Exploration of entropic uncertainty relation for two accelerating atoms immersed in a bath of electromagnetic field

The uncertainty principle as an elementary theory of quantum mechanics plays an important role in quantum information science. In this paper, we study the dynamics of quantum-memory-assisted entropic uncertainty relation for two accelerating atoms coupled with a bath of fluctuating electromagnetic field. The master equation that the system evolution obeys is firstly derived. We find that the mixedness is bound up with the entropic uncertainty. For equilibrium state, the tightness of uncertainty vanishes. For the initial maximum entangled state, the tightness of uncertainty experiences a slight increase and then declines to zero with evolution time. It is found that the greater acceleration makes the uncertainty faster reach a maximum value and stable value. For a fixed acceleration, the uncertainty with different two-atom separations converges to a fixed value. Furthermore, we utilize weak measurement reversal to manipulate the entropic uncertainty. Our explorations may suggest a method of probing entanglement, acceleration effect and vacuum fluctuation effect with entropic uncertainty.

[1]  W. Unruh.  Notes on black-hole evaporation , 1976 .

[2]  Zhiming Huang,et al.  Dynamics of entropic uncertainty for atoms immersed in thermal fluctuating massless scalar field , 2018, Quantum Inf. Process..

[3]  A. Rau,et al.  Quantum discord for two-qubit X states , 2010, 1002.3429.

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

[5]  M. Suhail Zubairy,et al.  Reversing entanglement change by a weak measurement , 2010 .

[6]  Kraus.  Complementary observables and uncertainty relations. , 1987, Physical review. D, Particles and fields.

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

[8]  Zhiming Huang,et al.  Geometry and dynamics of one-norm geometric quantum discord , 2016, Quantum Inf. Process..

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

[10]  Gerardo Adesso,et al.  Generalized Geometric Quantum Speed Limits , 2015, 1507.05848.

[11]  Zhiming Huang,et al.  Optimal Protection of Quantum Coherence in Noisy Environment , 2017 .

[12]  Min Yu,et al.  Controlling the quantum-memory-assisted entropic uncertainty relation by quantum-jump-based feedback control in dissipative environments , 2017, Quantum Inf. Process..

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

[14]  Zhiming Huang,et al.  Dynamics of quantum correlation of atoms immersed in a thermal quantum scalar fields with a boundary , 2018, Quantum Inf. Process..

[15]  M. Fang,et al.  The quantum entropic uncertainty relation and entanglement witness in the two-atom system coupling with the non-Markovian environments , 2014, 1811.01155.

[16]  Hongwei Yu,et al.  Entanglement dynamics for uniformly accelerated two-level atoms coupled with electromagnetic vacuum fluctuations , 2016, 1609.06820.

[17]  Ming-Liang Hu,et al.  Quantum-memory-assisted entropic uncertainty principle, teleportation, and entanglement witness in structured reservoirs , 2012, 1208.1655.

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

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

[20]  Wei Zhang,et al.  Equivalence of Quantum Resource Measures for X States , 2017 .

[21]  Zehua Tian,et al.  Entropic uncertainty relation in de Sitter space , 2015, 1501.00623.

[22]  Michael J. W. Hall,et al.  Heisenberg-style bounds for arbitrary estimates of shift parameters including prior information , 2012, 1201.4542.

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

[24]  Fu-Wu Ma,et al.  Quantum entanglement and quantum phase transition in the XY model with staggered Dzyaloshinskii-Moriya interaction , 2011, 1106.0901.

[25]  Francesco Petruccione,et al.  The Theory of Open Quantum Systems , 2002 .

[26]  Zhiming Huang,et al.  Dynamics of Quantum Correlation in de Sitter Spacetime , 2017 .

[27]  Heng Fan,et al.  Entropic uncertainty relations for multiple measurements , 2014, 1410.5177.

[28]  Liu Ye,et al.  Renormalization of quantum discord and Bell nonlocality in the XXZ model with Dzyaloshinskii–Moriya interaction , 2014 .

[29]  Zhiming Huang,et al.  Quantum coherence behaviors of fermionic system in non-inertial frame , 2016, Quantum Inf. Process..

[30]  M. Siahatgar,et al.  Phase diagram and entanglement of the Ising model with Dzyaloshinskii-Moriya interaction , 2008, 0804.4579.

[31]  Zhiming Huang,et al.  Dynamics of quantum entanglement in de Sitter spacetime and thermal Minkowski spacetime , 2017 .

[32]  S. Fei,et al.  Quantum Discord and Geometry for a Class of Two-qubit States , 2011, 1104.1843.

[33]  E. Sudarshan,et al.  Completely Positive Dynamical Semigroups of N Level Systems , 1976 .

[34]  S. Wehner,et al.  Entropic uncertainty and measurement reversibility , 2015, 1511.00267.

[35]  Ross D. Hoehn,et al.  Entropic uncertainty relations for Markovian and non-Markovian processes under a structured bosonic reservoir , 2017, Scientific Reports.

[36]  E. H. Kennard.  Zur Quantenmechanik einfacher Bewegungstypen , 1927 .

[37]  Zhiming Huang,et al.  Dynamics of quantum correlation and coherence in de Sitter universe , 2017, Quantum Inf. Process..

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

[39]  G. Lindblad.  On the generators of quantum dynamical semigroups , 1976 .

[40]  Iwo Bialynicki-Birula.  Formulation of the uncertainty relations in terms of the Rényi entropies , 2006 .

[41]  Zhiming Huang,et al.  Protecting quantum Fisher information in curved space-time , 2018 .

[42]  Sixia Yu,et al.  Quantum discord of two-qubit X states , 2011, 1102.0181.

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

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

[45]  Hongwei Yu,et al.  Entanglement dynamics for uniformly accelerated two-level atoms , 2015, 1501.03321.

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

[47]  Arun Kumar Pati,et al.  Quantum speed limit for mixed states using an experimentally realizable metric , 2014, 1403.5182.

[48]  M. Fang,et al.  Controlling of Entropic Uncertainty in Qubits System Under the Generalized Amplitude Damping Channel via Weak Measurements , 2016 .

[49]  Dong Wang,et al.  Entropic uncertainty for spin-1/2 XXX chains in the presence of inhomogeneous magnetic fields and its steering via weak measurement reversals , 2017 .

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

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

[52]  Zhiming Huang,et al.  Protecting Quantum Correlation from Correlated Amplitude Damping Channel , 2017 .

[53]  Tao Li,et al.  High-efficiency atomic entanglement concentration for quantum communication network assisted by cavity QED , 2015, Quantum Inf. Process..

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

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

[56]  Zhiming Huang,et al.  Dynamics of quantum correlation and coherence for two atoms coupled with a bath of fluctuating massless scalar field , 2017 .

[57]  S. Salimi,et al.  Tightening the entropic uncertainty bound in the presence of quantum memory , 2016, 1602.04296.

[58]  Patrick J. Coles,et al.  Improved entropic uncertainty relations and information exclusion relations , 2013, 1307.4265.

[59]  T. Wei,et al.  Mixed-state sensitivity of several quantum-information benchmarks (6 pages) , 2004, quant-ph/0407172.

[60]  Xiangfu Zou,et al.  Protecting Qutrit Quantum Coherence , 2017 .

[61]  Dariusz Kurzyk,et al.  Conditional entropic uncertainty relations for Tsallis entropies , 2018, Quantum Inf. Process..

[62]  Zhiming Huang,et al.  Quantum-memory-assisted entropic uncertainty in spin models with Dzyaloshinskii–Moriya interaction , 2018 .

[63]  Zhiming Huang,et al.  Simultaneous dense coding affected by fluctuating massless scalar field , 2018, Quantum Inf. Process..