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34 pages, 1302 KB

Open AccessArticle

Integrated Information in Relational Quantum Dynamics (RQD)

by Arash Zaghi

Appl. Sci. 2025, 15(13), 7521; https://doi.org/10.3390/app15137521 - 4 Jul 2025

Cited by 1 | Viewed by 614

We introduce a quantum integrated-information measure

Φ

for multipartite states within the Relational Quantum Dynamics (RQD) framework.

Φ (ρ)

is defined as the minimum quantum Jensen–Shannon distance between an n-partite density operator

ρ

and any product state over a bipartition of [...] Read more.

We introduce a quantum integrated-information measure

Φ

for multipartite states within the Relational Quantum Dynamics (RQD) framework.

Φ (ρ)

is defined as the minimum quantum Jensen–Shannon distance between an n-partite density operator

ρ

and any product state over a bipartition of its subsystems. We prove that its square root induces a genuine metric on state space and that

Φ

is monotonic under all completely positive trace-preserving maps. Restricting the search to bipartitions yields a unique optimal split and a unique closest product state. From this geometric picture, we derive a canonical entanglement witness directly tied to

Φ

and construct an integration dendrogram that reveals the full hierarchical correlation structure of

ρ

. We further show that there always exists an “optimal observer”—a channel or basis—that preserves

Φ

better than any alternative. Finally, we propose a quantum Markov blanket theorem: the boundary of the optimal bipartition isolates subsystems most effectively. Our framework unites categorical enrichment, convex-geometric methods, and operational tools, forging a concrete bridge between integrated information theory and quantum information science. Full article

(This article belongs to the Special Issue Quantum Communication and Quantum Information)

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9 pages, 537 KB

Open AccessFeature PaperArticle

Parameterized Multipartite Entanglement and Genuine Entanglement Measures Based on q-Concurrence

by Pan-Wen Ma, Hui Zhao, Shao-Ming Fei, Mei-Ming Zhang and Zhi-Xi Wang

Entropy 2024, 26(7), 535; https://doi.org/10.3390/e26070535 - 22 Jun 2024

Cited by 1 | Viewed by 1285

Abstract

We study genuine multipartite entanglement (GME) and multipartite k-entanglement based on q-concurrence. Well-defined parameterized GME measures and measures of multipartite k-entanglement are presented for arbitrary dimensional n-partite quantum systems. Our GME measures show that the

G H Z

state [...] Read more.

G H Z

state is more entangled than the W state. Moreover, our measures are shown to be inequivalent to the existing measures according to entanglement ordering. Detailed examples show that our measures characterize the multipartite entanglement finer than some existing measures, in the sense that our measures identify the difference of two different states while the latter fail. Full article

(This article belongs to the Collection Quantum Information)

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10 pages, 481 KB

Open AccessFeature PaperArticle

Multipartite Entanglement: A Journey through Geometry

by Songbo Xie, Daniel Younis, Yuhan Mei and Joseph H. Eberly

Entropy 2024, 26(3), 217; https://doi.org/10.3390/e26030217 - 29 Feb 2024

Cited by 11 | Viewed by 3044

Abstract

Genuine multipartite entanglement is crucial for quantum information and related technologies, but quantifying it has been a long-standing challenge. Most proposed measures do not meet the “genuine” requirement, making them unsuitable for many applications. In this work, we propose a journey toward addressing this issue by introducing an unexpected relation between multipartite entanglement and hypervolume of geometric simplices, leading to a tetrahedron measure of quadripartite entanglement. By comparing the entanglement ranking of two highly entangled four-qubit states, we show that the tetrahedron measure relies on the degree of permutation invariance among parties within the quantum system. We demonstrate potential future applications of our measure in the context of quantum information scrambling within many-body systems. Full article

(This article belongs to the Special Issue Quantum Optics: Trends and Challenges)

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15 pages, 306 KB

Open AccessArticle

When Is a Genuine Multipartite Entanglement Measure Monogamous?

by Yu Guo

Entropy 2022, 24(3), 355; https://doi.org/10.3390/e24030355 - 28 Feb 2022

Cited by 8 | Viewed by 2984

Abstract

A crucial issue in quantum communication tasks is characterizing how quantum resources can be quantified and distributed over many parties. Consequently, entanglement has been explored extensively. However, there are few genuine multipartite entanglement measures and whether it is monogamous is so far unknown. In this work, we explore the complete monogamy of genuine multipartite entanglement measure (GMEM) for which, at first, we investigate a framework for unified/complete GMEM according to the unified/complete multipartite entanglement measure we proposed in 2020. We find a way of inducing unified/complete GMEM from any given unified/complete multipartite entanglement measure. It is shown that any unified GMEM is completely monogamous, and any complete GMEM that is induced by given complete multipartite entanglement measure is completely monogamous. In addition, the previous GMEMs are checked under this framework. It turns out that the genuinely multipartite concurrence is not as good of a candidate as GMEM. Full article

(This article belongs to the Special Issue Quantum Information and Computation)

14 pages, 6135 KB

Open AccessArticle

Exact Time Evolution of Genuine Multipartite Correlations for N-Qubit Systems in a Common Thermal Reservoir

by Abhinash Kumar Roy, Sourabh Magare, Varun Srivastava and Prasanta K. Panigrahi

Quantum Rep. 2022, 4(1), 22-35; https://doi.org/10.3390/quantum4010003 - 15 Jan 2022

Cited by 2 | Viewed by 3746

Abstract

We investigate the dynamical evolution of genuine multipartite correlations for N-qubits in a common reservoir considering a non-dissipative qubits-reservoir model. We derive an exact expression for the time-evolved density matrix by modeling the reservoir as a set of infinite harmonic oscillators with a bilinear form of interaction Hamiltonian. Interestingly, we find that the choice of two-level systems corresponding to an initially correlated multipartite state plays a significant role in potential robustness against environmental decoherence. In particular, the generalized W-class Werner state shows robustness against the decoherence for an equivalent set of qubits, whereas a certain generalized GHZ-class Werner state shows robustness for inequivalent sets of qubits. It is shown that the genuine multipartite concurrence (GMC), a measure of multipartite entanglement of an initially correlated multipartite state, experiences an irreversible decay of correlations in the presence of a thermal reservoir. For the GHZ-class Werner state, the region of mixing parameters for which there exists GMC, shrinks with time and with increase in the temperature of the thermal reservoir. Furthermore, we study the dynamical evolution of the relative entropy of coherence and von-Neumann entropy for the W-class Werner state. Full article

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14 pages, 335 KB

Open AccessArticle

Exploring Multipartite Steering Effect Using Bell Operators

by Li-Yi Hsu and Shoichi Kawamoto

Entropy 2020, 22(1), 19; https://doi.org/10.3390/e22010019 - 23 Dec 2019

Cited by 1 | Viewed by 2988

Abstract

While Bell operators are exploited in detecting Bell nonlocality and entanglement classification, we demonstrate their usefulness in exploring Einstein–Podolsky–Rosen (EPR) steering, which represents the quantum correlation intermediate between entanglement and Bell nonlocality. We propose a task function that detects steerability of multi-qubit states in bipartite scenarios. A novel necessary and sufficient steering criterion is based on the superposition of the recursive Bell operators which are often employed for detecting Bell nonlocality. Utilizing the task function we can (i) reveal the one-to-one mapping relation between joint measurability and unsteerability, (ii) geometrically depict and compare the entanglement classification and the steering criteria and propose a geometrical measure, and (iii) compare the EPR steering with Bell nonlocality using an alternative task function. We extend the result to detect EPR steering for multi-qutrit cases and some numerical results are illustrated as examples. Finally, the steering criteria in a star-shaped quantum network is studied to see how the result is applied to a genuine multipartite steering case. Full article

(This article belongs to the Collection Quantum Information)

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