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- W3205392997 abstract "Abstract Since a rigorous framework for quantifying quantum coherence was established by Baumgratz et al (2014 Phys. Rev. Lett. 113 140401), many coherence measures have been found. For a given coherence measure C , extending the values of C on pure states to mixed states by the convex roof construction, we will get a valid coherence measure <?CDATA $bar{C}$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline overflow=scroll> <mml:mrow> <mml:mover accent=true> <mml:mrow> <mml:mi>C</mml:mi> </mml:mrow> <mml:mo>¯</mml:mo> </mml:mover> </mml:mrow> </mml:math> , we call <?CDATA $bar{C}$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline overflow=scroll> <mml:mrow> <mml:mover accent=true> <mml:mrow> <mml:mi>C</mml:mi> </mml:mrow> <mml:mo>¯</mml:mo> </mml:mover> </mml:mrow> </mml:math> the corresponding convex roof quantifier of C . Whether <?CDATA $C=bar{C}$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline overflow=scroll> <mml:mi>C</mml:mi> <mml:mo>=</mml:mo> <mml:mrow> <mml:mover accent=true> <mml:mrow> <mml:mi>C</mml:mi> </mml:mrow> <mml:mo>¯</mml:mo> </mml:mover> </mml:mrow> </mml:math> for a given coherence measure is an important question. In this work, we show that for the widely used coherence measure, l 1 norm of coherence <?CDATA ${C}_{{l}_{1}}$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline overflow=scroll> <mml:msub> <mml:mrow> <mml:mi>C</mml:mi> </mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>l</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> </mml:msub> </mml:math> , it holds that <?CDATA ${C}_{{l}_{1}}ne bar{{C}_{{l}_{1}}}$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline overflow=scroll> <mml:msub> <mml:mrow> <mml:mi>C</mml:mi> </mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>l</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> </mml:msub> <mml:mo>≠</mml:mo> <mml:mrow> <mml:mover accent=true> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>C</mml:mi> </mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>l</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> </mml:msub> </mml:mrow> <mml:mo>¯</mml:mo> </mml:mover> </mml:mrow> </mml:math> ." @default.
- W3205392997 created "2021-10-25" @default.
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- W3205392997 date "2022-03-08" @default.
- W3205392997 modified "2023-09-26" @default.
- W3205392997 title "l <sub>1</sub> norm of coherence is not equal to its convex roof quantifier" @default.
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