The dynamics of two entangled qubits exposed to classical noise: role of spatial and temporal noise correlations

We investigate the decay of two-qubit entanglement caused by the influence of classical noise. We consider the whole spectrum of cases ranging from independent to fully correlated noise affecting each qubit. We take into account different spatial symmetries of noises, and the regimes of noise autocorrelation time. The latter can be either much shorter than the characteristic qubit decoherence time (Markovian decoherence), or much longer (approaching the quasi-static bath limit). We express the entanglement of two-qubit states in terms of expectation values of spherical tensor operators which allows for transparent insight into the role of the symmetry of both the two-qubit state and the noise for entanglement dynamics.

[1]  B. Bellomo,et al.  Entanglement dynamics of two independent qubits in environments with and without memory , 2007, 0711.4799.

[2]  Daniel A. Lidar Review of Decoherence‐Free Subspaces, Noiseless Subsystems, and Dynamical Decoupling , 2014 .

[3]  R. Hanson,et al.  Decay of Rabi oscillations by dipolar-coupled dynamical spin environments. , 2009, Physical review letters.

[4]  T. Yu,et al.  Finite-time disentanglement via spontaneous emission. , 2004, Physical review letters.

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

[6]  A. C. Doherty,et al.  Suppressing qubit dephasing using real-time Hamiltonian estimation , 2014, Nature Communications.

[7]  R. Fox Application of cumulant techniques to multiplicative stochastic processes , 1974 .

[8]  Jacob M. Taylor,et al.  Dephasing of Quantum Bits by a Quasi-Static Mesoscopic Environment , 2006, Quantum Inf. Process..

[9]  J. Bergli,et al.  Bloch-sphere approach to correlated noise in coupled qubits , 2012, 1205.0457.

[10]  G. Falci,et al.  1 / f noise: Implications for solid-state quantum information , 2013, 1304.7925.

[11]  W. Zurek Decoherence, einselection, and the quantum origins of the classical , 2001, quant-ph/0105127.

[12]  J. J. Sakurai,et al.  Modern Quantum Mechanics , 1986 .

[13]  L. Aolita,et al.  Open-system dynamics of entanglement:a key issues review , 2014, Reports on progress in physics. Physical Society.

[14]  Todd A. Brun,et al.  Quantum Computing , 2011, Computer Science, The Hardware, Software and Heart of It.

[15]  A. Leggett,et al.  Dynamics of the dissipative two-state system , 1987 .

[16]  N. G. Van Kampen,et al.  A cumulant expansion for stochastic linear differential equations. I , 1974 .

[17]  G. Burkard,et al.  Non-Markovian qubit dynamics in the presence of 1 / f noise , 2008, 0803.0564.

[18]  Igor Bragar,et al.  Dynamics of entanglement of two electron spins interacting with nuclear spin baths in quantum dots , 2014, 1411.6269.

[19]  Robert B. Ash,et al.  Basic probability theory , 1970 .

[20]  J. Chwedeńczuk,et al.  Parameter estimation in memory-assisted noisy quantum interferometry , 2012, 1212.2528.

[21]  W. Wootters Entanglement of Formation of an Arbitrary State of Two Qubits , 1997, quant-ph/9709029.

[22]  G. Uhlenbeck,et al.  On the Theory of the Brownian Motion II , 1945 .

[23]  G. Falci,et al.  Initial decoherence in solid state qubits. , 2005, Physical review letters.

[24]  Dong Zhou,et al.  Disentanglement and decoherence from classical non-Markovian noise: random telegraph noise , 2009, Quantum Inf. Process..

[25]  T. Yu,et al.  Qubit disentanglement and decoherence via dephasing , 2003, quant-ph/0305078.

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

[27]  Dynamical-decoupling noise spectroscopy at an optimal working point of a qubit , 2013, 1308.3102.

[28]  R. Fox Critique of the generalized cumulant expansion method , 1976 .

[29]  G. Falci,et al.  Entanglement degradation in the solid state: interplay of adiabatic and quantum noise , 2010 .

[30]  G. Guo,et al.  Reducing decoherence in quantum-computer memory with all quantum bits coupling to the same environment , 1996, quant-ph/9612003.

[31]  B. Altshuler,et al.  Decoherence of a qubit by non-Gaussian noise at an arbitrary working point , 2006, cond-mat/0603575.

[32]  W. H. Zurek,et al.  Decoherence from spin environments , 2003, quant-ph/0312207.

[33]  Horodecki Information-theoretic aspects of inseparability of mixed states. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[34]  Lukasz Cywi'nski,et al.  Dephasing of Electron Spin Qubits due to their Interaction with Nuclei in Quantum Dots , 2010, 1009.4466.

[35]  R Hanson,et al.  Universal Dynamical Decoupling of a Single Solid-State Spin from a Spin Bath , 2010, Science.

[36]  M. Horodecki,et al.  Dynamics of quantum entanglement , 2000, quant-ph/0008115.

[37]  Dong Zhou,et al.  Suppression of decoherence and disentanglement by the exchange interaction , 2011 .

[38]  Zach DeVito,et al.  Opt , 2017 .

[39]  M. Trippenbach,et al.  Spin decoherence due to fluctuating fields. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[40]  Roy Billinton,et al.  Basic probability theory , 1992 .

[41]  W. A. Coish,et al.  Spin interactions, relaxation and decoherence in quantum dots , 2009, 0903.0527.

[42]  W. Wootters,et al.  Entanglement of a Pair of Quantum Bits , 1997, quant-ph/9703041.

[43]  Daniel Nigg,et al.  A quantum information processor with trapped ions , 2013, 1308.3096.

[44]  J. Skinner,et al.  On the relationship betweenT1 andT2 for stochastic relaxation models , 1987 .

[45]  G. Falci,et al.  Effects of low-frequency noise cross-correlations in coupled superconducting qubits , 2008, 0901.0083.

[46]  R. Feynman An Operator calculus having applications in quantum electrodynamics , 1951 .

[47]  T. Monz,et al.  14-Qubit entanglement: creation and coherence. , 2010, Physical review letters.

[48]  Y. Nazarov Quantum Noise in Mesoscopic Physics , 2003 .

[49]  M. Ban Entanglement, phase correlation and dephasing of two-qubit states , 2008 .

[50]  K. Blum Density Matrix Theory and Applications , 1981 .

[51]  Y. Gefen,et al.  Onset of dissipation in Zener dynamics: Relaxation versus dephasing , 1991 .

[52]  Dissipative effects in Josephson qubits , 2003, cond-mat/0309049.

[53]  Yuriy Makhlin,et al.  Dephasing of solid-state qubits at optimal points. , 2003, Physical review letters.

[54]  T. Yu,et al.  Entanglement evolution in a non-Markovian environment , 2009, 0906.5378.

[55]  Ting Yu,et al.  Sudden death of entanglement: Classical noise effects , 2006 .

[56]  J. Avron,et al.  Communications in Mathematical Physics Landau-Zener Tunneling for Dephasing Lindblad Evolutions , 2011 .

[57]  Ë. .. C. «. ski Dephasing of Electron Spin Qubits due to their Interaction with Nuclei in Quantum Dots , 2011 .

[58]  R. J. Schoelkopf,et al.  Qubits as Spectrometers of Quantum Noise , 2003 .

[59]  U. Weiss Quantum Dissipative Systems , 1993 .

[60]  R. Joynt,et al.  TOPOLOGY OF ENTANGLEMENT EVOLUTION OF TWO QUBITS , 2010, 1007.1749.

[61]  R. Kubo GENERALIZED CUMULANT EXPANSION METHOD , 1962 .

[62]  T. Yu,et al.  Sudden Death of Entanglement , 2009, Science.

[63]  S. Sarma,et al.  Hyperfine interaction induced dephasing of coupled spin qubits in semiconductor double quantum dots , 2013, 1304.6711.

[64]  Ting Yu,et al.  Evolution from entanglement to decoherence of bipartite mixed "X" states , 2005, Quantum Inf. Comput..

[65]  Ting Yu,et al.  Modulated entanglement evolution via correlated noises , 2009, Quantum Inf. Process..