Geometric quantum discord under noisy environment

In this work, we mainly analyze the dynamics of geometric quantum discord under a common dissipating environment. Our results indicate that geometric quantum discord is generated when the initial state is a product state. The geometric quantum discord increases from zero to a stable value with the increasing time, and the variations of stable values depend on the system size. For different initial product states, geometric quantum discord has some different behaviors in contrast with entanglement. For initial maximally entangled state, it is shown that geometric quantum discord decays with the increasing dissipated time. It is found that for EPR state, entanglement is more robust than geometric quantum discord, which is a sharp contrast to the existing result that quantum discord is more robust than entanglement in noisy environments. However, for GHZ state and W state, geometric quantum discord is more stable than entanglement. By the comparison of quantum discord and entanglement, we find that a common dissipating environment brings complicated effects on quantum correlation, which may deepen our understanding of physical impacts of decohering environment on quantum correlation. In the end, we analyze the effects of collective dephasing noise and rotating noise to a class of two-qubit X states, and we find that quantum correlation is not altered by the collective noises.

[1]  Marco Piani,et al.  Problem with geometric discord , 2012, 1206.0231.

[2]  M. Lewenstein,et al.  Quantum Entanglement , 2020, Quantum Mechanics.

[3]  Davide Girolami,et al.  Observable measure of bipartite quantum correlations. , 2011, Physical review letters.

[4]  Fu-Guo Deng,et al.  Geometric measure of quantum discord for a two-parameter class of states in a qubit–qutrit system under various dissipative channels , 2012, Quantum Inf. Process..

[5]  V. Vedral,et al.  Classical and quantum correlations under decoherence , 2009, 0905.3396.

[6]  Haozhen Situ,et al.  Controlled Simultaneous Teleportation and Dense Coding , 2014 .

[7]  S. Luo,et al.  Geometric measure of quantum discord , 2010 .

[8]  Thiago O. Maciel,et al.  Witnessed entanglement and the geometric measure of quantum discord , 2012, 1207.1298.

[9]  F. F. Fanchini,et al.  Robustness of quantum discord to sudden death , 2009, 0905.3376.

[10]  Yimin Liu,et al.  Analytic expressions of discord and geometric discord in Werner derivatives , 2014, Quantum Inf. Process..

[11]  Davide Girolami,et al.  Quantum resources for hybrid communication via qubit-oscillator states , 2012, 1205.0251.

[12]  W. Zurek,et al.  Quantum discord: a measure of the quantumness of correlations. , 2001, Physical review letters.

[13]  Yannick Ole Lipp,et al.  Quantum discord as resource for remote state preparation , 2012, Nature Physics.

[14]  Felipe F. Fanchini,et al.  Sudden change of quantum discord for a system of two qubits , 2013 .

[15]  R. Laflamme,et al.  Measuring geometric quantum discord using one bit of quantum information , 2012, 1202.4475.

[16]  Yichen Huang,et al.  Computing quantum discord is NP-complete , 2013, 1305.5941.

[17]  Daowen Qiu,et al.  Simultaneous dense coding , 2009, 0909.3613.

[18]  V. Vedral,et al.  Classical, quantum and total correlations , 2001, quant-ph/0105028.

[19]  Yimin Liu,et al.  Quantum correlation swapping , 2014, Quantum Information Processing.

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

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

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

[23]  Č. Brukner,et al.  Necessary and sufficient condition for nonzero quantum discord. , 2010, Physical review letters.

[24]  Zhan-jun Zhang.  Robust multiparty quantum secret key sharing over two collective-noise channels , 2006 .

[25]  R. Laflamme,et al.  Robust polarization-based quantum key distribution over a collective-noise channel. , 2003, Physical review letters.

[26]  Zheng-Fu Han,et al.  Geometric interpretation of the geometric discord , 2012, 1303.4827.

[27]  Animesh Datta,et al.  Quantum discord and the power of one qubit. , 2007, Physical review letters.

[28]  Animesh Datta.  Quantum discord between relatively accelerated observers , 2009 .

[29]  Jin-Liang Guo,et al.  Decoherent dynamics of quantum correlations in qubit–qutrit systems , 2013, Quantum Inf. Process..

[30]  T. Paterek,et al.  Unified view of quantum and classical correlations. , 2009, Physical review letters.

[31]  S. Luo.  Quantum discord for two-qubit systems , 2008 .

[32]  M. Plenio,et al.  Quantifying Entanglement , 1997, quant-ph/9702027.

[33]  Yimin Liu,et al.  Analytic expression of quantum correlations in qutrit Werner states undergoing local and nonlocal unitary operations , 2015, Quantum Inf. Process..

[34]  Yichen Huang,et al.  Quantum discord for two-qubit X states: Analytical formula with very small worst-case error , 2013, 1306.0228.

[35]  Animesh Datta,et al.  Role of entanglement and correlations in mixed-state quantum computation , 2007 .

[36]  Jiang Zhou,et al.  Dynamics of tripartite geometric quantifiers of correlations in a quantum spin system , 2013 .

[37]  Ying Qiao,et al.  Three-qubit entanglement generation of quantum states dissipating into a common environment , 2014, Quantum Inf. Process..

[38]  Vittorio Giovannetti,et al.  Local-channel-induced rise of quantum correlations in continuous-variable systems , 2011, 1108.2143.

[39]  Preeti Parashar,et al.  Tight lower bound on geometric discord of bipartite states , 2012 .

[40]  Pramod S. Joag,et al.  Tight lower bound to the geometric measure of quantum discord , 2010, 1010.1920.

[41]  Charles H. Bennett,et al.  Postulates for measures of genuine multipartite correlations , 2008, 0805.3060.

[42]  J. Piilo,et al.  Sudden transition between classical and quantum decoherence. , 2010, Physical review letters.

[43]  Yimin Liu,et al.  A note on quantum correlations in Werner states under two collective noises , 2014, Quantum Inf. Process..

[44]  Stefano Mancini,et al.  Entanglement dynamics for qubits dissipating into a common environment , 2012, 1210.5340.

[45]  A. Acín,et al.  Almost all quantum states have nonclassical correlations , 2009, 0908.3157.

[46]  B. Lanyon,et al.  Experimental quantum computing without entanglement. , 2008, Physical review letters.

[47]  Gian Luca Giorgi,et al.  Quantum discord and remote state preparation , 2013, 1306.6873.

[48]  M. S. Sarandy.  Classical correlation and quantum discord in critical systems , 2009, 0905.1347.

[49]  G. Vidal,et al.  Computable measure of entanglement , 2001, quant-ph/0102117.

[50]  H. Fan,et al.  Monogamy inequality in terms of negativity for three-qubit states , 2007, quant-ph/0702127.

[51]  F. F. Fanchini,et al.  System-reservoir dynamics of quantum and classical correlations , 2009, 0910.5711.

[52]  Davide Girolami,et al.  Interplay between computable measures of entanglement and other quantum correlations , 2011, 1111.3643.

[53]  Zhe Sun,et al.  Geometric measure of quantum discord under decoherence , 2010, Quantum Inf. Comput..

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

[55]  Daowen Qiu,et al.  The states of W-class as shared resources for perfect teleportation and superdense coding , 2007, quant-ph/0701030.