Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2111.07833

Beyond the entanglement of qubit pair in a mixed state

S. Shelly Sharma, Naresh Kumar Sharma

Published Nov 15, 2021• 1 citation
arXivHTMLPDF

Abstract

Given a multipartite quantum system that consists of two-level particles (qubits), one may or may not have access to all the subsystems. What can we know about the entanglement of the multiqubit system and residual correlations beyond two-tangle if we have access only to two-qubits at a time? Algebraic analysis of two-qubit states yields monogamy constraints on distribution of entanglement between sub-systems of an N-qubit state and criterion to determine if the state has multipartite entanglement. Monogamy constraints, reported in this letter, are relations between well known entanglement measures such as one-tangle, two-tangles and three-tangles of an N-qubit pure state.

DOI
10.48550/arxiv.2111.07833

Related papers

Exact monogamy constraints on entanglement of four-qubit pure states

S. Shelly Sharma

We report a set of monogamy constraints on one-tangle, two-tangles, three-tangles and four-way correlations of a general four-qubit pure state. It is found that given a two-qubit marginal $\rho$ of an $N$ qubit pure state $\left\vert \Psi_{N}\right\rangle $, the non-Hermitian matrix $\rho \widetilde{\rho}$ where $\widetilde{\rho}$ $=\left( \sigma_{y}\otimes \sigma_{y}\right) \rho^{\ast}\left( \sigma_{y}\otimes\sigma_{y}\right) $, contains information not only about the entanglement properties of the two-qubits in that state but also about the correlations of the pair of qubits with $\left( N-2\right) $ qubits in $\left\vert \Psi_{N}\right\rangle $. To extract information about tangles of a four-qubit state $\left\vert \Psi_{4}\right\rangle $, the coefficients in the characteristic polynomial of matrix $\rho\widetilde{\rho}$ are analytically expressed in terms of $2\times2$ matrices of state coefficients. A general monogamy relation satisfied by one-tangle, two-tangles, three-tangles, and residual correlations in a multiqubit state $\left\vert \Psi_{N}\right\rangle $ is also given.

•Feb 3, 2020•0 citations

Possibility of generalized monogamy relations for multipartite entanglement beyond three qubits

Christopher Eltschka, Andreas Osterloh, Jens Siewert

We discuss the possibility to interpret the residual entanglement for more than three qubits in terms of distributed multipartite entanglement or, in other words, possible extensions of the Coffman-Kundu-Wootters monogamy equality to higher qubit numbers. Existing knowledge on entanglement in multipartite systems puts narrow constraints on the form of such extensions. We study various examples for families of pure four-qubit states for which the characterization of three-qubit and four-qubit entanglement in terms of polynomial invariants is known. These examples indicate that, although families with such extensions do exist, a generalized monogamy equality cannot be found along those lines.

arXiv:0904.1034•Physical Review A•Sep 11, 2009•27 citations

Multipartite monogamy of entanglement for three qubit states

Priyabrata Char, Dipayan Chakraborty, Prabir Kumar Dey +4 more

Abstract The distribution of entanglement in a multiparty system can be described by the principle of monogamy. Monogamy is a fundamental characteristic of entanglement that restricts its distribution among more than two parties. In this work, our aim is to explore how quantum entanglement is distributed in accordance with monogamy relations, which utilize both genuine multipartite entanglement measures and bipartite entanglement measures. Specifically, we treat the source entanglement or the accessible entanglement as genuine multipartite entanglement measures and use the entanglement of formation for bipartite cases. For GHZ class states, we analytically demonstrate that the square of the source entanglement serves as an upper bound for the sum of the squares of the entanglement of formation of the reduced subsystems, with some exceptions in specific non-generic GHZ states. We will also present numerical evidence supporting this result for W-class states. In addition, we also explore the monogamy relationship by using accessible entanglement as an upper bound. Our analysis reveals an opposite but consistent pattern in the behavior of monogamy depending on whether source entanglement or accessible entanglement is used as the upper bound. This pattern emphasizes the dual nature of these two measures.

arXiv:2409.00865•Physica Scripta•Sep 2, 2025•2 citations

Shareability of correlations in multiqubit states: Optimization of nonlocal monogamy inequalities

Josep Amengual i Batle, Mosayeb Naseri, MAHMOOD GHORANNEVISS +3 more

It is a well-known fact that both quantum entanglement and nonlocality (implied by the violation of Bell inequalities) constitute quantum correlations that cannot be arbitrarily shared among subsystems. They are both monogamous, albeit in a different fashion. In the present contribution we focus on nonlocality monogamy relations such as the Toner-Verstraete, the Seevinck, and a derived monogamy inequality for three parties and compare them with multipartite nonlocality measures for the whole set of pure states distributed according to the Haar measure. In this numerical endeavor, we also see that, although monogamy relations for nonlocality cannot exist for more than three parties, in practice the exploration of the whole set of states for different numbers of qubits will return effective bounds on the maximum value of all bipartite Bell violations among subsystems. Hence, we shed light on the effective nonlocality monogamy bounds in the multiqubit case.

Physical Review A•Mar 20, 2017•46 citations

Upper bound on three-tangles of reduced states of four-qubit pure states

S. Shelly Sharma, Naresh Kumar Sharma

Closed formulas for upper bounds on three-tangles of three-qubit reduced states in terms of three-qubit--invariant polynomials of pure four-qubit states are obtained. Our results offer tighter constraints on total three-way entanglement of a given qubit with the rest of the system than those used by Regula et al. [Phys. Rev. Lett. 113, 110501 (2014) and Phys. Rev. Lett. 116, 049902(E) (2016)] to verify monogamy of four-qubit quantum entanglement.

arXiv:1610.03916•Physical Review A•Jun 6, 2017•3 citations

Monogamy of entanglement of formation

Thiago Rodrigues de Oliveira, Marcio F. Cornelio, F. F. Fanchini

It is well known that a particle cannot freely share entanglement with two or more particles. This restriction is generally called monogamy. However the formal quantification of such restriction is only known for some measures of entanglement and for two-level systems. The first and broadly known monogamy relation was established by Coffman, Kundu, and Wootters for the square of the concurrence. Since then, it is usually said that the entanglement of formation is not monogamous, as it does not obey the same relation. We show here that despite that, the entanglement of formation cannot be freely shared and therefore should be said to be monogamous. Furthermore, the square of the entanglement of formation does obey the same relation of the squared concurrence, a fact recently noted for three particles and extended here for N particles. Therefore the entanglement of formation is as monogamous as the concurrence. We also numerically study how the entanglement is distributed in pure states of three qubits and the relation between the sum of the bipartite entanglement and the classical correlation.

arXiv:1312.7287•Physical Review A•Mar 24, 2014•94 citations
Given a multipartite quantum system that consists of two-level particles (qubits), one may or may not have access to all the subsystems. What can we know about the entanglement of the multiqubit system and residual correlations beyond two-tangle if we have access only to two-qubits at a time? Algebraic analysis of two-qubit states yields monogamy constraints on distribution of entanglement between sub-systems of an N-qubit state and criterion to determine if the state has multipartite entanglement. Monogamy constraints, reported in this letter, are relations between well known entanglement measures such as one-tangle, two-tangles and three-tangles of an N-qubit pure state.
We report a set of monogamy constraints on one-tangle, two-tangles, three-tangles and four-way correlations of a general four-qubit pure state. It is found that given a two-qubit marginal ρ\rhoρ of an NNN qubit pure state $\left\vert \Psi_{N}\right\rangle $, the non-Hermitian matrix ρρ~\rho \widetilde{\rho}ρρ​ where ρ~\widetilde{\rho}ρ​ $=\left( \sigma_{y}\otimes \sigma_{y}\right) \rho^{\ast}\left( \sigma_{y}\otimes\sigma_{y}\right) $, contains information not only about the entanglement properties of the two-qubits in that state but also about the correlations of the pair of qubits with $\left( N-2\right) $ qubits in $\left\vert \Psi_{N}\right\rangle $. To extract information about tangles of a four-qubit state $\left\vert \Psi_{4}\right\rangle $, the coefficients in the characteristic polynomial of matrix ρρ~\rho\widetilde{\rho}ρρ​ are analytically expressed in terms of 2×22\times22×2 matrices of state coefficients. A general monogamy relation satisfied by one-tangle, two-tangles, three-tangles, and residual correlations in a multiqubit state $\left\vert \Psi_{N}\right\rangle $ is also given.
We discuss the possibility to interpret the residual entanglement for more than three qubits in terms of distributed multipartite entanglement or, in other words, possible extensions of the Coffman-Kundu-Wootters monogamy equality to higher qubit numbers. Existing knowledge on entanglement in multipartite systems puts narrow constraints on the form of such extensions. We study various examples for families of pure four-qubit states for which the characterization of three-qubit and four-qubit entanglement in terms of polynomial invariants is known. These examples indicate that, although families with such extensions do exist, a generalized monogamy equality cannot be found along those lines.
Abstract The distribution of entanglement in a multiparty system can be described by the principle of monogamy. Monogamy is a fundamental characteristic of entanglement that restricts its distribution among more than two parties. In this work, our aim is to explore how quantum entanglement is distributed in accordance with monogamy relations, which utilize both genuine multipartite entanglement measures and bipartite entanglement measures. Specifically, we treat the source entanglement or the accessible entanglement as genuine multipartite entanglement measures and use the entanglement of formation for bipartite cases. For GHZ class states, we analytically demonstrate that the square of the source entanglement serves as an upper bound for the sum of the squares of the entanglement of formation of the reduced subsystems, with some exceptions in specific non-generic GHZ states. We will also present numerical evidence supporting this result for W-class states. In addition, we also explore the monogamy relationship by using accessible entanglement as an upper bound. Our analysis reveals an opposite but consistent pattern in the behavior of monogamy depending on whether source entanglement or accessible entanglement is used as the upper bound. This pattern emphasizes the dual nature of these two measures.
It is a well-known fact that both quantum entanglement and nonlocality (implied by the violation of Bell inequalities) constitute quantum correlations that cannot be arbitrarily shared among subsystems. They are both monogamous, albeit in a different fashion. In the present contribution we focus on nonlocality monogamy relations such as the Toner-Verstraete, the Seevinck, and a derived monogamy inequality for three parties and compare them with multipartite nonlocality measures for the whole set of pure states distributed according to the Haar measure. In this numerical endeavor, we also see that, although monogamy relations for nonlocality cannot exist for more than three parties, in practice the exploration of the whole set of states for different numbers of qubits will return effective bounds on the maximum value of all bipartite Bell violations among subsystems. Hence, we shed light on the effective nonlocality monogamy bounds in the multiqubit case.
It is well known that a particle cannot freely share entanglement with two or more particles. This restriction is generally called monogamy. However the formal quantification of such restriction is only known for some measures of entanglement and for two-level systems. The first and broadly known monogamy relation was established by Coffman, Kundu, and Wootters for the square of the concurrence. Since then, it is usually said that the entanglement of formation is not monogamous, as it does not obey the same relation. We show here that despite that, the entanglement of formation cannot be freely shared and therefore should be said to be monogamous. Furthermore, the square of the entanglement of formation does obey the same relation of the squared concurrence, a fact recently noted for three particles and extended here for N particles. Therefore the entanglement of formation is as monogamous as the concurrence. We also numerically study how the entanglement is distributed in pure states of three qubits and the relation between the sum of the bipartite entanglement and the classical correlation.