Quantifying coherence.

@article{Baumgratz2014QuantifyingC,
  title={Quantifying coherence.},
  author={Tillmann Baumgratz and Marcus Cramer and Martin Bodo Plenio},
  journal={Physical review letters},
  year={2014},
  volume={113 14},
  pages={
          140401
        }
}
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… 

Coherence measure: Logarithmic coherence number

We introduce a measure of coherence, which is extended from the coherence rank via the standard convex roof construction, we call it the logarithmic coherence number. This approach is parallel to the

Coherence measures and optimal conversion for coherent states

The optimal conversion of coherent states under incoherent operations is presented which sheds some light on the coherence of a single copy of a pure state.

Quantifying coherence in terms of the pure-state coherence

Quantifying quantum coherence is a key task in the resource theory of coherence. Here we establish a good coherence monotone in terms of a state conversion process, which automatically endows the

Evaluating the robustness of k -coherence and k -entanglement

We show that two related measures of k-coherence, called the standard and generalized robustness of k-coherence, are equal to each other when restricted to pure states. As a direct application of the

The modified trace distance of coherence is constant on most pure states

Recently, the much-used trace distance of coherence was shown to not be a proper measure of coherence, so a modification of it was proposed. We derive an explicit formula for this modified trace

Resource-theoretic approach to vectorial coherence.

A formal resource-theoretic approach to assess the coherence between partially polarized electromagnetic fields, identifying two resource theories for the vectorial coherence: polarization-sensitive coherence and polarization-insensitive coherence.

Ordering states with coherence measures

This paper considers the two well-known coherence measures, the $$l_1$$l1 norm of coherence and the relative entropy of co efficacy and the coherence of formation, to show that there are the states for which the two measures give a different ordering.

Quantifying Dynamical Coherence with Dynamical Entanglement.

The dynamical coherence of an operation upper bounds the dynamical entanglement that can be generated from it with the help of additional incoherent operations, and it is shown that an analog to theEntanglement potential exists on the level of operations and serves as a valid quantifier for dynamicals coherence.

Robustness of Coherence: An Operational and Observable Measure of Quantum Coherence.

The robustness of coherence is defined and proven to be a full monotone in the context of the recently introduced resource theories of quantum coherence, and the measure is shown to be observable.

An Alternative Framework For Quantifying Coherence Of Quantum Channels

We present an alternative framework for quantifying the coherence of quantum channels, which contains three conditions: the faithfulness, nonincreasing under sets of all the incoherent superchannels
...

References

SHOWING 1-9 OF 9 REFERENCES

Commun

  • Math. Phys. 295, 829
  • 2010

New J

  • Phys. 10, 033023 (2008) ; I. Marvian and R.W. Spekkens, New J. Phys. 15, 033001
  • 2013

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

      Quantum Inf

      • Comput. 7, 1
      • 2007

      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

      Contemp

      • Phys. 54, 181
      • 2013

      and K

      • Zyczkowski,Quantum Inf. Comput. 9, 103
      • 2009

      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