SCIENCE CHINA Information Sciences, Volume 60, Issue 5: 052501(2017) https://doi.org/10.1007/s11432-016-9006-6

## Quantifying quantum information resources: a numerical study

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• ReceivedSep 30, 2016
• AcceptedDec 17, 2016
• PublishedMar 14, 2017
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### Abstract

Quantum systems present correlations, which cannot be offered by classical objects. These distinctive correlations are not only considered as fundamental features of quantum mechanics, but more importantly, they are regarded as critical resources for different quantum information tasks. For example, quantum entanglement has been established as the key resource for quantum communication, and quantum discord has been suggested as the resource in deterministic quantum computation with one qubit (DQC1). However, quantification of these resources is very difficult, especially for many-body situations. Here, we introduce a unified numerical method to quantify these resources in general multiqubit states and use it to investigate the robustness of quantum discord in multiqubit permutation-invariant states. Our method paves the way to quantitatively investigate the relation between the potential of quantum technologies and quantum resources, particularly, that between quantum computation and quantum correlations.

### Acknowledgment

Lixin HE acknowledges the support from Chinese National Fundamental Research Program (Grant No. 2011CB921200), National Natural Science Funds for Distinguished Young Scholars, and the Fundamental Research Funds for the Central Universities (Grant No. WK2470000006).

• Figure 1

Entanglement of 4-qubit permutation-invariant state, i.e., Eq. (14) mixed by $| S(4,1) \rangle$ and $| S(4,1) \rangle$. The analytical result is represented by solid line and the numerical result by open circles.

• Figure 2

Quantum discord of 4 and 5-qubit superpositions of two canonical orthonormal GHZ states as in (15). The 4-qubit numerical result is represented by open circles and the 5-qubit numerical result by crosses, compared to the analytical result represented by solid line.

• Figure 3

(Color online) Quantum discord of $3$ to $6$ qubit states (18) mixed by permutation-invariant states $| S(n,1) \rangle$ and $| S(n,1) \rangle$.

• Figure 4

(Color online) Quantum discord of 4-qubit mboxstates (19) mixed by $| S(4,1) \rangle$, $| S(4,1) \rangle$ and $| S(4,3) \rangle$, plotted on $\alpha$-$\beta$ plane.

• Figure 5

(Color online) Robustness of the turning point: Quantum discord of the original 4-qubit state in (19) when $\alpha=0$, and the states after tracing out one and two qubits from the original state. The turning point exists in all three states, showing its robustness.

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