Measurement-induced nonlocality based on the relative entropy

perspective of the relative entropy. This quantification leads to an operational interpretation for the measurementinduced nonlocality, namely, it is the maximal entropy increase after the locally invariant measurements. The relative entropy of nonlocality is upper bounded by the entropy of the measured subsystem. We establish a relationship between the relative entropy of nonlocality and the geometric nonlocality based on the HilbertSchmidt norm, and show that it is equal to the maximal distillable entanglement. Several trade-off relations are obtained for tripartite pure states. We also give explicit expressions for the relative entropy of nonlocality for Bell-diagonal states.

[1]  Schumacher,et al.  Limitation on the amount of accessible information in a quantum channel. , 1996, Physical review letters.

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

[3]  Hermann Kampermann,et al.  Linking quantum discord to entanglement in a measurement. , 2010, Physical review letters.

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

[5]  Patrick J. Coles,et al.  Information-theoretic treatment of tripartite systems and quantum channels , 2010, 1006.4859.

[6]  J. Oppenheim,et al.  Thermodynamical approach to quantifying quantum correlations. , 2001, Physical review letters.

[7]  E. Schrödinger.  Probability relations between separated systems , 1936, Mathematical Proceedings of the Cambridge Philosophical Society.

[8]  Li-Bin Fu.  Nonlocal effect of a bipartite system induced by local cyclic operation , 2006 .

[9]  Patrick J. Coles.  Unification of different views of decoherence and discord , 2011, 1110.1664.

[10]  M. Horodecki,et al.  Local versus nonlocal information in quantum-information theory: Formalism and phenomena , 2004, quant-ph/0410090.

[11]  V. Vedral.  The role of relative entropy in quantum information theory , 2001, quant-ph/0102094.

[12]  Wojciech Hubert Zurek.  Quantum discord and Maxwell's demons , 2003 .

[13]  Nicolas Gisin,et al.  Entanglement and non-locality are different resources , 2004, quant-ph/0412109.

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

[15]  Xiaoguang Wang,et al.  The upper bound and continuity of quantum discord , 2011 .

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

[17]  Valerio Scarani,et al.  An anomaly of non-locality , 2006, Quantum Inf. Comput..

[18]  N. Gisin,et al.  How much measurement independence is needed to demonstrate nonlocality? , 2010, Physical review letters.

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

[20]  J. Latorre,et al.  Quantum nonlocality in two three-level systems , 2001, quant-ph/0111143.

[21]  I. Devetak,et al.  Classical data compression with quantum side information , 2003 .

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

[23]  I. Chuang,et al.  Quantum Computation and Quantum Information: Introduction to the Tenth Anniversary Edition , 2010 .

[24]  V. Scarani,et al.  Quantum networks reveal quantum nonlocality. , 2010, Nature communications.

[25]  Nicolas Brunner,et al.  QUANTUM MECHANICS Steered towards non-locality , 2010 .

[26]  N. Gisin,et al.  Quantifying multipartite nonlocality. , 2009, Physical review letters.

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

[28]  Charles H. Bennett,et al.  Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states. , 1992, Physical review letters.

[29]  I. Ial,et al.  Nature Communications , 2010, Nature Cell Biology.

[30]  Martin B. Plenio,et al.  An introduction to entanglement measures , 2005, Quantum Inf. Comput..

[31]  Antonio Acín,et al.  Perfect quantum privacy implies nonlocality. , 2009, Physical review letters.

[32]  Shuangshuang Fu,et al.  Measurement-induced nonlocality. , 2011, Physical review letters.

[33]  Shuangshuang Fu,et al.  Global effects of quantum states induced by locally invariant measurements , 2010 .

[34]  Hermann Kampermann,et al.  On global effects caused by locally noneffective unitary operations , 2008, Quantum Inf. Comput..

[35]  Gerardo Adesso,et al.  All nonclassical correlations can be activated into distillable entanglement. , 2011, Physical review letters.