Quantifying coherence.

  title={Quantifying coherence.},
  author={Tillmann Baumgratz and Marcus Cramer and Martin Bodo Plenio},
  journal={Physical review letters},
  volume={113 14},
We introduce a rigorous framework for the quantification of coherence and identify intuitive and easily computable measures of coherence. We achieve this by adopting the viewpoint of coherence as a physical resource. By determining defining conditions for measures of coherence we identify classes of functionals that satisfy these conditions and other, at first glance natural quantities, that do not qualify as coherence measures. We conclude with an outline of the questions that remain to be… 

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These operations are incoherent in the sense that they map diagonal states to diagonal states, they are, however, a smaller set of operations

    To simplify notation, we do not specify the dimension d, the context should make this unambiguous

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      Note that we do not specify the Hilbert space structure

      • particular, H may describe compound quantum systems, e.g., H = 2 ⊗ . . . ⊗ 2 for a set of qubits


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      and K

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      Notably, for given non-trivial subspaces, the quantum operations that leave the fully incoherent states and the block diagonal structures invariant are not subsets of one another