Entropic uncertainty relation in a two-qutrit system with external magnetic field and Dzyaloshinskii–Moriya interaction under intrinsic decoherence

In this paper, we explore the dynamic behaviors of entropic uncertainty relation in a two-qutrit system which is in the presence of external magnetic field and Dzyaloshinskii–Moriya (DM) interaction under intrinsic decoherence. The effects of the isotropic bilinear interaction, the external magnetic field, the DM interaction strength, as well as the intrinsic decoherence on the entropic uncertainty relation have been demonstrated in detail. Compared with previous results, our results show that, controlling the isotropic bilinear interaction parameter J, the external magnetic field strength $$B_{0}$$B0, the DM interaction parameter D can result in inflation of the uncertainty, while increasing the intrinsic decoherence parameter can lift the uncertainty of the measurement. In particularly, under certain conditions (e.g., parameters J, $$B_{0}$$B0 and D are large enough), the entropic uncertainty will ultimately tend to a stable value and be immune to decoherence.

[1]  M. Żukowski,et al.  Security of Quantum Key Distribution with entangled Qutrits. , 2002, quant-ph/0207057.

[2]  Yang Zhang,et al.  Entropic Uncertainty Relation and Information Exclusion Relation for multiple measurements in the presence of quantum memory , 2015, Scientific Reports.

[3]  Milburn,et al.  Intrinsic decoherence in quantum mechanics. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[4]  G. Guo,et al.  Experimental investigation of the entanglement-assisted entropic uncertainty principle , 2010, 1012.0361.

[5]  J. Boileau,et al.  Conjectured strong complementary information tradeoff. , 2008, Physical review letters.

[6]  Maassen,et al.  Generalized entropic uncertainty relations. , 1988, Physical review letters.

[7]  Xu-Bo Zou,et al.  Dynamic algebraic approach to the system of a three-level atom in the Λ configuration , 1999 .

[8]  Anders Karlsson,et al.  Security of quantum key distribution using d-level systems. , 2001, Physical review letters.

[9]  C. Macchiavello,et al.  Tight entropic uncertainty relations for systems with dimension three to five , 2017, 1701.04304.

[10]  Patrick J. Coles,et al.  Uncertainty relations from simple entropic properties. , 2011, Physical review letters.

[11]  S. Solimeno,et al.  Homodyne estimation of quantum state purity by exploiting the covariant uncertainty relation , 2010, 1012.3297.

[12]  M. Bourennane,et al.  QUANTUM KEY DISTRIBUTION USING MULTILEVEL ENCODING , 2001 .

[13]  Xianqing Li-Jost,et al.  Uncertainty under quantum measures and quantum memory , 2017, Quantum Information Processing.

[14]  Patrick J. Coles,et al.  Entropic uncertainty relations and their applications , 2015, 1511.04857.

[15]  D. Deutsch.  Uncertainty in Quantum Measurements , 1983 .

[16]  Quantum-memory-assisted entropic uncertainty relation under noise , 2012, 1203.3331.

[17]  S. Severini,et al.  Entanglement and discord assisted entropic uncertainty relations under decoherence , 2014 .

[18]  R. Prevedel,et al.  Experimental investigation of the uncertainty principle in the presence of quantum memory and its application to witnessing entanglement , 2010, 1012.0332.

[19]  Ming-Liang Hu,et al.  Upper bound and shareability of quantum discord based on entropic uncertainty relations , 2013, 1301.7240.

[20]  Dong Wang,et al.  Exploration of quantum-memory-assisted entropic uncertainty relations in a noninertial frame , 2017 .

[21]  Cheng-Cheng Liu,et al.  Quantum-memory-assisted entropic uncertainty relation in a Heisenberg XYZ chain with an inhomogeneous magnetic field , 2017 .

[22]  Joseph M. Renes,et al.  Physical underpinnings of privacy , 2008 .

[23]  Ming‐Liang Hu,et al.  Competition between quantum correlations in the quantum-memory-assisted entropic uncertainty relation , 2012, 1212.0319.

[24]  T. Moriya.  Anisotropic Superexchange Interaction and Weak Ferromagnetism , 1960 .

[25]  H. P. Robertson.  The Uncertainty Principle , 1929 .

[26]  W. Heisenberg.  Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik , 1927 .

[27]  Dong Wang,et al.  Steering quantum-memory-assisted entropic uncertainty under unital and nonunital noises via filtering operations , 2017, Quantum Inf. Process..

[28]  M. Fang,et al.  Reducing quantum-memory-assisted entropic uncertainty by weak measurement and weak measurement reversal , 2015 .

[29]  Dong Wang,et al.  Exploring entropic uncertainty relation in the Heisenberg XX model with inhomogeneous magnetic field , 2017, Quantum Inf. Process..

[30]  H. Fan,et al.  Entropic uncertainty relations under the relativistic motion , 2013, 1309.7443.

[31]  Xiao Zheng,et al.  The effects of mixedness and entanglement on the properties of the entropic uncertainty in Heisenberg model with Dzyaloshinski–Moriya interaction , 2017, Quantum Inf. Process..

[32]  I. Dzyaloshinsky.  A thermodynamic theory of “weak” ferromagnetism of antiferromagnetics , 1958 .

[33]  Dong Wang,et al.  Entropic Uncertainty Relation Under Dissipative Environments and Its Steering by Local Non-unitary Operations , 2016 .

[34]  S P Walborn,et al.  Quantum key distribution with higher-order alphabets using spatially encoded qudits. , 2006, Physical review letters.

[35]  Mark M. Wilde,et al.  Quantum discord and classical correlation can tighten the uncertainty principle in the presence of quantum memory , 2012, 1204.3803.

[36]  Jian Zou,et al.  Tripartite states Bell-nonlocality sudden death with intrinsic decoherence , 2010 .

[37]  W. Heisenberg,et al.  The actual content of quantum theoretical kinematics and mechanics , 1983 .

[38]  R. Renner,et al.  Uncertainty relation for smooth entropies. , 2010, Physical review letters.