positive linear maps in matrix algebras. Publ. Res. Inst. Math. Sci., 34, 591-599(1998).

    [54] L. Xiao, T. Deng, K. Wang, G. Zhu, Z. Wang, W. Yi, P. Xue. Non-Hermitian bulk–boundary correspondence in quantum dynamics. Nat. Phys., 16, 761-766(2020).

    [55] L. Xiao, K. Wang, X. Zhan, Z. Bian, K. Kawabata, M. Ueda, W. Yi, P. Xue. Observation of critical phenomena in parity-time-symmetric quantum dynamics. Phys. Rev. Lett., 123, 230401(2019).

    [56] P. Xue, R. Zhang, H. Qin, X. Zhan, Z. H. Bian, J. Li, B. C. Sanders. Experimental quantum-walk revival with a time-dependent coin. Phys. Rev. Lett., 114, 140502(2015).

    [57] K. K. Wang, X. Qiu, L. Xiao, X. Zhan, Z. Bian, B. C. Sanders, W. Yi, P. Xue. Observation of emergent momentum-time skyrmions in parity-time-symmetric non-unitary quench dynamics. Nat. Commun., 10, 2293(2019).

    [58] L. Xiao, X. Zhan, Z. Bian, K. Wang, X. Wang, J. Li, K. Mochizuki, D. Kim, N. Kawakami, W. Yi, H. Obuse, B. C. Sanders, P. Xue. Observation of topological edge states in parity-time-symmetric quantum walks. Nat. Phys., 13, 1117-1123(2017).

    [59] K. Wang, X. Qiu, L. Xiao, X. Zhan, Z. Bian, W. Yi, P. Xue. Simulating dynamic quantum phase transitions in photonic quantum walks. Phys. Rev. Lett., 122, 020501(2019).

    Gaoyan Zhu, Chengjie Zhang, Kunkun Wang, Lei Xiao, Peng Xue. Experimental witnessing for entangled states with limited local measurements[J]. Photonics Research, 2022, 10(9): 2047
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