Tripartite entanglement and quantum correlation

Guo, Xingyu; Ma, Chen‐Te

doi:10.1007/jhep05(2021)185

Cited by 6 publications

(7 citation statements)

References 20 publications

(33 reference statements)

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“…3. Our study respects the three-qubit pure state [5]. The choice for fixing parameters has ambiguity in the three-qubit state [5].…”

Section: Connected R-matrixmentioning

confidence: 99%

“…Our study respects the three-qubit pure state [5]. The choice for fixing parameters has ambiguity in the three-qubit state [5]. The mixed separable state restricts the choice of fixing parameters.…”

Section: Connected R-matrixmentioning

confidence: 99%

“…This result implies that the negativity cannot detect some Quantum Entanglement in entangled states. The quantification of three-qubit pure state Quantum Entanglement is not enough if losing some measures [5,6]. A partial trace operation acting on a three-qubit pure state gives a two-qubit mixed one.…”

Section: Introductionmentioning

confidence: 99%

“…It is necessary to introduce the genuine tripartite-measure, three-tangle, to describe three-body entanglement [15]. However, the two largest eigenvalues of the generalized R-matrix (or three-point correlation matrix) work and quantify Quantum Entanglement [5,6]. We want to continue this approach to the two-qubit mixed state.…”

Section: Introductionmentioning

confidence: 99%

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Quantifying Quantum Entanglement in Two-Qubit Mixed State from Connected Correlator

Guo¹,

Ma²

2022

Preprint

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The connected correlation function contributes to Classical and Quantum Entanglement simultaneously. The separable state contains the non-zero connected correlation. It shows the difficulty of quantifying Quantum Entanglement. We propose a connected correlation matrix for quantifying Quantum Entanglement in the two-qubit mixed state. Our study begins from the three-qubit state. We partial trace over one qubit to obtain the mixed state. Therefore, one can characterize Quantum Entanglement in the two-qubit mixed state from the three-qubit entanglement measures. We show that the maximum violation of Bell's inequality lose one entanglement degree. When considering the connected correlation, the result contains all necessary entanglement measures. Hence we eliminate the non-connected sector. We classify the mixed states and then demonstrate that separable states have the lowest correlation in each classified class. The entanglement measure also monotonically increases for the correlation measure. Hence we successfully quantify Quantum Entanglement. We also compare the result to the logarithmic negativity. The negativity is increasing for the correlation measure but is not monotonic. In the end, we discuss whether the quantification reflects the degree of non-locality. We assume that the observable is a vector with the locality but violates the freedom of choice. The probability distribution of the local hidden variable needs to depend on a measurement setting. Hence the interpretation of Quantum Entanglement from the locality is possible.

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“…3. Our study respects the three-qubit pure state [5]. The choice for fixing parameters has ambiguity in the three-qubit state [5].…”

Section: Connected R-matrixmentioning

confidence: 99%

Section: Connected R-matrixmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Quantifying Quantum Entanglement in Two-Qubit Mixed State from Connected Correlator

Guo¹,

Ma²

2022

Preprint

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“…2. We then generalize the R-matrix to a 3-qubit state and show that it is a proper diagnosis of Quantum Entanglement [22] in Sec. 3.…”

Section: Introductionmentioning

confidence: 99%

Non-Locality$\neq$Quantum Entanglement

Guo¹,

Ma²

2021

Preprint

Self Cite

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The only entanglement quantity is concurrence in a 2-qubit pure state. The maximum violation of Bell's inequality is monotonically increasing for this quantity. Therefore, people expect that pure state entanglement is relevant to the quantum violation. To understand the relation between violation and entanglement, we extend the study to three qubits. We consider all possible 3-qubit operators with a symmetric permutation. When only turning on one entanglement measure, the numerical result shows a contradiction to the expectation. The maximum violation does not have the same behavior as in 2-qubit pure states. Therefore, we conclude "Violation =Quantum". In the end, we propose the generalized R-matrix or correlation matrix for the new diagnosis of Quantum Entanglement. We demonstrate the evidence by restoring the monotonically increasing result.

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Strength of the non-locality of two-qubit entangled states and its applications

Garg

Adhikari

2023

Phys. Scr.

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Non-locality is a feature of quantum mechanics that cannot be explained by local realistic theory. It can be detected by the violation of Bell's inequality. In this work, we have considered the evaluation of Bell's inequality with the help of the XOR game. In the XOR game, a two-qubit entangled state is shared between the two distant players. It may generate a non-local correlation between the players which contributes to the maximum probability of winning of the game. We have aimed to determine the strength of the non-locality through XOR game. Thus, we have defined a quantity $S_{NL}$ called the strength of non-locality, purely on the basis of the maximum probability of winning of the XOR game. We have also derived the relation between the introduced quantity $S_{NL}$ and the quantity $M$ introduced in \cite{horo3}, to study the non-locality of a two-qubit entangled state problem in depth. The quantity $M$ may be defined as the sum of the two largest eigenvalues of the correlation matrix of the given entangled state and it determines whether the given entangled state under probe is non-local. Further, we have explored the non-locality of any two-qubit entangled state, whose non-locality cannot be detected by the CHSH inequality.  Interestingly, we have found that the newly defined quantity $S_{NL}$ fails to detect non-locality for the entangled state, when the witness operator corresponding to $CHSH$ operator cannot detect the entangled state. To overcome this problem, we have modified the definition of the strength of non-locality and have shown that the modified definition may detect the non-locality of such entangled states, which were earlier undetected by $S_{NL}$. Furthermore, we have provided two applications of the strength $S_{NL}$ of the non-locality such as (i) establishment of a link between the two-qubit non-locality determined by $S_{NL}$ and the three-qubit non-locality determined by the Svetlichny operator and (ii) determination of the upper bound of the power of the controller in terms of $S_{NL}$ in controlled quantum teleportation.

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Tripartite entanglement and quantum correlation

Cited by 6 publications

References 20 publications

Quantifying Quantum Entanglement in Two-Qubit Mixed State from Connected Correlator

Quantifying Quantum Entanglement in Two-Qubit Mixed State from Connected Correlator

Non-Locality$\neq$Quantum Entanglement

Strength of the non-locality of two-qubit entangled states and its applications

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