Computer Science ›› 2020, Vol. 47 ›› Issue (1): 40-50.doi: 10.11896/jsjkx.190400432

• Computer Science Theory • Previous Articles     Next Articles

Uncertainty Principle as Related to Quantum Computation

Renata WONG   

  1. (Department of Computer Science and Technology,Nanjing University,Nanjing 210093,China)1;
    (State Key Laboratory for Novel Software Technology at Nanjing University,Nanjing 210093,China)2
  • Received:2019-04-10 Published:2020-01-19
  • About author:Renata WONG,doctoral student.Her main research interests include quantum computing,protein structure prediction,physics and linguistics.
  • Supported by:
    This work was supported by the National Key R&D Program of China (2019YFA0308700) and Natural Science Foundation of Jiangsu Province (BK20191249).

Abstract: The high expectations regarding the computational potential of quantum computation stem from quantum mechanical features,such as the principle of superposition,the phenomenon of entanglement,the destructive and constructive interference.Besides the presumed advantages of quantum computation over classical computation,there exist impediments that appear to be affecting the former but not the latter.One of them are the two uncertainty principles traditionally ascribed to Werner Heisenberg.The uncertainty principle formulated originally by Heisenberg pertains to the inability of measuring a quantum system with non-quantum instruments without affecting it.This principle is different from the later development postulating an inherent inability of non-commuting observables to be measured precisely.At present state of technological development and within the current formulation and interpretation of quantum mechanics,both versions of the uncertainty affect the speed attainable by a quantum computer.Recently,the two uncertainty principles have received more attention.In his improvement to Heisenberg’s principle,Ozawa took into account both types of uncertainty mentioned above.Furthermore,research into entropic uncertainty has shown that Heisenberg’s uncertainty can be seen as a lower bound of Hirschmann’s uncertainty,thereby indicating that quantum computation may need to consider other types of uncertainties,such as information uncertainty,as well.

Key words: Quantum computing, Uncertainty principle, Uncertainty relations, Entropic uncertainty

CLC Number: 

  • TP3-0
[1]MANIN Y.Вычислимое и невычислимое [S].Советское Радио,1980.
[2]FEYNMAN R.Simulating physics with computers [J].International Journal of Theoretical Physics,1982,21(6/7):467-488.
[3]BENIOFF P A.Quantum mechanical Hamiltonian models of Turing machines [J].Journal of Statistical Physics,1982,29(3):515-546.
[4]DEUTSCH D.Quantum theory,the Church-Turing principle, and the universal quantum Turing machine [J].Proceedings of the Royal Society of London,1985,404(1818):97-117.
[5]SIMON D.On the power of quantum computation [C]∥Foundations of Computer Science.IEEE,1994:116-123.
[6]DEUTSCH D,JOZSA R.Rapid solution of problems by quantum computation [J].Proceedings of the Royal Society of London,1992,439(1907):553-558.
[7]BERNSTEIN E,VAZIRANI U.Quantum complexity theory
[C]∥Proc.25th Annual ACM Symposium on Theory of Computing.ACM,1993:11-20.
[8]SHOR P.Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer [J].SIAM Journal on Scientific and Statistical Computing,1994,26:1484-1509.
[9]BERNSTEIN D,HENINGER N,LOU P,et al.Post-quantum RSA:Report 217/351[R].Cryptology ePrint Archive,2017.
[10]MOORE G.Cramming more components onto integrated circuits [J].Electronics,1965,38(8):114-117.
[11]GREENLAW R,HOOVER H,RUZZO W.Limits to parallel computation:P-completeness theory [M].Oxford University Press,1995.
[12]LADNER R.The circuit value problem is log space complete for P [J].SIGACT News,1975,7(1):18-20.
[13]EINSTEIN A.Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt [J].Annalen der Physik,1905,17:132-148.
[14]VON NEUMANN J.Mathematische Grundlagen der Quantenmechanik [M].Springer,1932.
[15]RANGAN C,BLOCH A M,MONROE C,et al.Control of trapped-ion quantum states with optical pulses [J].Physical Review Letters,2004,92(11):113004.
[16]HUANG G M,TARN T J,CLARK J W.On the controllability of quantum-mechanical systems [J].Journal of Mathematical Physics,1983,24(11):2608- 2618.
[17]LAU H K,POOSER R,SIOPSIS G,et al.Quantum Machine Learning over Infinite Dimensions [J].arXiv:1603.06222.Physical Review Letters,2017(118):080501.
[18]BORN M.Zur Quantenmechanik der Stoβvorgänge [J]. Zeitschrift für Physik,1926,37:863-867.
[19]HEISENBERG W.Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik [J].Zeitschrift für Physik,1927,43(3):172-198.
[20]ROBERTSON H.The uncertainty principle [J].Physical Re- view,1929,34:163-164.
[21]BACH R,POPE D,LIOU S H,et al.Controlled double-slit electron diffraction [J].New Journal of Physics,2013,15:033018.
[22]SCHRÖDINGER E.An undulatory theory of the mechanics of atoms and molecules [J].Physical Review,1926,28(6):1049-1070.
[23]PAULI W.Die allgemeinen Prinzipien der Wellenmechanik
[M]∥Handbuch der Physik (24).Springer,1933.
[24]GARRISON J,WONG J.Canonically conjugate pairs,uncertainty relations,and phase operators [J].Journal of Mathematical Physics,1970,11(8):2242-2249.
[25]POISSON J.Poisson bracket [J].Journal de l’École Polytechnique,1809,8:266.
[26]MANDELSTAM L,TAMM I.The uncertainty relation between energy and time in nonrelativistic quantum mechanics [J].Journal of Physics (USSR),1945,9(4):249-254.
[27]AHARONOV Y,BOHM D.Time in the Quantum Theory and the Uncertainty Relation for Time and Energy [J].Physical Review,1961,122(5):1649-1658.
[28]BRIGGS J S.A derivation of the time-energy uncertainty relation [J].Journal of Physics Conference Series,2008,99:012002.
[29]KLEIN U.What is the limit of quantum theory? [J].American Journal of Physics,2012,80(11):1009.
[30]SEN D,SENGUPTA S.A critique of the classical limit problem of quantum mechanics [J].Foundations of Physics Letters,2006,19:403-412.
[31]SREDNICKI M.Quantum Field Theory [M].Cambridge University Press,2007.
[32]BUNGE M.The turn of the tide [M]∥Quantum theory and reality.Springer,1967.
[33]HEISENBERG W.Die physikalischen Prinzipien der Quantentheorie [M].S.Hirzel,1930.
[34]UFFINK J.The rate of evolution of a quantum state[J].Ameri- can Journal of Physics,1993,61:935.
[35]MARGOLUS N,LEVITIN L B.The maximum speed of dynami- cal evolution [J].Physica D,1998,120:188.
[36]DEFFNER S,CAMPBELL S.Quantum speed limits:from Heisenberg’s uncertainty principle to optimal quantum control [J].Journal of Physics A,2017,50(45):453001.
[37]LEVITIN L B,TOFFOLI Y.Fundamental limit on the rate of quantum dynamics:The unified bound is tight [J].Physical Review Letters,2009,103:160502.
[38]LLOYD S.Ultimate physical limits to computation [J].Nature,2000,406:1047-1054.
[39]COLES R,KANIEWSKI J,WEHNER S.Equivalence of wave-particle duality to entropic uncertainty [J].Nature Communications,2014,5:5814ôarXiv:1403.4687.
[40]COLES R,BERTA M,TOMAMICHEL M,et al.Entropic uncertainty relations and their applications [J].Reviews of Mo-dern Physics,2017,89(1):015002-1.
[41]DüRR S,REMPE G.Can wave-particle duality be based on the uncertainty relation? [J].American Journal of Physics,2000,68:1021-1024.
[42]BUSCH P,SHILLADAY C.Complementarity and uncertainty in Mach-Zehnder interferometry and beyond [J].Physics Reports,2006,435:1-31.
[43]YOUNG T.Bakerian Lecture:Experiments and calculations rela- tive to physical optics [J].Philosophical Transactions of the Royal Society,1804,94:1-16.
[44]ROZEMA L A,DARABI A,MAHLER D H,et al.Violation of Heisenberg’s measurement-disturbance relationship by weak measurements [J].Physical Review Letters,2012,109:100404.
[45]MARGENAU H.Measurements in quantum mechanics [J]. Annals of Physics,1963,23(3):469-485.
[46]POPPER K.Quantum mechanics without “the observer” [M]∥Quantum theory and reality.Springer,1967.
[47]BALLENTINE L E.The statistical interpretation of quantum mechanics [J].Review of Modern Physics,1970,42(4):358-381.
[48]OZAWA M.Uncertainty relations for noise and disturbance in generalized quantum measurements [J].Annals of Physics,2003,311(2):350-416.
[49]OZAWA M.Uncertainty relations for joint measurements of noncommuting observables [J].Physics Letters A,2004,320:367-374.
[50]BAEK S-Y,KANEDA F,OZAWA M,et al.Experimental violation and reformulation of the Heisenberg’s error-disturbance uncertainty relation [R].Scientific Reports 3,2013.
[51]HIRSCHMAN I I.A note on entropy [J].American Journal of Mathematics,1957,79(1):152-156.
[52]COLES P J,BERTA M,TOMAMICHEL M,et al.Entropic uncertainty relations and their applications [J].Review of Modern Physics,2017,89(1):015002.
[53]MAASSEN H,UFFINK J B M.Generalized entropic uncertainty relations [J].Physical review Letters,1988,60(12):1103-1106.
[54]DEUTSCH D.Uncertainty in quantum measurements [J]. Physical Review Letters,1982,50(9):631-633.
[55]BIAłYNICKI-BIRULA I,MYCIELSKI J.Uncertainty relations for information entropy in wave mechanics [J].Communications in Mathematical Physics,1975,44(2):129-132.
[1] LI Li. Survey on Multi-winner Voting Theory [J]. Computer Science, 2021, 48(1): 217-225.
[2] WANG Li-xing, CAO Fu-yuan. Huber Loss Based Nonnegative Matrix Factorization Algorithm [J]. Computer Science, 2020, 47(11): 80-87.
[3] MAN Rui, YANG Ping, JI Cheng-yu, XU Bo-wen. Survey of Classification Methods of Breast Cancer Histopathological Images [J]. Computer Science, 2020, 47(11A): 145-150.
[4] WANG Rui-jie, LI Jun-huai, WANG Kan, WANG Huai-jun, SHANG Xun-chao, TU Peng-jia. Feature Selection Method for Behavior Recognition Based on Improved Feature Subset Discrimination [J]. Computer Science, 2020, 47(11A): 204-208.
[5] LI Xing-guo, REN Yi-mei, TIAN Jing, TANG Jing-qi. Application of SFRA Method in AC Servo System [J]. Computer Science, 2020, 47(11A): 628-631.
[6] WANG Meng, DING Zhi-jun. New Device Fingerprint Feature Selection and Model Construction Method [J]. Computer Science, 2020, 47(7): 257-262.
[7] HAN Hui-jian, SONG Xin-fang, ZHANG Hui. Fuzzy Cognitive Map Method for Forecasting Urban Water Demand [J]. Computer Science, 2019, 46(11A): 47-51.
[8] ZHU Zhi-cheng, LIU Jia-wei, YAN Shao-hong. Research and Application of Multi-label Learning in Intelligent Recommendation [J]. Computer Science, 2019, 46(11A): 189-193.
[9] SUN Zhi, SUN Xue-jiao. Survey of Skyline Processing in P2P Environments [J]. Computer Science, 2018, 45(11A): 63-70.
[10] YANG Feng-kai, CHENG Su-xia. Method for Visual Adjustment of Two-camera Position Based on GA-BP Neural Network [J]. Computer Science, 2018, 45(11A): 185-188.
[11] LI Meng-jun, LI Wen-wei. Adaptive Adjustment Algorithm of Mobile Phone Screen Brightness Based on Visual Characteristics [J]. Computer Science, 2019, 46(2): 255-260.
[12] ZHAO Tian-qi, LU Dian-jie, LIU Yi-liang, ZHANG Gui-juan. Content-aware and Group-buying Based Cloud Video Delivery Networks [J]. Computer Science, 2018, 45(6A): 342-347.
[13] CHEN Jin-yin, XIONG Hui, ZHENG Hai-bin. Parameters Optimization for SVM Based on Particle Swarm Algorithm [J]. Computer Science, 2018, 45(6): 197-203.
[14] WANG Yang, LI Peng, JI Yi-mu, FAN Wei-bei, ZHANG Yu-jie, WANG Ru-chuan, CHEN Guo-liang. High Performance Computing and Astronomical Data:A Survey [J]. Computer Science, 2020, 47(1): 1-6.
Full text



[1] LEI Li-hui and WANG Jing. Parallelization of LTL Model Checking Based on Possibility Measure[J]. Computer Science, 2018, 45(4): 71 -75 .
[2] SUN Qi, JIN Yan, HE Kun and XU Ling-xuan. Hybrid Evolutionary Algorithm for Solving Mixed Capacitated General Routing Problem[J]. Computer Science, 2018, 45(4): 76 -82 .
[3] ZHANG Jia-nan and XIAO Ming-yu. Approximation Algorithm for Weighted Mixed Domination Problem[J]. Computer Science, 2018, 45(4): 83 -88 .
[4] WU Jian-hui, HUANG Zhong-xiang, LI Wu, WU Jian-hui, PENG Xin and ZHANG Sheng. Robustness Optimization of Sequence Decision in Urban Road Construction[J]. Computer Science, 2018, 45(4): 89 -93 .
[5] SHI Wen-jun, WU Ji-gang and LUO Yu-chun. Fast and Efficient Scheduling Algorithms for Mobile Cloud Offloading[J]. Computer Science, 2018, 45(4): 94 -99 .
[6] ZHOU Yan-ping and YE Qiao-lin. L1-norm Distance Based Least Squares Twin Support Vector Machine[J]. Computer Science, 2018, 45(4): 100 -105 .
[7] LIU Bo-yi, TANG Xiang-yan and CHENG Jie-ren. Recognition Method for Corn Borer Based on Templates Matching in Muliple Growth Periods[J]. Computer Science, 2018, 45(4): 106 -111 .
[8] GENG Hai-jun, SHI Xin-gang, WANG Zhi-liang, YIN Xia and YIN Shao-ping. Energy-efficient Intra-domain Routing Algorithm Based on Directed Acyclic Graph[J]. Computer Science, 2018, 45(4): 112 -116 .
[9] CUI Qiong, LI Jian-hua, WANG Hong and NAN Ming-li. Resilience Analysis Model of Networked Command Information System Based on Node Repairability[J]. Computer Science, 2018, 45(4): 117 -121 .
[10] WANG Zhen-chao, HOU Huan-huan and LIAN Rui. Path Optimization Scheme for Restraining Degree of Disorder in CMT[J]. Computer Science, 2018, 45(4): 122 -125 .