Robustness of \(\varLambda \) -entanglement of multipartite states

By introducing the relative robustness of \(\varLambda \)-entanglement of a multipartite state related to a \(\varLambda \)-separable state, the robustness of \(\varLambda \)-entanglement of a multipartite state is defined as the minimum of the relative robustness of \(\varLambda \)-entanglement of a state related to all \(\varLambda \)-separable states. It is proved that, as a function on the set of all quantum states of an n-partite system, robustness of \(\varLambda \)-entanglement is nonnegative, lower semi-continuous, and convex, and it is zero if and only if the state is \(\varLambda \)-separable. Thus, robustness of \(\varLambda \)-entanglement not only quantifies the endurance of \(\varLambda \)-entanglement of a state against linear noise, but also can be used to distinguish \(\varLambda \)-separable states from \(\varLambda \)-entangled states. Furthermore, influences of a quantum channel on robustness of \(\varLambda \)-entanglement are discussed.

[1]  Nathan K Langford,et al.  Generation of hyperentangled photon pairs. , 2005, Physical review letters.

[2]  T. Gao,et al.  Efficient k-separability criteria for mixed multipartite quantum states , 2012, 1204.2864.

[3]  G. Vidal,et al.  Robustness of entanglement , 1998, quant-ph/9806094.

[4]  A C Doherty,et al.  Steering, entanglement, nonlocality, and the Einstein-Podolsky-Rosen paradox. , 2007, Physical review letters.

[5]  V. Vedral,et al.  Entanglement measures and purification procedures , 1997, quant-ph/9707035.

[6]  H. Cao,et al.  Some Characterizations of EPR Steering , 2018, International Journal of Theoretical Physics.

[7]  T. Gao,et al.  Separability criteria for several classes of n-partite quantum states , 2010, 1006.4516.

[8]  C. H. Bennett,et al.  Unextendible product bases and bound entanglement , 1998, quant-ph/9808030.

[9]  Yajing Fan,et al.  Continuity of the robustness of contextuality of empirical models , 2016 .

[10]  Jiangfeng Du,et al.  Geometrical interpretation for robustness of entanglement , 2000 .

[11]  Ying Yang,et al.  Einstein-Podolsky-Rosen Steering Inequalities and Applications , 2018, Entropy.

[12]  M. Lewenstein,et al.  Classification of mixed three-qubit states. , 2001, Physical review letters.

[13]  Hans J. Briegel,et al.  Multipartite entanglement in spin chains , 2005, quant-ph/0502160.

[14]  W. M. Liu,et al.  Bound of entanglement of assistance and monogamy constraints , 2009, 0904.2809.

[15]  H. Cao,et al.  Robustness of quantum correlations against linear noise , 2016 .

[16]  Otfried Guhne,et al.  Separability criteria for genuine multiparticle entanglement , 2009, 0905.1349.

[17]  Zhihua Guo,et al.  Partial correlations in multipartite quantum systems , 2014, Inf. Sci..

[18]  M. Huber,et al.  Criterion for K-separability in mixed multipartite states , 2010, 1002.2953.

[19]  H. Cao,et al.  Structures of Three Types of Local Quantum Channels Based on Quantum Correlations , 2015 .

[20]  M. Steiner.  Generalized robustness of entanglement , 2003, quant-ph/0304009.

[21]  H. Cao,et al.  Local quantum channels preserving classical correlations , 2013 .

[22]  Marcus Huber,et al.  Detection of high-dimensional genuine multipartite entanglement of mixed states. , 2009, Physical review letters.

[23]  J. Uffink,et al.  Partial separability and entanglement criteria for multiqubit quantum states , 2007, 0710.5326.

[24]  Klaus Mølmer,et al.  Entanglement and extreme spin squeezing. , 2000, Physical review letters.

[25]  Charles H. Bennett,et al.  Mixed-state entanglement and quantum error correction. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[26]  O. Gühne,et al.  Characterizing the width of entanglement , 2016 .

[27]  W. Dur,et al.  Multiparticle entanglement and its experimental detection , 2000 .

[28]  Xiao Shu,et al.  Quantum steering in tripartite quantum systems , 2018, SCIENTIA SINICA Physica, Mechanica & Astronomica.

[29]  H. Cao,et al.  Distinguishing classical correlations from quantum correlations , 2012 .

[30]  Marek Zukowski,et al.  All-versus-nothing violation of local realism by two-photon, four-dimensional entanglement. , 2005, Physical review letters.

[31]  H. Cao,et al.  Characterizing Bell nonlocality and EPR steering , 2018, Science China Physics, Mechanics & Astronomy.

[32]  H. Cao,et al.  Separability criterions of multipartite states , 2018, The European Physical Journal D.

[33]  Daniel Cavalcanti,et al.  Inequivalence of entanglement, steering, and Bell nonlocality for general measurements , 2015, 1501.03332.

[34]  Paul G. Kwiat,et al.  Hyper-entangled states , 1997 .

[35]  S. Popescu,et al.  Thermodynamics and the measure of entanglement , 1996, quant-ph/9610044.

[36]  Géza Tóth,et al.  Optimal spin squeezing inequalities detect bound entanglement in spin models. , 2007, Physical review letters.

[37]  H. Cao,et al.  Generalized Steering Robustness of Bipartite Quantum States , 2018 .