×

zbMATH — the first resource for mathematics

Uncertainty-reality complementarity and entropic uncertainty relations. (English) Zbl 1411.81046
MSC:
81P05 General and philosophical questions in quantum theory
81S05 Commutation relations and statistics as related to quantum mechanics (general)
62J10 Analysis of variance and covariance (ANOVA)
81P16 Quantum state spaces, operational and probabilistic concepts
94A17 Measures of information, entropy
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Shannon, C., The mathematical theory of communication, Bell Syst. Tech. J., 27, 379, (1948) · Zbl 1154.94303
[2] Lombardi, O.; Holik, F.; Vanni, L., What is quantum information?, Stud. Hist. Phil. Mod. Phys., 56, 17, (2016) · Zbl 1349.81063
[3] Białynicki-Birula, I.; Mycielski, J., Uncertainty relations for information entropy in wave mechanics, Commun. Math. Phys., 44, 129, (1975)
[4] Deutsch, D., Uncertainty in quantum measurements, Phys. Rev. Lett., 50, 631, (1983)
[5] Maassen, H.; Uffink, J. B M., Generalized entropic uncertainty relations, Phys. Rev. Lett., 60, 1103, (1988)
[6] Buscemi, F.; Hall, M. J W.; Ozawa, M.; Wilde, M. M., Noise and disturbance in quantum measurements: an information-theoretic approach, Phys. Rev. Lett., 112, (2014)
[7] de Vicente, J. I.; Sánchez-Ruiz, J., Improved bounds on entropic uncertainty relations, Phys. Rev. A, 77, (2008)
[8] Puchała, Z.; Rudnicki, Ł; Życzkowski, K., Majorization entropic uncertainty relations, J. Phys. A: Math. Theor., 46, (2013) · Zbl 1270.81116
[9] Friedland, S.; Gheorghiu, V.; Gour, G., Universal uncertainty relations, Phys. Rev. Lett., 111, (2013)
[10] Coles, P.; Piani, M., Improved entropic uncertainty relations and information exclusion relations, Phys. Rev. A, 89, (2014)
[11] Rudnicki, Ł; Puchała, Z.; Życzkowski, K., Strong majorization entropic uncertainty relations, Phys. Rev. A, 89, (2014)
[12] Korzekwa, K.; Lostaglio, M.; Jennings, D.; Rudolph, T., Quantum and classical entropic uncertainty relations, Phys. Rev. A, 89, (2014)
[13] Zozor, S.; Bosyk, G. M.; Portesi, M., General entropy-like uncertainty relations in finite dimensions, J. Phys. A: Math. Theor., 47, (2014) · Zbl 1305.81098
[14] Kaniewski, J.; Tomamichel, M.; Wehner, S., Entropic uncertainty from effective anticommutators, Phys. Rev. A, 90, (2014)
[15] Puchała, Z.; Rudnicki, Ł; Krawiec, A.; Życzkowski, K., Majorization uncertainty relations for mixed quantum states, J. Phys. A: Math. Theor., 51, (2018) · Zbl 1390.81056
[16] Coles, P. J.; Berta, M.; Tomamichel, M.; Wehner, S., Entropic uncertainty relations and their applications, Rev. Mod. Phys., 89, (2017)
[17] Wehner, S.; Winter, A., Entropic uncertainty relations—a survey, New J. Phys., 12, (2010) · Zbl 1360.94176
[18] Bialynicki-Birula, I.; Rudnicki, Ł; Sen, K. D., Entropic uncertainty relations in quantum physics, Statistical Complexity: Applications in Electronic Structure, 1-34, (2011), Berlin: Springer, Berlin
[19] Partovi, M. H., Entropic formulation of uncertainty for quantum measurements, Phys. Rev. Lett., 50, 1883, (1983)
[20] Bialynicki-Birula, I., Entropic uncertainty relations, Phys. Lett. A, 103, 253, (1984)
[21] Bialynicki-Birula, I., Formulation of the uncertainty relations in terms of the Rényi entropies, Phys. Rev. A, 74, (2006)
[22] Rudnicki, Ł; Walborn, S. P.; Toscano, F., Optimal uncertainty relations for extremely coarse-grained measurements, Phys. Rev. A, 85, (2012)
[23] Rudnicki, Ł, Majorization approach to entropic uncertainty relations for coarse-grained observables, Phys. Rev. A, 91, (2015)
[24] Toscano, F.; Tasca, D. S.; Rudnicki, Ł; Walborn, S. P., Uncertainty relations for coarse-grained measurements: an overview, Entropy, 20, 454, (2018)
[25] Walborn, S. P.; Taketani, B. G.; Salles, A.; Toscano, F.; de Matos Filho, R. L., Entropic entanglement criteria for continuous variables, Phys. Rev. Lett., 103, (2009)
[26] Saboia, A.; Toscano, F.; Walborn, S. P., Family of continuous-variable entanglement criteria using general entropy functions, Phys. Rev. A, 83, (2011)
[27] Tasca, D. S.; Rudnicki, Ł; Gomes, R. M.; Toscano, F.; Walborn, S. P., Reliable entanglement detection under coarse-grained measurements, Phys. Rev. Lett., 110, (2013)
[28] Schneeloch, J.; Dixon, P. B.; Howland, G. A.; Broadbent, C. J.; Howell, J. C., Violation of continuous-variable Einstein–Podolsky–Rosen steering with discrete measurements, Phys. Rev. Lett., 110, (2013)
[29] Schneeloch, J.; Broadbent, C. J.; Walborn, S. P.; Cavalcanti, E. G.; Howell, J. C., EPR steering inequalities from entropic uncertainty relations, Phys. Rev. A, 87, (2013)
[30] Schneeloch, J.; Broadbent, C. J.; Howell, J. C., Improving Einstein–Podolsky–Rosen steering inequalities with state information, Phys. Lett. A, 378, 766, (2014) · Zbl 1323.81011
[31] Koashi, M., Unconditional security of quantum key distribution and the uncertainty principle, J. Phys.: Conf. Ser., 36, 98, (2006)
[32] Brandão, F.; Horodecki, M.; Ng, N.; Oppenheim, J.; Wehner, S., The second laws of quantum thermodynamics, Proc. Natl Acad. Sci., 112, 3275, (2015)
[33] Baumgratz, T.; Cramer, M.; Plenio, M. B., Quantifying coherence, Phys. Rev. Lett., 113, (2014)
[34] Braunstein, S. L.; Caves, C. M., Information-theoretic Bell inequalities, Phys. Rev. Lett., 61, 662, (1988)
[35] Cerf, N. J.; Adami, C., Entropic Bell inequalities, Phys. Rev. A, 55, 3371, (1997)
[36] Chaves, R.; Luft, L.; Gross, D., Causal structures from entropic information: geometry and novel scenarios, New J. Phys., 16, (2014)
[37] Chaves, R.; Budroni, C., Entropic nonsignalling correlations, Phys. Rev. Lett., 116, (2016)
[38] Dieguez, P. R.; Angelo, R. M., Information-reality complementarity: the role of measurements and quantum reference frames, Phys. Rev. A, 97, (2018)
[39] Bilobran, A. L O.; Angelo, R. M., A measure of physical reality, Europhys. Lett., 112, 40005, (2015)
[40] Berta, M.; Christandl, M.; Colbeck, R.; Renes, J. M.; Renner, R., The uncertainty principle in the presence of quantum memory, Nat. Phys., 6, 659, (2010)
[41] Horodecki, R.; Horodecki, M., Information-theoretic aspects of inseparability of mixed states, Phys. Rev. A, 54, 1838, (1996)
[42] Coles, P. J.; Kaniewski, J.; Wehner, S., Equivalence of wave-particle duality to entropic uncertainty, Nat. Commun., 5, 5814, (2014)
[43] Frank, R. L.; Lieb, E. H., Extended quantum conditional entropy and quantum uncertainty inequalities, Commun. Math. Phys., 323, 487, (2013) · Zbl 1280.81022
[44] Furrer, F.; Berta, M.; Tomamichel, M.; Scholz, V. B.; Christandl, M., Position-momentum uncertainty relations in the presence of quantum memory, J. Math. Phys., 55, (2014) · Zbl 1309.81116
[45] Hall, M. J W., Universal geometric approach to uncertainty, entropy, and information, Phys. Rev. A, 59, 2602, (1999)
[46] Hall, M. J W., Information exclusion principle for complementary observables, Phys. Rev. Lett., 74, 3307, (1995) · Zbl 1020.81532
[47] Grudka, A.; Horodecki, M.; Horodecki, P.; Horodecki, R.; Kłobus, W.; Pankowski, Ł, Conjectured strong complementary-correlations tradeoff, Phys. Rev. A, 88, (2013)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.