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:0901.1280 · Physical Review Letters

Broadcast Copies Reveal the Quantumness of Correlations

Marco Piani, Matthias Christandl, C. E. Mora, Paweł Horodecki

Published Jun 25, 2009• 77 citations
arXivHTMLPDF

Abstract

We study the quantumness of bipartite correlations by proposing a quantity that combines a measure of total correlations-mutual information-with the notion of broadcast copies-i.e., generally nonfactorized copies-of bipartite states. By analyzing how our quantity increases with the number of broadcast copies, we are able to classify classical, separable, and entangled states. This motivates the definition of the broadcast regularization of mutual information, the asymptotic minimal mutual information per broadcast copy, which we show to have many properties of an entanglement measure.

DOI
10.1103/physrevlett.102.250503

Related papers

Monogamy of correlations for broadcast copies of entangled states

Marco Piani, Matthias Christandl, Paweł Horodecki +2 more

By combining a measure of total correlations, mutual information, and the notion of broadcast —i.e. generally non‐factorized— copies of states of distributed systems, we are able to characterize in a single framework different levels of quantumness of correlations, corresponding to the classification of strictly classical, separable, and entangled states. We find that the broadcast regularization of mutual information —defined as the minimal per‐copy mutual information between parties, when they share an infinite amount of broadcast copies— besides having by construction an appealing interpretation, satisfies many of the properties of an entanglement measure. In particular, it vanishes for separable states while it is strictly positive for all entangled states. The latter fact may be considered a signature of monogamy of entangled correlations.

AIP conference proceedings•Jan 1, 2009•0 citations

Extracting an entanglement signature from only classical mutual information

David J. Starling, Curtis J. Broadbent, John C. Howell

We introduce a quantity which is formed using classical notions of mutual information and which is computed using the results of projective measurements. This quantity constitutes a sufficient condition for entanglement and represents the amount of information that can be extracted from a bipartite system for spacelike separated observers. In addition to discussion, we provide simulations as well as experimental results for the singlet and maximally correlated mixed states.

Physical Review A•Sep 6, 2011•1 citation

Decomposition of bipartite states with applications to quantum no-broadcasting theorems

Shunlong Luo, Wei Sun

Correlations in bipartite quantum states are fundamental objects in quantum information theory. A canonical framework for studying correlations is the entangled versus separable dichotomy in which the decompositions of separable states as convex combinations of product states play an instrumental role. In this paper, motivated by both the representation of separable states and quantum no-broadcasting considerations, we establish a constructive decomposition representation for any bipartite state. As applications, we prove the conjectures proposed by Luo [Lett. Math. Phys. 92, 143 (2010)] concerning no-unilocal broadcasting for quantum correlations and further provide a unified picture for the celebrated quantum no-broadcasting theorem for noncommuting states by Barnum et al. [Phys. Rev. Lett. 76, 2818 (1996)], and the elegant no-local-broadcasting theorem for quantum correlations by Piani et al. [Phys. Rev. Lett. 100, 090502 (2008)]. The results reveal some intrinsic relation between quantumness of correlations and noncommutativity of states, and in particular, provide a characterization for zero quantum discord introduced by Ollivier and Zurek [Phys. Rev. Lett. 88, 017901 (2001)] from the broadcasting perspective. Furthermore, it is indicated that the distinction between the decomposition for general bipartite states and that for separable states might be useful in studying entanglement versus separability.

Physical Review A•Jul 30, 2010•66 citations

Mutual Information: A way to quantify correlations

Marcelo Tisoc, J. Beltrán

Within the framework of Information Theory, the existence of correlations between two random variables means that we can obtain information about one of them, just by measuring or observing the other random variable. In certain cases, this kind of relationship allows obtaining information about a variable even when the other is separated by a very large distance, that is, the process of obtaining information is non-local, an example (if not the only) is the quantum entanglement. These features of correlations make it interesting and important to study, classify and quantify them. The correlations are classified into classical correlations and quantum correlations, in addition they are quantified through the mutual information. Here we will present a natural way to define classical mutual information and then we will generalize it to the quantum case. Furthermore, every term in the definitions of mutual information will be interpreted using the concepts of classical and quantum entropy.

Revista Brasileira de Ensino de Física•Jan 1, 2022•6 citations

Extracting classical correlations from a bipartite quantum system

S. Hamieh, J. Qi, David J. Siminovitch +1 more

In this paper, we discuss the problem of splitting of the total correlations for a bipartite quantum state described by the Von Neumann mutual information into classical and quantum parts. We propose a measure of the classical correlations as the difference between the Von Neumann mutual information and the relative entropy of entanglement. We compare this measure with different measures proposed in the literature.

arXiv:quant-ph/0211006•Physical Review A•Jan 9, 2003•16 citations

Quantum, classical, and total amount of correlations in a quantum state

Berry Groisman, Sandu Popescu, Andreas Winter

We give an operational definition of the quantum, classical, and total amounts of correlations in a bipartite quantum state. We argue that these quantities can be defined via the amount of work (noise) that is required to erase (destroy) the correlations: for the total correlation, we have to erase completely, for the quantum correlation we have to erase until a separable state is obtained, and the classical correlation is the maximal correlation left after erasing the quantum correlations. In particular, we show that the total amount of correlations is equal to the quantum mutual information, thus providing it with a direct operational interpretation. As a by-product, we obtain a direct, operational, and elementary proof of strong subadditivity of quantum entropy.

arXiv:quant-ph/0410091•Physical Review A•Sep 13, 2005•613 citations
We study the quantumness of bipartite correlations by proposing a quantity that combines a measure of total correlations-mutual information-with the notion of broadcast copies-i.e., generally nonfactorized copies-of bipartite states. By analyzing how our quantity increases with the number of broadcast copies, we are able to classify classical, separable, and entangled states. This motivates the definition of the broadcast regularization of mutual information, the asymptotic minimal mutual information per broadcast copy, which we show to have many properties of an entanglement measure.
By combining a measure of total correlations, mutual information, and the notion of broadcast —i.e. generally non‐factorized— copies of states of distributed systems, we are able to characterize in a single framework different levels of quantumness of correlations, corresponding to the classification of strictly classical, separable, and entangled states. We find that the broadcast regularization of mutual information —defined as the minimal per‐copy mutual information between parties, when they share an infinite amount of broadcast copies— besides having by construction an appealing interpretation, satisfies many of the properties of an entanglement measure. In particular, it vanishes for separable states while it is strictly positive for all entangled states. The latter fact may be considered a signature of monogamy of entangled correlations.
Correlations in bipartite quantum states are fundamental objects in quantum information theory. A canonical framework for studying correlations is the entangled versus separable dichotomy in which the decompositions of separable states as convex combinations of product states play an instrumental role. In this paper, motivated by both the representation of separable states and quantum no-broadcasting considerations, we establish a constructive decomposition representation for any bipartite state. As applications, we prove the conjectures proposed by Luo [Lett. Math. Phys. 92, 143 (2010)] concerning no-unilocal broadcasting for quantum correlations and further provide a unified picture for the celebrated quantum no-broadcasting theorem for noncommuting states by Barnum et al. [Phys. Rev. Lett. 76, 2818 (1996)], and the elegant no-local-broadcasting theorem for quantum correlations by Piani et al. [Phys. Rev. Lett. 100, 090502 (2008)]. The results reveal some intrinsic relation between quantumness of correlations and noncommutativity of states, and in particular, provide a characterization for zero quantum discord introduced by Ollivier and Zurek [Phys. Rev. Lett. 88, 017901 (2001)] from the broadcasting perspective. Furthermore, it is indicated that the distinction between the decomposition for general bipartite states and that for separable states might be useful in studying entanglement versus separability.
Within the framework of Information Theory, the existence of correlations between two random variables means that we can obtain information about one of them, just by measuring or observing the other random variable. In certain cases, this kind of relationship allows obtaining information about a variable even when the other is separated by a very large distance, that is, the process of obtaining information is non-local, an example (if not the only) is the quantum entanglement. These features of correlations make it interesting and important to study, classify and quantify them. The correlations are classified into classical correlations and quantum correlations, in addition they are quantified through the mutual information. Here we will present a natural way to define classical mutual information and then we will generalize it to the quantum case. Furthermore, every term in the definitions of mutual information will be interpreted using the concepts of classical and quantum entropy.
We give an operational definition of the quantum, classical, and total amounts of correlations in a bipartite quantum state. We argue that these quantities can be defined via the amount of work (noise) that is required to erase (destroy) the correlations: for the total correlation, we have to erase completely, for the quantum correlation we have to erase until a separable state is obtained, and the classical correlation is the maximal correlation left after erasing the quantum correlations. In particular, we show that the total amount of correlations is equal to the quantum mutual information, thus providing it with a direct operational interpretation. As a by-product, we obtain a direct, operational, and elementary proof of strong subadditivity of quantum entropy.