# Non-commutativity measure of quantum discord

@article{Guo2016NoncommutativityMO, title={Non-commutativity measure of quantum discord}, author={Yu Guo}, journal={Scientific Reports}, year={2016}, volume={6} }

Quantum discord is a manifestation of quantum correlations due to non-commutativity rather than entanglement. Two measures of quantum discord by the amount of non-commutativity via the trace norm and the Hilbert-Schmidt norm respectively are proposed in this paper. These two measures can be calculated easily for any state with arbitrary dimension. It is shown by several examples that these measures can reflect the amount of the original quantum discord.

## 17 Citations

### Study on Non-Commutativity Measure of Quantum Discord

- PhysicsMathematics
- 2019

In this paper, we are concerned with the non-commutativity measure of quantum discord. We first present an explicit expression of the non-commutativity measure of quantum discord in the two-qubit…

### Non-commutative measure of quantum correlations under local operations

- MathematicsQuantum Inf. Process.
- 2019

The results accentuate the potentialities of recently introduced measures of quantum correlations based on the amount of non-commutativity quantified by the Hilbert–Schmidt norm and exhibit them as valid monotones in a resource theory of quantum correlation with free operations restricted to the appropriate local channels.

### Quantum discord of states arising from graphs

- MathematicsQuantum Inf. Process.
- 2017

This work attempts to develop a graph theoretic study of quantum discord that corresponds to a necessary and sufficient condition of zero quantum discord states which says that the blocks of density matrix corresponding to azero quantum discord state are normal and commute with each other.

### Problem of quantifying quantum correlations with non-commutative discord

- Computer ScienceQuantum Inf. Process.
- 2017

This work analyzes a non-commutativity measure of quantum correlations recently proposed by Guo and argues that a minimization procedure over the set of all possible representations of the quantum state is required and the optimal basis turns out to be that of Schmidt’s.

### Zero discord quantum states arising from weighted digraphs

- MathematicsArXiv
- 2017

This paper determines the class of quantum states whose density matrix representation can be derived from graph Laplacian matrices associated with a weighted directed graph and they are called graph LaPLacian quantum states and applies these results on some important mixed quantum states, such as the Werner, Isotropic, and $X-states.

### Nonclassicality of local bipartite correlations

- Physics
- 2017

Simulating quantum nonlocality and steering requires augmenting pre-shared randomness with non-vanishing communication cost. This prompts the question of how one may provide such an operational…

### Quantum discord and its allies: a review of recent progress

- PhysicsReports on progress in physics. Physical Society
- 2018

We review concepts and methods associated with quantum discord and related topics. We also describe their possible connections with other aspects of quantum information and beyond, including quantum…

### Geometric Quantum Discord in the Heisenberg XX Model with Three-Spin Interactions

- Physics
- 2017

Quantum discord is a resource for quantum information processing tasks, and seeking flexible ways to control it is of practical significance. We investigate the trace distance, Bures distance, and…

### Revisiting the behavior of quantum correlations under nondissipative decoherence by means of the correlation matrix

- PhysicsPhysica A: Statistical Mechanics and its Applications
- 2020

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