Dynamics of the Quantum Discord with Weak Measurement for a Two-atom System in Thermal Reservoirs
American Journal of Modern Physics
Volume 9, Issue 5, September 2020, Pages: 68-72
Received: Sep. 23, 2020;
Accepted: Nov. 5, 2020;
Published: Nov. 11, 2020
Views 21 Downloads 39
Mei Bai, School of Physical Science and Technology, Tian Gong University, Tianjin, China
Hong Jia Xu, School of Physical Science and Technology, Tian Gong University, Tianjin, China
Xue Qun Yan, School of Physical Science and Technology, Tian Gong University, Tianjin, China
Weak measurement is a kind of state partial collapse measurement developed on the basis of von Neumann measurement and positive operator value measurement, which allows us to explore the quantum world which has the least influence on the research system. Based on the weak measurement theory, the dynamics of quantum discord for two isolated atoms in their own thermal reservoirs is presented. We examine the time evolution of both standard quantum discord and quantum discord with weak measurement for the two-atom system, and analyzes the differences between the standard quantum discord and quantum discord with weak measurement in the evolution process with time, as well as the general role of the strength parameter in determing the discord and affecting its dynamic evolution. We show that quantum discords depend on how weak or strong one perturbs the quantum system. We also show that the difference of the standard quantum discord and the quantum discord with weak measurements increases as the strength parameter decreases. This means that the weak measurements can capture more quantum discord of a bipartite system. Our results show that the weak measurement performed on one of the subsystems can lead to the quantum discord that is a more natural measure of quantum correlations than the standard quantum discord captured by the projective measurements.
Hong Jia Xu,
Xue Qun Yan,
Dynamics of the Quantum Discord with Weak Measurement for a Two-atom System in Thermal Reservoirs, American Journal of Modern Physics.
Vol. 9, No. 5,
2020, pp. 68-72.
E. Knill, R. Laflamme, “Power of One Bit of Quantum Information”, Phys. Rev. Lett, 81, 5672-5675, December 1998.
L. C. Céleri, J. Maziero, J, R. M. Serra, “Theoretical and experimental aspects of quantum discord and related measures”, Int. J. Quantum Inf, 09, 1837, July 2011.
K. Modi, A. Brodutch, H. Cable, T. Paterek, V. Vedral, “The classical-quantum boundary for correlations: Discord and related measures”, Rev. Mod. Phys, 84, 1655-1707, November 2012.
W. H. Zurek, “Quantum discord and Maxwell’s demons”, Phys. Rev. A, 67, 012320, January 2003.
X. Q. Yan, Z. L. Yue, “Dynamics of quantum and classical correlations of a two-atom system in thermal reservoirs”, Chaos, Solitons & Fractals., 57, 117-122, December 2013.
M. Ali, A. R. P. Rau, G. Alber, “Quantum discord for two-qubit X states”, Phys. Rev. A, 81, 042105, April 2010.
S. Luo, “Quantum discord for two-qubit systems”, Phys. Rev. A, 77, 042303, April 2008.
G. Manzano, F. Plastina, R. Zambrini, “Optimal Work Extraction and Thermodynamics of Quantum Measurements and Correlations”, Phys. Rev. Lett., 121, 120602, September 2018.
E. Chitambar, G. Gour, “Quantum resource theories”, Rev. Mod. Phys, 91, 025001, April 2019.
A. Streltsov, G. Adesso, M. B. Plenio, “Colloquium: Quantum coherence as a resource”, Rev. Mod. Phys, 89, 041003 (34), October 2017.
J. Ma, B. Yadin, D. Girolami, V. Vedral, M. Gu, “Converting Coherence to Quantum Correlations”, Phys. Rev. Lett., 116, 160407, April 2016.
E. Knill, R. Laflamme, “Power of One Bit of Quantum Information”, Phys. Rev. Lett., 81, 5672, December 1998.
A. Datta, A. Shaji, C. M. Caves, “Quantum Discord and the Power of One Qub”, Phys. Rev. Lett., 100, 050502, February 2008.
B. P. Lanyon, M. Barbieri, M. P. Almeida, A. G. White, “Experimental Quantum Computing without Entanglement”, Phys. Rev. Lett., 101, 200501, November 2008.
M. Piani, P. Horodecki, R. Horodecki, “No-Local-Broadcasting Theorem for Multipartite Quantum Correlations”, Phys. Rev. Lett., 100, 090502, March 2008.
D. Cavalcanti, L. Aolita, S. Boixo, K. Modi, M. Piani, A. Winter, “Operational interpretations of quantum discord”, Phys. Rev. A, 83, 032324, March 2011.
V. Mdhok, A. Datta, “Interpreting quantum discord through quantum state merging”, Phys. Rev. A, 83, 032323, March 2011.
J. Wang, et al, Opt. Comm. 285, 2961, 2012.
H. Olliver, W. H. Zurek, “Quantum Discord: A Measure of the Quantumness of Correlations”, Phys. Rev. Lett., 88, 017901, December 2001.
Y. Aharonov, D. Z. Albert, L. Vaidman, “How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100”, Phys. Rev. Lett., 60, 1351, April 1988.
I. M. Duck, P. M. Stevenson, E. C. G. Sudarshan, “The sense in which a "weak measurement" of a spin-½ particle's spin component yields a value 100”, Phys. Rev. D, 40, 2112, September 1989.
O. Oreshkov, T. A. Brun, “Weak measurements are universal”, Phys. Rev. Lett., 95, 110409, November 2005.
M. Szyniszewski, A. Romito, H. Schomerus, “Entanglement transition from variable-strength weak measurements”, Phys. Rev. B, 100, 064204, August 2019.
Y. H. Chen, T. A. Brun, “Qubit positive-operator-valued measurements by destructive weak measurements”, Phys. Rev. A, 99, 062121, June 2019.
M. H. Wang, Q. Y. Cai, “High-fidelity quantum cloning of two nonorthogonal quantum states via weak measurements”, Phys. Rev. A, 99, 012324, January 2019.
L. Rosales-Zárate, B. Opanchuk, M. D. Reid, “Weak measurements and quantum weak values for NOON states”, Phys. Rev. A, 97, 032123, March 2019.
P. Wang, C. Chen, X. Peng, J. Wrachtrup, R. B. Liu, “Characterization of Arbitrary-Order Correlations in Quantum Baths by Weak Measurement”, Phys. Rev. Lett., 123, 050603, August 2019.
M. A. Nielsen, I. L. Chuang, “Quantum computation and Quantum Information”, Cambridge University press: Cambridge, 2000.
N. W. M. Ritchie, J. G. Story, R. G. Hulet, “Realization of a measurement of a ‘‘weak value”, Phys. Rev. Lett., 66, 1107-1110, March 1991.
G. J. Pryde, J. L. O’Brien, A. G. White, T. C. Ralph, H. M. Wiseman, “Measurement of Quantum Weak Values of Photon Polarization”, Phys. Rev. Lett., 94, 220405, June 2005.
J. Maziero, L. C. Céleri, R. M. Serra, V. Vedral, “Classical and quantum correlations under decoherence”, Phys. Rev. A, 80, 044102, October 2009.
M. O. Scully, M. S. Zubairy, Quantum Optics; Cambridge University Press: Cambridge, 1997.