Abstract
We study the effect of weak measurements on the entropic uncertainty in two-qubit system under the generalized amplitude damping channel. Our results show that, the entropic uncertainty in qubits system can be reduced under weak measurements by choosing appropriate measuring strength, which provides a new method to break through the restriction of uncertainty relation in quantum mechanics.
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References
Bertal, M., et al.: The uncertainty principle in the presence of quantum memory. Nat. Phys. 6, 659 (2010)
Heisenberg, W.: The actual content of quantum theoretical kinematics and mechanics. Z. Phys. 43, 172 (1927)
Robertson, H.P.: The uncertainty principle. Phys. Rev. 34, 163 (1929)
Bialynicki-Birula, I.: Rényi entropy and the uncertainty relations. AIP Conf. Proc. 889, 52 (2006)
Maassen, H., Uffink, J.B.M.: Generalized entropic uncertainty relations. Phys. Rev. Lett. 60, 1103 (1988)
Kim, Y.-H., Shih, Y.: Experimental realization of popper’s experiment: Violation of the uncertainty principle? Found Phys. 29, 1849 (1999)
Renes, J.M., Boileau, J.-C.: Conjectured strong complementary information tradeoff. Phys. Rev. Lett. 103, 020402 (2009)
Li, C.F., Xu, J.S., Xu, X.Y., Li, K., Guo, G.C.: Experimental investigation of the entanglement-assisted entropic uncertainty principle. Nat. Phys. 7, 752 (2011)
Breuer H.-P., Petruccione, F.: The Theory of Open Quantum Systems. Oxford University Press, Oxford (2002)
Xu, Z.Y., Yang, W.L., Feng, M.: Quantum-memory-assisted entropic uncertainty relation under noise. Phys. Rev. A 86, 012113 (2012)
Nielson, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2002)
Aharonov, Y., Aberlt, D. Z., Vaidman, L.: 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 (1988)
Korotkov, A. N.: Continuous quantum measurement of a double dot. Phys. Rev. B 60, 5737 (1999)
Korotkov, A. N., Jordan, A. N.: Undoing a weak quantum measurement of a solid-state qubit. Phys. Rev. Lett. 97, 166805 (2006)
Korotkov, A.N., Keane, K.: Decoherence suppression by quantum measurement reversal. Phys. Rev. A 81, 040103(R) (2010)
Wang, S.C., et al.: Protecting quantum states from decoherence of finite temperature using weak measurement. Phys. Rev. A 89, 022318 (2014)
Jordan, A.N., Korotkov, A.N.: Uncollapsing the wavefunction by undoing quantum measurements. Contemp. Phys. 51, 125 (2010)
Katz, N., et al.: Coherent state evolution in a superconducting qubit from partial-collapse measurement. Science 312, 1498 (2006)
Katz, N., et al.: Reversal of the weak measurement of a quantum state in a superconducting phase qubit. Phys. Rev. Lett. 101, 200401 (2008)
Kim Y.-S., et al.: Protecting entanglement from decoherence using weak measurement and quantum measurement reversal. Nat. Phys. 8, 117 (2011)
Kim Y.-S., et al.: Reversing the weak quantum measurement for a photonic qubit. Opt. Express 17, 11978 (2009)
Yu, T., Eberly, J.H.: Environment-induced sudden death of entanglement. Science 316, 579 (2007)
Yu, T., Eberly, J.H.: Sudden death of entanglement. Science 323, 598 (2009)
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This work is supported by the National Natural Science Foundation of China (Grant No. 11374096 and 11074072).
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Zhang, SY., Fang, MF. & Yu, M. Controlling of Entropic Uncertainty in Qubits System Under the Generalized Amplitude Damping Channel via Weak Measurements. Int J Theor Phys 55, 1824–1832 (2016). https://doi.org/10.1007/s10773-015-2822-9
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DOI: https://doi.org/10.1007/s10773-015-2822-9