Coherence non-activating measurement

We define the coherence non-activating measurement as the positive operator-valued measurement which gives the same result whether or not the coherence in a quantum state is destroyed. A connection is built between the coherence activating ability of a measurement and its ability to steer quantum states when coherence non-activating measurement is free. Then we study the quantum discord based on coherence non-activating measurement and its behavior under local incoherent operations. Our results contribute to the study of resource non-activating condition, which is a complementary to the well-studied resource non-generating condition.

[1]  V. Vedral,et al.  Quantum processes which do not use coherence , 2015, 1512.02085.

[2]  Alexander Streltsov,et al.  Genuine quantum coherence , 2015, 1511.08346.

[3]  S. Luo.  Using measurement-induced disturbance to characterize correlations as classical or quantum , 2008 .

[4]  G. Gour,et al.  Comparison of incoherent operations and measures of coherence , 2016 .

[5]  J. Åberg.  Quantifying Superposition , 2006, quant-ph/0612146.

[6]  Alexei Gilchrist,et al.  A resource theory of quantum measurements , 2019, Journal of Physics A: Mathematical and Theoretical.

[7]  M. Plenio,et al.  Colloquium: quantum coherence as a resource , 2016, 1609.02439.

[8]  Yi Peng,et al.  Quantum coherence and geometric quantum discord , 2017, Physics Reports.

[9]  Aharon Brodutch,et al.  Criteria for measures of quantum correlations , 2012, Quantum Inf. Comput..

[10]  I. Walmsley,et al.  Quasiprobability representation of quantum coherence , 2018, Physical Review A.

[11]  Seth Lloyd,et al.  Resource Destroying Maps. , 2016, Physical review letters.

[12]  H. Fan,et al.  Necessary and sufficient conditions for local creation of quantum correlation , 2011, 1112.3141.

[13]  Ryuji Takagi,et al.  General Resource Theories in Quantum Mechanics and Beyond: Operational Characterization via Discrimination Tasks , 2019, Physical Review X.

[14]  Seth Lloyd,et al.  Diagonal quantum discord , 2017, Journal of Physics A: Mathematical and Theoretical.

[15]  M. Plenio,et al.  Quantifying coherence. , 2013, Physical review letters.

[16]  T. Paterek,et al.  The classical-quantum boundary for correlations: Discord and related measures , 2011, 1112.6238.

[17]  Otfried Gühne,et al.  Joint measurability of generalized measurements implies classicality. , 2014, Physical review letters.

[18]  Martin B. Plenio,et al.  Quantifying Operations with an Application to Coherence. , 2018, Physical review letters.

[19]  A. Winter,et al.  Operational Resource Theory of Coherence. , 2015, Physical review letters.

[20]  B. Sanders,et al.  Nonzero Classical Discord. , 2014, Physical review letters.

[21]  Hermann Kampermann,et al.  Behavior of quantum correlations under local noise. , 2011, Physical review letters.

[22]  Xueyuan Hu.  Channels that do not generate coherence , 2016 .

[23]  I. Walmsley,et al.  Quasistates and quasiprobabilities , 2018, Physical Review A.

[24]  Patrick J. Coles,et al.  Entropic uncertainty relations and their applications , 2015, 1511.04857.

[25]  Eric Chitambar,et al.  Critical Examination of Incoherent Operations and a Physically Consistent Resource Theory of Quantum Coherence. , 2016, Physical review letters.

[26]  Paweł Horodecki,et al.  Quantum Steering Inequality with Tolerance for Measurement-Setting Errors: Experimentally Feasible Signature of Unbounded Violation. , 2017, Physical review letters.

[27]  S. Fei,et al.  Accessible coherence and coherence distribution , 2017, 1704.07958.

[28]  Tamás Vértesi,et al.  Joint measurability, Einstein-Podolsky-Rosen steering, and Bell nonlocality. , 2014, Physical review letters.

[29]  Maassen,et al.  Generalized entropic uncertainty relations. , 1988, Physical review letters.

[30]  G. Gour.  Quantum resource theories in the single-shot regime , 2016, 1610.04247.