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

Communications in Theoretical Physics

Monogamy of Measurement-Induced Nonlocality Based on Relative Entropy

Yu Luo, Zhengjun Xi, Yongming Li

Published Nov 1, 2014• 4 citations
Publisher

Abstract

In this paper, using relative entropy, we study monogamous properties of measurement-induced nonlocality based on relative entropy. Depending on different measurement sides, we provide necessary and sufficient conditions for two types of monogamy inequalities. By the concept of nonlocality monogamy score, we find a necessary condition of the vanished nonlocality monogamy score for arbitrary three-party states. In addition, two types of necessary and sufficient conditions of the vanished nonlocality monogamy scores are obtained for any pure states. As an application, we show that measurement-induced nonlocality based on relative entropy can be viewed as a "nonlocality witness" to distinguish generalized GHZ states from the generalized W states.

DOI
10.1088/0253-6102/62/5/08

Related papers

Monogamy of measurement-induced nonlocality

Ajoy Sen, Debasis Sarkar, Amit Bhar

Measurement-Induced NonLocality was introduced by Luo and Fu (Phys. Rev. Lett. \textbf{106}, 120401,(2011)) as a measure of nonlocality in a bipartite state. In this paper we will discuss monogamy property of measurement-induced nonlocality for some three- and four-qubit classes of states. Unlike discord, we find quite surprising results in this situation. Both the GHZ and W states satisfy monogamy relations in the three-qubit case, however, in general there are violations of monogamy relations in both the GHZ-class and W-class states. In case of four-qubit system, monogamy holds for most of the states in the generic class. Four qubit GHZ does not satisfy monogamy relation, but W-state does. We provide several numerical results including counterexamples regarding monogamy nature of measurement induced nonlocality. We will also extend our results of generalized W-class to n-qubit.

arXiv:1201.2041•Journal of Physics A Mathematical and Theoretical•Sep 19, 2012•18 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

Are General Quantum Correlations Monogamous?

Alexander Streltsov, Gerardo Adesso, Marco Piani +1 more

Quantum entanglement and quantum nonlocality are known to exhibit monogamy; that is, they obey strong constraints on how they can be distributed among multipartite systems. Quantum correlations that comprise and go beyond entanglement are quantified by, e.g., quantum discord. It was observed recently that for some states quantum discord is not monogamous. We prove, in general, that any measure of correlations that is monogamous for all states and satisfies reasonable basic properties must vanish for all separable states: only entanglement measures can be strictly monogamous. Monogamy of other than entanglement measures can still be satisfied for special, restricted cases: we prove that the geometric measure of discord satisfies the monogamy inequality on all pure states of three qubits.

arXiv:1112.3967•Physical Review Letters•Aug 1, 2012•171 citations

Unmasking the polygamous nature of quantum nonlocality

Paweł Cieśliński, Lukas Knips, Mateusz Kowalczyk +4 more

Quantum mechanics imposes limits on the statistics of certain observables. Perhaps the most famous example is the uncertainty principle. Similar trade-offs also exist for the simultaneous violation of multiple Bell inequalities. In the simplest case of three observers, it has been shown that if two observers violate a Bell inequality, then none of them can violate any Bell inequality with the third observer, a property called monogamy of Bell violations. Forms of Bell monogamy have been linked to the no-signaling principle, and the inability of simultaneous violations of all inequalities is regarded as their fundamental property. Here, we show that the Bell monogamy does not hold universally and that in fact the only monogamous situation exists for only three observers. Consequently, the nature of quantum nonlocality is truly polygamous. We present a systematic methodology for identifying quantum states, measurements, and tight Bell inequalities that do not obey the monogamy principle for any number of more than three observers. The identified polygamous inequalities enable any subset of [Formula: see text] observers to reveal nonlocality, which is also shown experimentally by measuring Bell-type correlations of six-photon Dicke states. Our findings may be exploited for multiparty quantum key distribution as well as simultaneous self-testing of multiple nodes in quantum networks.

arXiv:2312.04373•Proceedings of the National Academy of Sciences•Oct 25, 2024•7 citations

Conditions for monogamy of quantum correlations: Greenberger-Horne-Zeilinger versus W states

R. Prabhu, Arun Kumar Pati, Aditi Sen +1 more

Quantum correlations are expected to respect all the conditions required for them to be good measures of quantumness in the bipartite scenario. In a multipartite setting, sharing entanglement between several parties is restricted by the monogamy of entanglement. We take over the concept of monogamy to an information-theoretic quantum correlation measure, and find that it violates monogamy in general. Using the notion of interaction information, we identify necessary and sufficient conditions for the measure to obey monogamy, for arbitrary pure and mixed quantum states. We show that while three-qubit generalized Greenberger-Horne-Zeilinger states follow monogamy, generalized $W$ states do not.

arXiv:1108.5168•Physical Review A•Apr 30, 2012•107 citations

Measurement-induced nonlocality in the W and Greenberger–Horne–Zeilinger superposition states

Qin Lin, Yan-Kui Bai, Ming-Yong Ye +1 more

Measurement-induced nonlocality (MIN) is a newly defined quantity to measure correlations in bipartite quantum states [Luo S and Fu S 2011 Phys. Rev. Lett. 106 120401]. MIN in the n -qubit W and Greenberger–Horne–Zeilinger (GHZ) superposition states is considered. It is revealed that n =3 and n ≥ 4 states have very different characteristics, especially the monogamy relation about MIN, and the monogamy equality of MIN is held in all n -qubit W states ( n ≥ 3).

Chinese Physics B•Feb 26, 2015•4 citations
In this paper, using relative entropy, we study monogamous properties of measurement-induced nonlocality based on relative entropy. Depending on different measurement sides, we provide necessary and sufficient conditions for two types of monogamy inequalities. By the concept of nonlocality monogamy score, we find a necessary condition of the vanished nonlocality monogamy score for arbitrary three-party states. In addition, two types of necessary and sufficient conditions of the vanished nonlocality monogamy scores are obtained for any pure states. As an application, we show that measurement-induced nonlocality based on relative entropy can be viewed as a "nonlocality witness" to distinguish generalized GHZ states from the generalized W states.
Measurement-Induced NonLocality was introduced by Luo and Fu (Phys. Rev. Lett. \textbf{106}, 120401,(2011)) as a measure of nonlocality in a bipartite state. In this paper we will discuss monogamy property of measurement-induced nonlocality for some three- and four-qubit classes of states. Unlike discord, we find quite surprising results in this situation. Both the GHZ and W states satisfy monogamy relations in the three-qubit case, however, in general there are violations of monogamy relations in both the GHZ-class and W-class states. In case of four-qubit system, monogamy holds for most of the states in the generic class. Four qubit GHZ does not satisfy monogamy relation, but W-state does. We provide several numerical results including counterexamples regarding monogamy nature of measurement induced nonlocality. We will also extend our results of generalized W-class to n-qubit.
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.
Quantum entanglement and quantum nonlocality are known to exhibit monogamy; that is, they obey strong constraints on how they can be distributed among multipartite systems. Quantum correlations that comprise and go beyond entanglement are quantified by, e.g., quantum discord. It was observed recently that for some states quantum discord is not monogamous. We prove, in general, that any measure of correlations that is monogamous for all states and satisfies reasonable basic properties must vanish for all separable states: only entanglement measures can be strictly monogamous. Monogamy of other than entanglement measures can still be satisfied for special, restricted cases: we prove that the geometric measure of discord satisfies the monogamy inequality on all pure states of three qubits.
Quantum mechanics imposes limits on the statistics of certain observables. Perhaps the most famous example is the uncertainty principle. Similar trade-offs also exist for the simultaneous violation of multiple Bell inequalities. In the simplest case of three observers, it has been shown that if two observers violate a Bell inequality, then none of them can violate any Bell inequality with the third observer, a property called monogamy of Bell violations. Forms of Bell monogamy have been linked to the no-signaling principle, and the inability of simultaneous violations of all inequalities is regarded as their fundamental property. Here, we show that the Bell monogamy does not hold universally and that in fact the only monogamous situation exists for only three observers. Consequently, the nature of quantum nonlocality is truly polygamous. We present a systematic methodology for identifying quantum states, measurements, and tight Bell inequalities that do not obey the monogamy principle for any number of more than three observers. The identified polygamous inequalities enable any subset of [Formula: see text] observers to reveal nonlocality, which is also shown experimentally by measuring Bell-type correlations of six-photon Dicke states. Our findings may be exploited for multiparty quantum key distribution as well as simultaneous self-testing of multiple nodes in quantum networks.
Quantum correlations are expected to respect all the conditions required for them to be good measures of quantumness in the bipartite scenario. In a multipartite setting, sharing entanglement between several parties is restricted by the monogamy of entanglement. We take over the concept of monogamy to an information-theoretic quantum correlation measure, and find that it violates monogamy in general. Using the notion of interaction information, we identify necessary and sufficient conditions for the measure to obey monogamy, for arbitrary pure and mixed quantum states. We show that while three-qubit generalized Greenberger-Horne-Zeilinger states follow monogamy, generalized WWW states do not.