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:1608.06914 · Physical Review A

Activation of nonmonogamous multipartite quantum states

Saptarshi Roy, Tamoghna Das, Asutosh Kumar, Aditi Sen, Ujjwal Sen

Published Jul 12, 2018• 6 citations
arXivHTMLPDF

Abstract

The monogamy relation for quantum correlations is not satisfied by all measures for all multiparty quantum states. We prove that an arbitrary quantum state which is nonmonogamous for negativity will become monogamous if a finite number of copies of the same state is provided. We refer to this as activation of nonmonogamous states. We also show that multiple copies of a state satisfy monogamy for negativity if it does so for a single copy. The results are true for all quantum states of an arbitrary number of parties. Moreover, we find that for a three-qubit pure state, we can find another state such that they individually violate the monogamy relation for negativity and when taken together they can satisfy the three-party monogamy relation. This holds for all three-qubit pure states except $1%$ states from the W class, while it is true for all three-qubit pure states when a four-party monogamy relation is used to check for their activation. We connect monogamy of negativity with genuine multipartite entanglement.

DOI
10.1103/physreva.98.012310

Related papers

Superactivation of monogamy relations for nonadditive quantum correlation measures

Zhi‐Xiang Jin, Shao-Ming Fei

We investigate the general monogamy and polygamy relations satisfied by quantum correlation measures. We show that there exist two real numbers $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ such that for any quantum correlation measure $Q,{Q}^{x}$ is monogamous if $x\ensuremath{\ge}\ensuremath{\alpha}$ and polygamous if $0\ensuremath{\le}x\ensuremath{\le}\ensuremath{\beta}$ for a given multipartite state $\ensuremath{\rho}$. For $\ensuremath{\beta}<x<\ensuremath{\alpha}$, we show that the monogamy relation can be superactivated by finite $m$ copies ${\ensuremath{\rho}}^{\ensuremath{\bigotimes}m}$ of $\ensuremath{\rho}$ for nonadditive correlation measures. As a detailed example, we use the negativity as the quantum correlation measure to illustrate such superactivation of monogamy properties. A tighter monogamy relation is presented at last.

arXiv:1903.11355•Physical Review A•Mar 26, 2019•30 citations

Effect of a large number of parties on the monogamy of quantum correlations

Asutosh Kumar, R. Prabhu, Aditi Sen +1 more

Monogamy is a nonclassical property that restricts the sharability of quantum correlation among the constituents of a multipartite quantum system. Quantum correlations may satisfy or violate monogamy for quantum states, which was tested mainly for three-qubit states. Here we establish a sufficient condition for monogamy of arbitrary quantum correlation measures of states of an arbitrary number of parties, using which and further numerical results, we obtain evidence for monogamy of measures such as distillable entanglement and relative entropy of entanglement, which are physically important but mathematically intractable, for almost all quantum states of a moderate number of parties. The result is generic and holds for a large class of quantum correlation measures. Nonetheless, we identify important zero Haar measure classes of pure states that remain nonmonogamous with respect to quantum discord and quantum work deficit, irrespective of the number of qubits.

arXiv:1312.6640•Physical Review A•Jan 30, 2015•32 citations

Lower bounds on the violation of the monogamy inequality for quantum correlation measures

Asutosh Kumar, Himadri Shekhar Dhar

In multiparty quantum systems, the monogamy inequality proposes an upper bound on the distribution of bipartite quantum correlation between a single party and each of the remaining parties in the system, in terms of the amount of quantum correlation shared by that party with the rest of the system taken as a whole. However, it is well known that not all quantum correlation measures universally satisfy the monogamy inequality. In this work, we aim at determining the nontrivial value by which the monogamy inequality can be violated by a quantum correlation measure. Using an information-theoretic complementarity relation between the normalized purity and quantum correlation in any given multiparty state, we obtain a nontrivial lower bound on the negative monogamy score for the quantum correlation measure. In particular, for the three-qubit states the lower bound is equal to the negative von Neumann entropy of the single qubit reduced density matrix. We analytically examine the tightness of the derived lower bound for certain $n$-qubit quantum states. Further, we report numerical results of the same for monogamy violating correlation measures using Haar uniformly generated three-qubit states.

arXiv:1603.02957•Physical Review A•Jun 27, 2016•10 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

A monogamy equalities of complementarity relation and distribute entanglement for multi-qubit pure states

Xin-Wei Zha, Yanpeng Zhang

We propose a method to detect genuine quantum correlation for multi-qubit pure states. We then derive a complementarity relations for pure quantum states of N qubits. We prove that in all many-qubit systems there exist strict monogamy laws for quantum correlations. On the other hand, it is known that the entanglement monogamy equality proposed by Coffman, Kundu, and Wootters is in general not true for multiqubit states. Inducing from the CKW equality, we find a proper form of entanglement monogamy equality for arbitrary quantum states. The total quantum correlation of qubit k with the remaining qubits Rk can be characterizes. Furthermore, the quantum correlation of qubit mn with the remaining qubits Rmn can also be obtained. Furthermore, some monogamy relations have been obtained.

arXiv:1603.05743•Mar 18, 2016•0 citations
The monogamy relation for quantum correlations is not satisfied by all measures for all multiparty quantum states. We prove that an arbitrary quantum state which is nonmonogamous for negativity will become monogamous if a finite number of copies of the same state is provided. We refer to this as activation of nonmonogamous states. We also show that multiple copies of a state satisfy monogamy for negativity if it does so for a single copy. The results are true for all quantum states of an arbitrary number of parties. Moreover, we find that for a three-qubit pure state, we can find another state such that they individually violate the monogamy relation for negativity and when taken together they can satisfy the three-party monogamy relation. This holds for all three-qubit pure states except 11%1 states from the W class, while it is true for all three-qubit pure states when a four-party monogamy relation is used to check for their activation. We connect monogamy of negativity with genuine multipartite entanglement.
We investigate the general monogamy and polygamy relations satisfied by quantum correlation measures. We show that there exist two real numbers $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ such that for any quantum correlation measure Q,QxQ,{Q}^{x}Q,Qx is monogamous if $x\ensuremath{\ge}\ensuremath{\alpha}$ and polygamous if $0\ensuremath{\le}x\ensuremath{\le}\ensuremath{\beta}$ for a given multipartite state $\ensuremath{\rho}$. For $\ensuremath{\beta}<x<\ensuremath{\alpha}$, we show that the monogamy relation can be superactivated by finite mmm copies ${\ensuremath{\rho}}^{\ensuremath{\bigotimes}m}$ of $\ensuremath{\rho}$ for nonadditive correlation measures. As a detailed example, we use the negativity as the quantum correlation measure to illustrate such superactivation of monogamy properties. A tighter monogamy relation is presented at last.
Monogamy is a nonclassical property that restricts the sharability of quantum correlation among the constituents of a multipartite quantum system. Quantum correlations may satisfy or violate monogamy for quantum states, which was tested mainly for three-qubit states. Here we establish a sufficient condition for monogamy of arbitrary quantum correlation measures of states of an arbitrary number of parties, using which and further numerical results, we obtain evidence for monogamy of measures such as distillable entanglement and relative entropy of entanglement, which are physically important but mathematically intractable, for almost all quantum states of a moderate number of parties. The result is generic and holds for a large class of quantum correlation measures. Nonetheless, we identify important zero Haar measure classes of pure states that remain nonmonogamous with respect to quantum discord and quantum work deficit, irrespective of the number of qubits.
In multiparty quantum systems, the monogamy inequality proposes an upper bound on the distribution of bipartite quantum correlation between a single party and each of the remaining parties in the system, in terms of the amount of quantum correlation shared by that party with the rest of the system taken as a whole. However, it is well known that not all quantum correlation measures universally satisfy the monogamy inequality. In this work, we aim at determining the nontrivial value by which the monogamy inequality can be violated by a quantum correlation measure. Using an information-theoretic complementarity relation between the normalized purity and quantum correlation in any given multiparty state, we obtain a nontrivial lower bound on the negative monogamy score for the quantum correlation measure. In particular, for the three-qubit states the lower bound is equal to the negative von Neumann entropy of the single qubit reduced density matrix. We analytically examine the tightness of the derived lower bound for certain nnn-qubit quantum states. Further, we report numerical results of the same for monogamy violating correlation measures using Haar uniformly generated three-qubit states.
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.
We propose a method to detect genuine quantum correlation for multi-qubit pure states. We then derive a complementarity relations for pure quantum states of N qubits. We prove that in all many-qubit systems there exist strict monogamy laws for quantum correlations. On the other hand, it is known that the entanglement monogamy equality proposed by Coffman, Kundu, and Wootters is in general not true for multiqubit states. Inducing from the CKW equality, we find a proper form of entanglement monogamy equality for arbitrary quantum states. The total quantum correlation of qubit k with the remaining qubits Rk can be characterizes. Furthermore, the quantum correlation of qubit mn with the remaining qubits Rmn can also be obtained. Furthermore, some monogamy relations have been obtained.