Welcome to Journal of University of Chinese Academy of Sciences,Today is
Innovation Article

Experimental test of the uncertainty relations for mixed states

  • WANG Shuang ,
  • LI Junli ,
  • WANG Hui ,
  • MENG Fangxia ,
  • QIAO Congfeng
Expand
  • 1. College of Materials Science and Opto-Electronic Technology, University of Chinese Academy of Sciences, Beijing 100049, China;
    2. School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

Received date: 2020-07-13

  Revised date: 2020-07-31

  Online published: 2021-11-16

Abstract

The uncertainty relation lies at the heart of quantum theory and behaves as a trade-off relation between the inherent uncertainties of incompatible observables. Many experiments have been devoted to the test of the various uncertainty relations, where the quantum system are mainly prepared in pure states. Here we present an experimental investigation of the direct sum majorization uncertainty relation optimal majorization uncertainty for mixed states using the coherent light. By measuring the Stokes parameters of the polarized beams, the direct sum majorization uncertainty relation for general mixed states is verified. The experimental results show that the tested majorization uncertainty relation is optimized for the mixed states.

Cite this article

WANG Shuang , LI Junli , WANG Hui , MENG Fangxia , QIAO Congfeng . Experimental test of the uncertainty relations for mixed states[J]. Journal of University of Chinese Academy of Sciences, 2021 , 38(6) : 735 -740 . DOI: 10.7523/j.issn.2095-6134.2021.06.003

References

[1] Heisenberg W. Vber den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik[J]. Zeit Phys, 1927, 43:172-198.
[2] Robertson H P. The uncertainty principle[J]. Phys Rev, 1929, 34:163-164.
[3] Deutsch D. Uncertainty in quantum measurements[J]. Physical Review Letters, 1983, 50(9):631-633.
[4] Maassen H, Uffink J B M. Generalized entropic uncertainty relations[J]. Phys Rev Lett, 1988, 60:1103-1106.
[5] Liu S, Mu L Z, Fan H. Entropic uncertainty relations for multiple measurements[J]. Phys Rev A, 2015, 91:042133.
[6] Zozor S, Bosyk G M, Portesi M. On a generalized entropic uncertainty relation in the case of the qubit[J]. Phys A:Math Theor, 2013, 46:465301.
[7] Friedland S, Gheorghiu V, Gour G. Universal uncertainty relations[J], Phys Rev Lett, 2013, 111:230401.
[8] Puchała Z, Rudnicki Ł, Z·yczkowski K. Majorization entropic uncertainty relations[J]. Phys A:Math Theor, 2013, 46:272002.
[9] Li J L, Qiao C F. The optimal uncertainty relation[J]. Ann Phys (Berlin), 2019, 531:1970036.
[10] Coles P J, Berta M, Tomamichel M, et al. Entropic uncertainty relations and their applications[J]. Rev Mod Phys, 2017, 89:015002.
[11] Li J L, Qiao C F. Reformulating the quantum uncertainty relation[J]. Sci Rep, 2015, 5:12708.
[12] Berta M, Christandl M, Colbeck R, et al. The uncertainty principle in the presence of quantum memory[J]. Nat Physics, 2010, 6:659-662.
[13] Wang D, Ming F, Hu M L, et al. Quantum-memory-assisted entropic uncertainty relations[J]. Ann Phys (Berlin), 2019, 531:1900124.
[14] Ming F, Wang D, Fan X G, et al. Improved tripartite uncertainty relation with quantum memory[J]. Phys Rev A, arXiv preprint arXiv:2004.04356, 2020, 102:012206.
[15] Wang K, Zhan X, Bian Z, et al. Experimental investigation of the stronger uncertainty relations for all incompatible observables[J]. Phys Rev A, 2016, 93:052108.
[16] Chen Z X, Li J L, Song Q C, et al. Experimental investigation of multi-observable uncertainty relations[J]. Phys Rev A, 2017, 96:062123.
[17] Chen Z X, Wang H, Li J L, et al. Tight N-observable uncertainty relations and their experimental demonstrations[J]. Sci Rep, 2019, 9:5687.
[18] Fan B W, Wang K K, Xiao L, et al. Experimental test of a stronger multiobservable uncertainty relation[J]. Phys Rev A, 2018, 98:032118.
[19] Xiao L, Fan B W, Wang K K, et al. Direct experimental test of forward and reverse uncertainty relations[J]. Phys Rev Research, 2020, 2:023106.
[20] Yuan Y, Xiao Y, Hou Z, et al. Experimental investigation of majorization uncertainty relations in the high-dimensional systems[J]. arXiv preprint arXiv:1901.00853, 2019.
[21] Yuan Y, Xiao Y L, Hou Z B, et al. Strong majorization uncertainty relations:theory and experiment[J]. arXiv preprint arXiv:1912.13383, 2019.
[22] Ma W C, Chen B, Liu Y, et al. Experimental demonstration of uncertainty relations for the triple components of angular momentum[J]. Phys Rev Lett, 2017, 118:180402.
[23] Xing J, Zhang Y R, Liu S, et al. Experimental investigation of quantum entropic uncertainty relations for multiple measurements in pure diamond[J]. Sci Rep, 2017, 7:2563.
[24] Wang H, Li J L, Wang S, et al. Experimental investigation of the uncertainty relations with coherent light[J]. Quant Inf Process, 2019, 19:38.
[25] Sponar S, Danner A, Obigane K, et al. Experimental test of tight state-independent preparation uncertainty relations for qubits[J]. Phys Rev A, arXiv preprint arXiv:2002.10725, 2020, 102(4):042204.
[26] Saleh B E A, Teich M C. Fundamentals of photonics[M]. 2nd ed. Hoboken, New Jersey:Wiley-Interscience, 2007:195-203.
[27] James D F V, Kwiat P G, Munro W J, et al. Measurement of qubits[J]. Phys Rev A, 2001, 64:052312.
[28] Wang X G, Yu C S, Yi X X. An alternative quantum fidelity for mixed states of qudits[J] Phys Lett A, 2008, 373(1):58-60.
Outlines

/