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Probability density functions of quantum mechanical observable uncertainties. (English) Zbl 1511.81085

MSC:

81S07 Uncertainty relations, also entropic
81P16 Quantum state spaces, operational and probabilistic concepts

References:

[1] Heisenberg, W., Über den anschaulichen inhalt der quantentheoretischen kinematik und mechanik, Z. Phys., 43, 172-198 (1927) · JFM 53.0853.05 · doi:10.1007/BF01397280
[2] Dammeier, L.; Schwonneck, R.; Werner, R. F., Uncertainty relations for angular momentum, New J. Phys., 17 (2015) · Zbl 1448.81035 · doi:10.1088/1367-2630/17/9/093046
[3] Li, J. L.; Qiao, C. F., Reformulating the quantum uncertainty relation, Sci. Rep., 5, 12708 (2015) · doi:10.1038/srep12708
[4] de Guise, H.; Maccone, L.; Sanders, B. C.; Shukla, N., State-independent uncertainty relations, Phys. Rev. A, 98 (2018) · doi:10.1103/PhysRevA.98.042121
[5] Giorda, P.; Maccone, L.; Riccardi, A., State-independent uncertainty relations from eigenvalue minimization, Phys. Rev. A, 99 (2019) · doi:10.1103/PhysRevA.99.052121
[6] Xiao, Y.; Guo, C.; Meng, F.; Jing, N.; Yung, M-H, Incompatibility of observables as state-independent bound of uncertainty relations, Phys. Rev. A, 100 (2019) · doi:10.1103/PhysRevA.100.032118
[7] Sponar, S.; Danner, A.; Obigane, K.; Hack, S.; Hasegawa, Y., Experimental test of tight state-independent preparation uncertainty relations for qubits, Phys. Rev. A, 102 (2020) · doi:10.1103/PhysRevA.102.042204
[8] Seife, C., Do deeper principles underlie quantum uncertainty and nonlocality?, Science, 309, 98 (2005) · doi:10.1126/science.309.5731.98
[9] Hofmann, H. F.; Takeuchi, S., Violation of local uncertainty relations as a signature of entanglement, Phys. Rev. A, 68 (2003) · doi:10.1103/PhysRevA.68.032103
[10] Gühne, O., Characterizing entanglement via uncertainty relations, Phys. Rev. Lett., 92 (2004) · doi:10.1103/PhysRevLett.92.117903
[11] Gühne, O.; Tóth, G., Entanglement detection, Phys. Rep., 474, 1 (2009) · doi:10.1016/j.physrep.2009.02.004
[12] Schwonnek, R.; Dammeier, L.; Werner, R. F., State-independent uncertainty relations and entanglement detection in noisy systems, Phys. Rev. Lett., 119 (2017) · doi:10.1103/PhysRevLett.119.170404
[13] Qian, C.; Li, J-L; Qiao, C-F, State-independent uncertainty relations and entanglement detection, Quantum Inf. Process., 17, 84 (2018) · Zbl 1395.81045 · doi:10.1007/s11128-018-1855-4
[14] Zhao, Y-Y; Xiang, G. Y.; Hu, X. M.; Liu, B. H.; Li, C. F.; Guo, G. C.; Schwonnek, R.; Wolf, R., Entanglement detection by violations of noisy uncertainty relations:a proof of principle, Phys. Rev. Lett., 122 (2019) · doi:10.1103/PhysRevLett.122.220401
[15] Oppenheim, J.; Wehner, S., The uncertainty principle determines the nonlocality of quantum mechanics, Science, 330, 1072-1074 (2010) · Zbl 1226.81013 · doi:10.1126/science.1192065
[16] Kennard, E. H., Zur Quantenmechanik einfacher Bewegungstypen, Z. Phys., 44, 326-352 (1927) · JFM 53.0853.02 · doi:10.1007/BF01391200
[17] Weyl, H., Gruppentheorie und Quantenmechanik (1928), Hirzel: Leipzig, Hirzel · JFM 54.0954.03
[18] Robertson, H. P., The uncertainty principle, Phys. Rev., 34, 163-164 (1929) · doi:10.1103/PhysRev.34.163
[19] Schrödinger, E., Zum heisenbergschen unscharfeprinzip, Sitzungsberichte der Preussischen Akademie der Wissenschaften, Physikalisch-Mathematische Klasse, 14, 296-303 (1930) · JFM 56.0754.05
[20] Busch, P.; Reardon-Smith, O., On quantum uncertainty relations and uncertainty regions (1901)
[21] Zhang, L.; Wang, J., Average of uncertainty product for bounded observables, Open Syst. Inf. Dyn., 25 (2018) · Zbl 1401.81060 · doi:10.1142/S1230161218500087
[22] Maccone, L.; Pati, A. K., Stronger uncertainty relations for all incompatible observables, Phys. Rev. Lett., 113 (2014) · doi:10.1103/PhysRevLett.113.260401
[23] Hastings, M. B., Superadditivity of communication capacity using entangled inputs, Nat. Phys., 5, 255-257 (2009) · doi:10.1038/nphys1224
[24] Christandl, M.; Doran, B.; Kousidis, S.; Walter, M., Eigenvalue distributions of reduced density matrices, Commun. Math. Phys., 332, 1-52 (2014) · Zbl 1304.81051 · doi:10.1007/s00220-014-2144-4
[25] Dartois, S.; Lionni, L.; Nechita, I., The joint distribution of the marginals of multipartite random quantum states, Random Matrices: Theory Appl., 9 (2020) · Zbl 1476.81018 · doi:10.1142/S2010326320500100
[26] Zhang, L.; Wang, J.; Chen, Z. H., Spectral density of mixtures of random density matrices for qubits, Phys. Lett. A, 382, 1516-1523 (2018) · Zbl 1396.81103 · doi:10.1016/j.physleta.2018.04.018
[27] Zhang, L.; Jiang, Y. X.; Wu, J. D., Duistermaat-Heckman measure and the mixture of quantum states, J. Phys. A: Math. Theor., 52 (2019) · Zbl 1509.81030 · doi:10.1088/1751-8121/ab5297
[28] Venuti, L. C.; Zanardi, P., Probability density of quantum expectation values, Phys. Lett. A, 377, 1854-1861 (2013) · Zbl 1302.81045 · doi:10.1016/j.physleta.2013.05.041
[29] Zhang, L.; Luo, S.; Fei, S-M; Wu, J., Uncertainty regions of observables and state-independent uncertainty relations, Quantum Inf. Process., 20, 357 (2021) · Zbl 1508.81892 · doi:10.1007/s11128-021-03303-w
[30] Hoskins, R. F., Delta Function (2009), Amsterdam: Elsevier, Amsterdam
[31] Zhang, L., Dirac delta function of matrix argument, Int. J. Theor. Phys., 60, 2445-2472 (2021) · Zbl 1528.26005 · doi:10.1007/s10773-020-04598-8
[32] Bauer, M.; Zuber, J-B, On products of delta distributions and resultants, SIGMA, 16, 083 (2020) · Zbl 1468.46047
[33] Petz, D.; Tóth, G., Matrix variances with projections, Acta Sci. Math., 78, 683-688 (2012) · Zbl 1289.81006 · doi:10.1007/BF03651392
[34] Bhatia, R.; Davis, C., A better bound on the variance, Am. Math. Mon., 107, 353-357 (2000) · Zbl 1009.15009 · doi:10.1080/00029890.2000.12005203
[35] Zhang, L.; Ma, Z.; Chen, Z.; Fei, S-M, Coherence generating power of unitary transformations via probabilistic average, Quantum Inf. Process., 17, 186 (2018) · Zbl 1448.81187 · doi:10.1007/s11128-018-1928-4
[36] Gutkin, E.; Życzkowski, K., Joint numerical ranges, quantum maps, and joint numerical shadows, Linear Algebr. Appl., 438, 2394-2404 (2013) · Zbl 1266.15034 · doi:10.1016/j.laa.2012.10.043
[37] Gallay, T.; Serre, D., The numerical measure of a complex matrix, Commun. Pure Appl. Math., 65, 287-336 (2012) · Zbl 1244.15015 · doi:10.1002/cpa.20374
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