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:2410.01646 · Physical Review A

Bounding conditional entropy of bipartite states with Bell operators

Jan Horodecki, Piotr Mironowicz

Published Nov 21, 2024• 2 citations
arXivHTMLPDF

Abstract

Quantum information theory explores numerous properties that surpass classical paradigms, offering novel applications and benefits. Among these properties, negative conditional von Neumann entropy (CVNE) is particularly significant in entangled quantum systems, serving as an indicator of potential advantages in various information-theoretic tasks, despite its indirect observability. In this paper, we investigate the relationship between CVNE and the violation of Bell inequalities. Our goal is to establish upper bounds on CVNE through semidefinite programming applied to entangled qubits and qutrits, utilizing selected Bell operators. Our findings reveal that a semi-device-independent certification of negative CVNE is achievable and could be practically beneficial. We further explore two types of robustness: robustness against detection efficiency loopholes, measured by relative violation, and robustness against white noise and imperfections in state preparation, measured by critical visibility. Additionally, we analyze parametrized families of Bell inequalities to identify optimal parameters for different robustness criteria. This study demonstrates that different Bell inequalities exhibit varying degrees of robustness depending on the desired properties, such as the type of noise resistance or the target level of negative CVNE. By bridging the gap between Bell inequalities and CVNE, our research enhances understanding of the quantum properties of entangled systems and offers insights for practical quantum information processing tasks.

DOI
10.1103/physreva.110.052429

Related papers

Witnessing negative conditional entropy

Mahathi Vempati, Nirman Ganguly, Indranil Chakrabarty +1 more

Quantum states that possess negative conditional von Neumann entropy provide quantum advantage in several information-theoretic protocols including superdense coding, state merging, distributed private randomness distillation, and one-way entanglement distillation. While entanglement is an important resource, only a subset of entangled states have negative conditional von Neumann entropy. In this work, we characterize the class of density matrices having non-negative conditional von Neumann entropy as convex and compact. This allows us to prove the existence of a Hermitian operator (a witness) for the detection of states having negative conditional entropy for bipartite systems in arbitrary dimensions. We show two constructions of such witnesses. For one of the constructions, the expectation value of the witness in a state is an upper bound to the conditional entropy of the state. We pose the problem of obtaining a tight upper bound to the set of conditional entropies of states in which an operator gives the same expectation value. We solve this convex optimization problem numerically for a two qubit case and find that this enhances the usefulness of our witnesses. We also find that for a particular witness, the estimated tight upper bound matches the value of conditional entropy for Werner states. We explicate the utility of our work in the detection of useful states in several protocols.

arXiv:2001.11237•Physical Review A•Jul 19, 2021•22 citations

Engineering robust quantum resources from maximal violations of subcorrelation Bell inequalities

Ahmed Abdelsalam, Ahmed M. Ghander, Mamdouh Shams El-Din +1 more

Abstract Bell inequalities have long been essential for the device-independent detection of entanglement. This study introduces subcorrelation Bell inequalities as a robust framework for detecting entanglement and probing quantum non-locality. We derived a family of such inequalities, categorized according to their dependence on measurement settings, and numerically identified 19 distinct quantum states that achieve the maximal violation of these inequalities. Importantly, our focus on maximal violation is not for its own sake but because, in this framework, maximal violation directly corresponds to maximal robustness of nonlocal correlations against particle loss. This connection reveals a broad class of multipartite entangled states that remain resilient under loss, making them highly relevant for practical implementations of quantum information protocols. We further characterized their entanglement properties using concurrence and the geometric measure, confirming their utility for critical areas such as quantum communication, cryptography, and device-independent protocols. The framework established herein sets the stage for future investigations, including the generalization of these inequalities to higher-dimensional systems and a more comprehensive characterization of their robustness against various forms of noise, thereby expanding the potential for non-local states to drive progress in quantum technologies.

Physica Scripta•Apr 24, 2026•0 citations

Semi-device-independent bounds on entanglement

Yeong-Cherng Liang, Tamás Vértesi, Nicolas Brunner

Detection and quantification of entanglement in quantum resources are two key steps in the implementation of various quantum-information processing tasks. Here, we show that Bell-type inequalities are not only useful in verifying the presence of entanglement but can also be used to bound the entanglement of the underlying physical system. Our main tool consists of a family of Clauser-Horne-like Bell inequalities that cannot be violated maximally by any finite-dimensional maximally entangled state. Using these inequalities, we demonstrate the explicit construction of both lower and upper bounds on the concurrence for two-qubit states. The fact that these bounds arise from Bell-type inequalities also allows them to be obtained in a semi-device-independent manner, that is, with assumption of the dimension of the Hilbert space but without resorting to any knowledge of the actual measurements being performed on the individual subsystems.

arXiv:1012.1513•Physical Review A•Feb 24, 2011•82 citations

Witnessing negative Conditional Entropy as an Operational Resource

Mahathi Vempati, Nirman Ganguly, Indranil Chakrabarty +1 more

Quantum states that possess negative conditional von Neumann entropy provide quantum advantage in several protocols including superdense coding, state merging, distributed private randomness distillation and one-way entanglement distillation. While entanglement is an important resource, only a subset of entangled states have negative conditional von Neumann entropy. Despite this utility, a proper resource theory for conditional von Neumann entropy has not been developed, unlike that of entanglement. We pave the way for such a resource theory by characterizing the class of density matrices having non-negative conditional von Neumann entropy as convex and compact. This allows us to prove the existence of a Hermitian operator (a witness) for the detection of states having negative conditional entropy for bipartite systems in arbitrary dimensions. We show constructions of this witness and explicate its utility in the detection of useful states in the above-mentioned protocols. We provide a local decomposition of the witness and probe its implications in the context of the uncertainty principle.

•Jan 30, 2020•1 citation

Higher quantum bound for the Vértesi-Bene-Bell inequality and the role of positive operator-valued measures regarding its threshold detection efficiency

Johanna F. Barra, Esteban S. Gómez, Gustavo Cañas +3 more

Recently, V\'ertesi and Bene [Phys. Rev. A 82, 062115 (2010)] derived a two-qubit Bell inequality ${I}_{\mathrm{CH}3}$, which they show to be maximally violated only when more general positive operator-valued measures (POVMs) are used instead of the usual von Neumann measurements. Here we consider a general parametrization for the three-element POVM involved in the Bell test and obtain a higher quantum bound for the ${I}_{\mathrm{CH}3}$ inequality. With a higher quantum bound for ${I}_{\mathrm{CH}3}$, we investigate whether there is an experimental setup that can be used for observing that POVMs give higher violations in Bell tests based on this inequality. We analyze the maximum errors supported by the inequality to identify a source of entangled photons that can be used for the test. Then we study whether POVMs are also relevant in the more realistic case where partially entangled states are used in the experiment. Finally, we investigate the required efficiencies of the ${I}_{\mathrm{CH}3}$ inequality, and the type of measurements involved, for closing the detection loophole. We obtain the result that POVMs allow for the lowest threshold detection efficiency, and that it is comparable to the minimal required detection efficiency (in the case of two qubits) of the Clauser-Horne-Bell inequality.

arXiv:1207.0712•Physical Review A•Oct 15, 2012•4 citations

Violation of Bell-type Inequalities on Mutually-commuting von Neumann Algebra Models of Entanglement Swapping Networks

Bingke Zheng, Shuyuan Yang, Jinchuan Hou +1 more

Violation of Bell inequalities in bipartite systems represented by mutually-commuting von Neumann algebras has pioneered the study of vacuum entanglement in algebraic quantum field theory. It is unexpected that the maximal violation of Bell inequality can discover algebraic structures. In the paper, we establish the mutually-commuting von Neumann algebra model for entanglement swapping networks and Bell-type inequalities on this model. It generalizes the bipartite case to the ternary case. These algebras are all general von Neumann algebras, which provide a natural perspective to investigate Bell nonlocality in quantum networks in the infinitely-many-degree-of-freedom setting. We determine various bounds for Bell-type inequalities based on the structure of von Neumann algebras, and identify the algebraic structural conditions required for their violation. Finally, we show that the maximal violation of Bell-type inequalities in entanglement swapping networks can be used to determine partially the type classification of the underlying von Neumann algebras.

math.FACross-listedarXiv:2603.01466•Mar 3, 2026•0 citations
Quantum information theory explores numerous properties that surpass classical paradigms, offering novel applications and benefits. Among these properties, negative conditional von Neumann entropy (CVNE) is particularly significant in entangled quantum systems, serving as an indicator of potential advantages in various information-theoretic tasks, despite its indirect observability. In this paper, we investigate the relationship between CVNE and the violation of Bell inequalities. Our goal is to establish upper bounds on CVNE through semidefinite programming applied to entangled qubits and qutrits, utilizing selected Bell operators. Our findings reveal that a semi-device-independent certification of negative CVNE is achievable and could be practically beneficial. We further explore two types of robustness: robustness against detection efficiency loopholes, measured by relative violation, and robustness against white noise and imperfections in state preparation, measured by critical visibility. Additionally, we analyze parametrized families of Bell inequalities to identify optimal parameters for different robustness criteria. This study demonstrates that different Bell inequalities exhibit varying degrees of robustness depending on the desired properties, such as the type of noise resistance or the target level of negative CVNE. By bridging the gap between Bell inequalities and CVNE, our research enhances understanding of the quantum properties of entangled systems and offers insights for practical quantum information processing tasks.
Quantum states that possess negative conditional von Neumann entropy provide quantum advantage in several information-theoretic protocols including superdense coding, state merging, distributed private randomness distillation, and one-way entanglement distillation. While entanglement is an important resource, only a subset of entangled states have negative conditional von Neumann entropy. In this work, we characterize the class of density matrices having non-negative conditional von Neumann entropy as convex and compact. This allows us to prove the existence of a Hermitian operator (a witness) for the detection of states having negative conditional entropy for bipartite systems in arbitrary dimensions. We show two constructions of such witnesses. For one of the constructions, the expectation value of the witness in a state is an upper bound to the conditional entropy of the state. We pose the problem of obtaining a tight upper bound to the set of conditional entropies of states in which an operator gives the same expectation value. We solve this convex optimization problem numerically for a two qubit case and find that this enhances the usefulness of our witnesses. We also find that for a particular witness, the estimated tight upper bound matches the value of conditional entropy for Werner states. We explicate the utility of our work in the detection of useful states in several protocols.
Abstract Bell inequalities have long been essential for the device-independent detection of entanglement. This study introduces subcorrelation Bell inequalities as a robust framework for detecting entanglement and probing quantum non-locality. We derived a family of such inequalities, categorized according to their dependence on measurement settings, and numerically identified 19 distinct quantum states that achieve the maximal violation of these inequalities. Importantly, our focus on maximal violation is not for its own sake but because, in this framework, maximal violation directly corresponds to maximal robustness of nonlocal correlations against particle loss. This connection reveals a broad class of multipartite entangled states that remain resilient under loss, making them highly relevant for practical implementations of quantum information protocols. We further characterized their entanglement properties using concurrence and the geometric measure, confirming their utility for critical areas such as quantum communication, cryptography, and device-independent protocols. The framework established herein sets the stage for future investigations, including the generalization of these inequalities to higher-dimensional systems and a more comprehensive characterization of their robustness against various forms of noise, thereby expanding the potential for non-local states to drive progress in quantum technologies.
Detection and quantification of entanglement in quantum resources are two key steps in the implementation of various quantum-information processing tasks. Here, we show that Bell-type inequalities are not only useful in verifying the presence of entanglement but can also be used to bound the entanglement of the underlying physical system. Our main tool consists of a family of Clauser-Horne-like Bell inequalities that cannot be violated maximally by any finite-dimensional maximally entangled state. Using these inequalities, we demonstrate the explicit construction of both lower and upper bounds on the concurrence for two-qubit states. The fact that these bounds arise from Bell-type inequalities also allows them to be obtained in a semi-device-independent manner, that is, with assumption of the dimension of the Hilbert space but without resorting to any knowledge of the actual measurements being performed on the individual subsystems.
Quantum states that possess negative conditional von Neumann entropy provide quantum advantage in several protocols including superdense coding, state merging, distributed private randomness distillation and one-way entanglement distillation. While entanglement is an important resource, only a subset of entangled states have negative conditional von Neumann entropy. Despite this utility, a proper resource theory for conditional von Neumann entropy has not been developed, unlike that of entanglement. We pave the way for such a resource theory by characterizing the class of density matrices having non-negative conditional von Neumann entropy as convex and compact. This allows us to prove the existence of a Hermitian operator (a witness) for the detection of states having negative conditional entropy for bipartite systems in arbitrary dimensions. We show constructions of this witness and explicate its utility in the detection of useful states in the above-mentioned protocols. We provide a local decomposition of the witness and probe its implications in the context of the uncertainty principle.
Recently, V\'ertesi and Bene [Phys. Rev. A 82, 062115 (2010)] derived a two-qubit Bell inequality ICH3{I}_{\mathrm{CH}3}ICH3​, which they show to be maximally violated only when more general positive operator-valued measures (POVMs) are used instead of the usual von Neumann measurements. Here we consider a general parametrization for the three-element POVM involved in the Bell test and obtain a higher quantum bound for the ICH3{I}_{\mathrm{CH}3}ICH3​ inequality. With a higher quantum bound for ICH3{I}_{\mathrm{CH}3}ICH3​, we investigate whether there is an experimental setup that can be used for observing that POVMs give higher violations in Bell tests based on this inequality. We analyze the maximum errors supported by the inequality to identify a source of entangled photons that can be used for the test. Then we study whether POVMs are also relevant in the more realistic case where partially entangled states are used in the experiment. Finally, we investigate the required efficiencies of the ICH3{I}_{\mathrm{CH}3}ICH3​ inequality, and the type of measurements involved, for closing the detection loophole. We obtain the result that POVMs allow for the lowest threshold detection efficiency, and that it is comparable to the minimal required detection efficiency (in the case of two qubits) of the Clauser-Horne-Bell inequality.
Violation of Bell inequalities in bipartite systems represented by mutually-commuting von Neumann algebras has pioneered the study of vacuum entanglement in algebraic quantum field theory. It is unexpected that the maximal violation of Bell inequality can discover algebraic structures. In the paper, we establish the mutually-commuting von Neumann algebra model for entanglement swapping networks and Bell-type inequalities on this model. It generalizes the bipartite case to the ternary case. These algebras are all general von Neumann algebras, which provide a natural perspective to investigate Bell nonlocality in quantum networks in the infinitely-many-degree-of-freedom setting. We determine various bounds for Bell-type inequalities based on the structure of von Neumann algebras, and identify the algebraic structural conditions required for their violation. Finally, we show that the maximal violation of Bell-type inequalities in entanglement swapping networks can be used to determine partially the type classification of the underlying von Neumann algebras.