Dynamics and protection of quantum correlations in a qubit–qutrit system subjected locally to a classical random field and colored noise

This paper investigates the evolution and protection of quantum correlations (entanglement and quantum discord (QD) in particular), in a hybrid system formed by a qubit subjected to an external random field and a qutrit subjected to a colored noise generated either by a single or collection of many random bistable fluctuators (RBFs). Two different input states namely the one- and two-parameter class of states of qubit–qutrit are investigated. Entanglement and QD are quantified by means of negativity and geometric QD and their protection investigated by recourse to the weak measurement (WM) and weak measurement reversal (WMR) technique. It is shown that the immunity of entanglement and QD against decoherence can be efficiently increased by properly adjusting the parameters of the input states, no matter the spectrum of the colored noise and the number of RBFs considered. Moreover, it is shown that the WM and WMR technique fails in protecting entanglement in the studied system, but can effectively protect QD from the detrimental impacts of the decoherence. In fact, it is shown that performing a WM followed by a WMR on the qubit of the system allows to shield the QD of the system from decoherence even when the decoherence process is strengthen by considering a large number of RBFs affecting the qutrit.

[1]  A. G. White,et al.  Experimental verification of decoherence-free subspaces. , 2000, Science.

[2]  Giuseppe Compagno,et al.  Preserving entanglement and nonlocality in solid-state qubits by dynamical decoupling , 2014, 1408.6881.

[3]  L. C. Fai,et al.  Dynamics of entanglement and state-space trajectories followed by a system of four-qubit in the presence of random telegraph noise: common environment (CE) versus independent environments (IEs) , 2017, 1707.02762.

[4]  Yong-Su Kim,et al.  Experimental demonstration of decoherence suppression via quantum measurement reversal. , 2011, Optics express.

[5]  Davide Girolami,et al.  The geometric approach to quantum correlations: computability versus reliability , 2013, 1301.3526.

[6]  E. Knill,et al.  DYNAMICAL DECOUPLING OF OPEN QUANTUM SYSTEMS , 1998, quant-ph/9809071.

[7]  Yoon-Ho Kim,et al.  Quantum discord protection from amplitude damping decoherence. , 2015, Optics express.

[8]  Yong-Su Kim,et al.  Protecting entanglement from decoherence using weak measurement and quantum measurement reversal , 2012 .

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

[10]  Steane,et al.  Error Correcting Codes in Quantum Theory. , 1996, Physical review letters.

[11]  G. Falci,et al.  Hidden entanglement in the presence of random telegraph dephasing noise , 2012, 1210.1122.

[12]  Gerardo Adesso,et al.  Universal freezing of quantum correlations within the geometric approach , 2014, Scientific Reports.

[13]  Claudia Benedetti,et al.  EFFECTS OF CLASSICAL ENVIRONMENTAL NOISE ON ENTANGLEMENT AND QUANTUM DISCORD DYNAMICS , 2012, 1209.4201.

[14]  L. C. Fai,et al.  Dynamics of tripartite quantum entanglement and discord under a classical dephasing random telegraph noise , 2017 .

[15]  Xing Xiao,et al.  Protecting qutrit-qutrit entanglement by weak measurement and reversal , 2013, 1311.4692.

[16]  Fabio Sciarrino,et al.  Experimental on-demand recovery of entanglement by local operations within non-Markovian dynamics , 2014, Scientific Reports.

[17]  A. Basit,et al.  Protecting quantum coherence and discord from decoherence of depolarizing noise via weak measurement and measurement reversal , 2017 .

[18]  Dong Wang,et al.  Exploration quantum steering, nonlocality and entanglement of two-qubit X-state in structured reservoirs , 2017, Scientific Reports.

[19]  Dong Wang,et al.  Recovering the lost steerability of quantum states within non-Markovian environments by utilizing quantum partially collapsing measurements , 2017, 1709.05922.

[20]  G. Karpat,et al.  Correlation dynamics of qubit–qutrit systems in a classical dephasing environment , 2011, 1110.2040.

[21]  M. Fang,et al.  Quantum correlations of three-qubit states driven by a classical random external field , 2015 .

[22]  L. C. Fai,et al.  Dynamics of tripartite quantum correlations in mixed classical environments: The joint effects of the random telegraph and static noises , 2017 .

[23]  Arthur Tsamouo Tsokeng,et al.  Quantum correlations and decoherence dynamics for a qutrit–qutrit system under random telegraph noise , 2017, Quantum Inf. Process..

[24]  Yoon-Ho Kim,et al.  Experimental demonstration of delayed-choice decoherence suppression , 2014, Nature Communications.

[25]  Daniel A. Lidar,et al.  Decoherence-Free Subspaces for Quantum Computation , 1998, quant-ph/9807004.

[26]  Claudia Benedetti,et al.  Time-evolution of entanglement and quantum discord of bipartite systems subject to 1/fα noise , 2013, 2013 22nd International Conference on Noise and Fluctuations (ICNF).

[27]  G. Falci,et al.  Hidden entanglement, system-environment information flow and non-Markovianity , 2014, 1402.1948.

[28]  Pawel Horodecki,et al.  Distributed correlations and information flows within a hybrid multipartite quantum-classical system , 2015 .

[29]  Arthur Tsamouo Tsokeng,et al.  Free and bound entanglement dynamics in qutrit systems under Markov and non-Markov classical noise , 2018, Quantum Inf. Process..

[30]  Gerardo Adesso,et al.  Frozen quantum coherence. , 2014, Physical review letters.

[31]  Arthur Tsamouo Tsokeng,et al.  Disentanglement and quantum states transitions dynamics in spin-qutrit systems: dephasing random telegraph noise and the relevance of the initial state , 2018, Quantum Inf. Process..

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

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

[34]  Zhong-Xiao Man,et al.  Cavity-based architecture to preserve quantum coherence and entanglement , 2015, Scientific Reports.

[35]  L. C. Fai,et al.  Decoherence and tripartite entanglement dynamics in the presence of Gaussian and non-Gaussian classical noise , 2017 .

[36]  Shor,et al.  Scheme for reducing decoherence in quantum computer memory. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[37]  Erika Andersson,et al.  Revival of quantum correlations without system-environment back-action , 2010, 1009.5710.

[38]  Decoherence and protection of entanglement of a system of three qubits driven by a classical Gaussian distributed fluctuating field , 2018, Physics Letters A.

[39]  Guang-Can Guo,et al.  Experimental recovery of quantum correlations in absence of system-environment back-action , 2013, Nature Communications.

[40]  Jian Zou,et al.  Feed-forward control for quantum state protection against decoherence , 2014, 1402.4921.

[41]  Pernel Nguenang Nganyo,et al.  Frozen entanglement and quantum correlations of one-parameter qubit−qutrit states under classical noise effects , 2019, Physics Letters A.

[42]  B. Shao,et al.  Protecting quantum Fisher information of N-qubit GHZ state by weak measurement with flips against dissipation , 2017, Scientific Reports.

[43]  M. G. A. Paris,et al.  Dynamics of quantum correlations in colored-noise environments , 2012, 1212.1484.

[44]  Role of Weak Measurements on States Ordering and Monogamy of Quantum Correlation , 2013, 1304.5074.

[45]  Paolo Bordone,et al.  Time evolution of tripartite quantum discord and entanglement under local and nonlocal random telegraph noise , 2013, 1302.1430.

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

[47]  M. Ozawa.  Entanglement measures and the Hilbert-Schmidt distance , 2000, quant-ph/0002036.

[48]  Engineering decoherence for two-qubit systems interacting with a classical environment , 2014, 1408.3010.

[49]  Yoon-Ho Kim,et al.  Avoiding entanglement sudden death using single-qubit quantum measurement reversal. , 2014, Optics express.

[50]  Martin Tchoffo,et al.  Dynamical evolution of entanglement of a three-qubit system driven by a classical environmental colored noise , 2018, Quantum Inf. Process..

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

[52]  J. Cresser,et al.  Master equations with memory for systems driven by classical noise , 2010 .

[53]  G. Tóth,et al.  Entanglement detection , 2008, 0811.2803.

[54]  L. C. Fai,et al.  Quantum correlations and coherence dynamics in qutrit-qutrit systems under mixed classical environmental noises , 2017 .

[55]  Martin Tchoffo,et al.  Quantum correlations dynamics and decoherence of a three-qubit system subject to classical environmental noise , 2016 .

[56]  Daniel A. Lidar,et al.  High fidelity quantum gates via dynamical decoupling. , 2010, Physical review letters.

[57]  G. Falci,et al.  Recovering entanglement by local operations , 2012, 1207.3294.

[58]  Xiaogang Li,et al.  Protecting nonlocality of multipartite states by feed-forward control , 2018, Quantum Inf. Process..

[59]  G. Adesso,et al.  Comparative investigation of the freezing phenomena for quantum correlations under nondissipative decoherence , 2013, 1304.1163.

[60]  Ali Mortezapour,et al.  Protecting quantum resources via frequency modulation of qubits in leaky cavities , 2018, Scientific Reports.

[61]  Rosario Lo Franco,et al.  Protecting entanglement by adjusting the velocities of moving qubits inside non-Markovian environments , 2017 .

[62]  Michael J. W. Hall,et al.  Finding the Kraus decomposition from a master equation and vice versa , 2007, 0801.4100.

[63]  Farzam Nosrati,et al.  Control of noisy entanglement preparation through spatial indistinguishability , 2019 .

[64]  L. C. Fai,et al.  Effects of static noise on the dynamics of quantum correlations for a system of three qubits , 2017 .