# 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…

## Topics from this paper

## 1,184 Citations

Coherence measure: Logarithmic coherence number

- PhysicsPhysical Review A
- 2019

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

- Mathematics, PhysicsQuantum Inf. Comput.
- 2015

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.

Evaluating the robustness of
k
-coherence and
k
-entanglement

- PhysicsPhysical Review A
- 2018

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

- Physics, MathematicsJournal of Physics A: Mathematical and Theoretical
- 2018

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.

- Computer Science, MedicineOptics letters
- 2018

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

- Mathematics, Computer ScienceQuantum Inf. Process.
- 2016

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.

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

- Medicine, PhysicsPhysical review letters
- 2016

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.

Variance Measure of Coherence of Quantum Pure States

- PhysicsInternational Journal of Theoretical Physics
- 2019

We provide an expression for the measure of coherence of quantum pure states, which is obtained by quantifying the deviation or distance between the measured state and the maximally coherent states…

Entanglement as the Symmetric Portion of Correlated Coherence.

- Medicine, PhysicsPhysical review letters
- 2018

The constructions that are presented can be extended to include more general notions of nonclassical correlations, leading to quantifiers that are related to quantum discord, thus providing an avenue for unifying all such notions of quantum correlations under a single framework.

Coherence measure in terms of the Tsallis relative α entropy

- Mathematics, MedicineScientific Reports
- 2017

A family of coherence quantifiers which are closely related to the Tsallis relative α entropy are established and it is proved that this family of quantifiers satisfy all the standard criteria and particularly cover several typical coherence measures.

## References

SHOWING 1-10 OF 27 REFERENCES

"J."

- 1890

however (for it was the literal soul of the life of the Redeemer, John xv. io), is the peculiar token of fellowship with the Redeemer. That love to God (what is meant here is not God’s love to men)…

“A and B”:

- Sophonisba Breckinridge
- 2019

Direct fabrication of large micropatterned single crystals. p1205 21 Feb 2003. (news): Academy plucks best biophysicists from a sea of mediocrity. p994 14 Feb 2003.

Phys

- Rev.131, 2766
- 1963

Phys

- Rev. Lett. 112, 170403
- 2014

Contemp

- Phys. 54, 181
- 2013

Int

- J. Mod. Phys. B27, 1345019
- 2013

New J

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

Phys

- Rev. Lett. 111, 250404
- 2013

Commun

- Math. Phys. 295, 829
- 2010

Phys

- Rev. A80, 012307
- 2009