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:0805.3060 · Physical Review A

Postulates for measures of genuine multipartite correlations

Charles H. Bennett, Andrzej Grudka, Michał Horodecki, Paweł Horodecki, Ryszard Horodecki

Published Jan 24, 2011• 76 citations
arXivHTMLPDF

Abstract

A lot of research has been done on multipartite correlations, but the problem of satisfactorily defining genuine multipartite correlations---those not trivially reducible to lower partite correlations---remains unsolved. In this paper we propose three reasonable postulates which each measure or indicator of genuine multipartite correlations (or genuine multipartite entanglement) should satisfy. We also introduce the concept of degree of correlations, which gives partial characterization of multipartite correlations. Then, we show that covariance does not satisfy two postulates and hence it cannot be used as an indicator of genuine multipartite correlations. Finally, we propose a candidate for a measure of genuine multipartite correlations based on the work that can be drawn from a local heat bath by means of a multipartite state.

DOI
10.1103/physreva.83.012312

Related papers

Note on genuine multipartite classical correlations

Andrzej Grudka, Michał Horodecki, Paweł Horodecki +1 more

We discuss the problem of coexistence of genuine quantum multipartite correlations and classical multipartite correlations. We introduce a postulate which any measure of genuine multipartite classical correlations should satisfy. We show that covariance does not satisfy this postulate. Finally we propose a definition of genuine multipartite correlations and illustrate it with examples.

arXiv:0802.1633•Feb 12, 2008•1 citation

Genuine multipartite entanglement measures based on multi-party teleportation capability

Minjin Choi, Eunok Bae, Soojoon Lee

Quantifying entanglement is vital to understand entanglement as a resource in quantum information processing, and many entanglement measures have been suggested for this purpose. When mathematically defining an entanglement measure, we should consider the distinguishability between entangled and separable states, the invariance under local transformation, the monotonicity under local operations and classical communication, and the convexity. These are reasonable requirements but may be insufficient, in particular when taking into account the usefulness of quantum states in multi-party quantum information processing. Therefore, if we want to investigate multipartite entanglement as a resource, then it can be necessary to consider the usefulness of quantum states in multi-party quantum information processing when we define a multipartite entanglement measure. In this paper, we define new multipartite entanglement measures for three-qubit systems based on the three-party teleportation capability, and show that these entanglement measures satisfy the requirements for being genuine multipartite entanglement measures. We also generalize our entanglement measures for N-qubit systems, where [Formula: see text], and discuss that these quantities may be good candidates to measure genuine multipartite entanglement.

arXiv:2211.15986•Scientific Reports•Sep 11, 2023•10 citations

Quantifying Genuine Multipartite Correlations and their Pattern Complexity

Davide Girolami, Tommaso Tufarelli, Cristian E. Susa

We propose an information-theoretic framework to quantify multipartite correlations in classical and quantum systems, answering questions such as what is the amount of seven-partite correlations in a given state of ten particles? We identify measures of genuine multipartite correlations, i.e., statistical dependencies that cannot be ascribed to bipartite correlations, satisfying a set of desirable properties. Inspired by ideas developed in complexity science, we then introduce the concept of weaving to classify states that display different correlation patterns, but cannot be distinguished by correlation measures. The weaving of a state is defined as the weighted sum of correlations of every order. Weaving measures are good descriptors of the complexity of correlation structures in multipartite systems.

arXiv:1706.04562•Physical Review Letters•Oct 6, 2017•34 citations

Detection of genuine multipartite entanglement in multipartite systems

Zhao, J., Zhao, H., Naihuan Jing +1 more

We investigate genuine multipartite entanglement in general multipartite systems. Based on the norms of the correlation tensors of a multipartite state under various partitions, we present an analytical sufficient criterion for detecting the genuine four-partite entanglement. The results are generalized to arbitrary multipartite systems.

•Jan 1, 2019•6 citations

Genuine Measure of Multipartite Entanglement and its Monogamy Relation.

Yu Jing Guo, Lin Zhang

Although many different entanglement measures have been proposed so far, much less is known in the multipartite case, which leads to the previous monogamy relations in literatures are not complete. We establish here a strict framework for defining multipartite entanglement measure (MEM): apart from the postulates of bipartite measure [i.e., vanishing on separable and nonincreasing under local operations and classical communication (LOCC)], a genuine MEM should additionally satisfy the \textit{unification condition} and the \textit{hierarchy condition}. We then come up with a \textit{complete monogamy formula} under the unified MEM (an MEM is called a unified MEM if it satisfies the unification condition). Consequently, we propose MEMs which are multipartite extensions of entanglement of formation (EoF), concurrence, tangle, the convex-roof extension of negativity and negativity, respectively. We show that multipartite extensions of the bipartite measures that are defined by the convex-roof structure are completely monogamous, the extensions of EoF, concurrence and tangle are genuine MEMs (an MEM is called a genuine MEM if it satisfies both the unification condition and the hierarchy condition), and multipartite extensions of both negativity and the convex-roof extension of negativity are unified MEMs but not genuine MEMs.

•Aug 22, 2019•0 citations

Observable measures of multipartite entanglement

Francois Payn, Davide Girolami

Multipartite entanglement is the premier resource for quantum technologies. Yet, its exact quantification in the laboratory is notoriously challenging, typically requiring the full knowledge of high dimensional quantum states. Here, we construct observable bounds to multipartite entanglement for systems of arbitrary size, which are functions of the local and global state purities, and correlation functions. First, we derive experimentally accessible upper and lower limits to both the bipartite entanglement of formation and the squashed entanglement of bipartite systems, by leveraging cornerstone results of quantum information theory: the entropy strong subadditivity inequality and the Koashi-Winter monogamy relation. Then, we convert them into bounds to the entanglement up to degree k for arbitrary states, and to the genuine k-partite entanglement, by employing a recently proposed method. Finally, we analytically and numerically test these results, by bounding the multipartite entanglement of several relevant states and mixtures, including the important classes of GHZ, Dicke, W states, and random pure states.

quant-pharXiv:2605.01375•May 5, 2026•0 citations
A lot of research has been done on multipartite correlations, but the problem of satisfactorily defining genuine multipartite correlations---those not trivially reducible to lower partite correlations---remains unsolved. In this paper we propose three reasonable postulates which each measure or indicator of genuine multipartite correlations (or genuine multipartite entanglement) should satisfy. We also introduce the concept of degree of correlations, which gives partial characterization of multipartite correlations. Then, we show that covariance does not satisfy two postulates and hence it cannot be used as an indicator of genuine multipartite correlations. Finally, we propose a candidate for a measure of genuine multipartite correlations based on the work that can be drawn from a local heat bath by means of a multipartite state.
Quantifying entanglement is vital to understand entanglement as a resource in quantum information processing, and many entanglement measures have been suggested for this purpose. When mathematically defining an entanglement measure, we should consider the distinguishability between entangled and separable states, the invariance under local transformation, the monotonicity under local operations and classical communication, and the convexity. These are reasonable requirements but may be insufficient, in particular when taking into account the usefulness of quantum states in multi-party quantum information processing. Therefore, if we want to investigate multipartite entanglement as a resource, then it can be necessary to consider the usefulness of quantum states in multi-party quantum information processing when we define a multipartite entanglement measure. In this paper, we define new multipartite entanglement measures for three-qubit systems based on the three-party teleportation capability, and show that these entanglement measures satisfy the requirements for being genuine multipartite entanglement measures. We also generalize our entanglement measures for N-qubit systems, where [Formula: see text], and discuss that these quantities may be good candidates to measure genuine multipartite entanglement.
We propose an information-theoretic framework to quantify multipartite correlations in classical and quantum systems, answering questions such as what is the amount of seven-partite correlations in a given state of ten particles? We identify measures of genuine multipartite correlations, i.e., statistical dependencies that cannot be ascribed to bipartite correlations, satisfying a set of desirable properties. Inspired by ideas developed in complexity science, we then introduce the concept of weaving to classify states that display different correlation patterns, but cannot be distinguished by correlation measures. The weaving of a state is defined as the weighted sum of correlations of every order. Weaving measures are good descriptors of the complexity of correlation structures in multipartite systems.
Although many different entanglement measures have been proposed so far, much less is known in the multipartite case, which leads to the previous monogamy relations in literatures are not complete. We establish here a strict framework for defining multipartite entanglement measure (MEM): apart from the postulates of bipartite measure [i.e., vanishing on separable and nonincreasing under local operations and classical communication (LOCC)], a genuine MEM should additionally satisfy the \textit{unification condition} and the \textit{hierarchy condition}. We then come up with a \textit{complete monogamy formula} under the unified MEM (an MEM is called a unified MEM if it satisfies the unification condition). Consequently, we propose MEMs which are multipartite extensions of entanglement of formation (EoF), concurrence, tangle, the convex-roof extension of negativity and negativity, respectively. We show that multipartite extensions of the bipartite measures that are defined by the convex-roof structure are completely monogamous, the extensions of EoF, concurrence and tangle are genuine MEMs (an MEM is called a genuine MEM if it satisfies both the unification condition and the hierarchy condition), and multipartite extensions of both negativity and the convex-roof extension of negativity are unified MEMs but not genuine MEMs.
Multipartite entanglement is the premier resource for quantum technologies. Yet, its exact quantification in the laboratory is notoriously challenging, typically requiring the full knowledge of high dimensional quantum states. Here, we construct observable bounds to multipartite entanglement for systems of arbitrary size, which are functions of the local and global state purities, and correlation functions. First, we derive experimentally accessible upper and lower limits to both the bipartite entanglement of formation and the squashed entanglement of bipartite systems, by leveraging cornerstone results of quantum information theory: the entropy strong subadditivity inequality and the Koashi-Winter monogamy relation. Then, we convert them into bounds to the entanglement up to degree k for arbitrary states, and to the genuine k-partite entanglement, by employing a recently proposed method. Finally, we analytically and numerically test these results, by bounding the multipartite entanglement of several relevant states and mixtures, including the important classes of GHZ, Dicke, W states, and random pure states.