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

AIP conference proceedings

Quantum Entangled State and Its Characterization

Masanori Ohya

Published Jan 1, 2005• 6 citations
Publisher

Abstract

We review the operational structure of quantum entanglement studied by Belavkin and Ohya. The separability of quantum compound state is discussed from the operational points of view. The information degree of entanglement is calculated for the entangled PPT state as an example of bound entangled state shown by Horodecki family.
DOI
10.1063/1.1874581

Related papers

On correlations and mutual entropy in quantum composed systems

Yuji Hirota, Dariusz Chruściński, Takashi Matsuoka +1 more

We study the correlations of classical and quantum systems from the information theoretical points of view. We analyze a simple measure of correlations based on entropy (such measure was already investigated as the degree of entanglement by Belavkin, Matsuoka and Ohya). Contrary to naive expectation, it is shown that separable state might possesses stronger correlation than an entangled state.

arXiv:1109.3438•Sep 15, 2011•1 citation

Quantum entanglements and entangled mutual entropy

V. P. Belavkin, Masanori Ohya

The mathematical structure of quantum entanglement is studied and classified from the point of view of quantum compound states. We show that t he classical-quantum correspondences such as encodings can be treated as dia gonal (d-) entanglements. The mutual entropy of the d-compound and entangled states lead to two different types of entropies for a given quantum state: t he von Neumann entropy, which is achieved as the supremum of the information over all d-entanglements, and the dimensional entropy, which is achieved at the standard entanglement, the true quantum entanglement, coinciding with a d-entanglement only in the case of pure marginal states. The q-capacity of a quantum noiseless channel, defined as the supremum over all entanglements, i s given by the logarithm of the dimensionality of the input algebra. It doub les the classical capacity, achieved as the supremum over all d-entanglement s (encodings), which is bounded by the logarithm of the dimensionality of a maximal Abelian subalgebra.

arXiv:quant-ph/9812082•Dec 30, 1998•13 citations

Entanglements and compound states in quantum information theory

V. P. Belavkin, Masanori Ohya

Quantum entanglements, describing truly quantum couplings, are stu died and classified from the point of view of quantum compound states. We show that c lassical-quantum correspondences such as quantum encodings can be treated as d-entanglements leading to a special class of the separable compound states. The mutual information of the d-compound and entangled states lead to two di fferent types of entropies for a given quantum state: the von Neumann entrop y, which is achieved as the supremum of the information over all d-entanglem ents, and the dimensional entropy, which is achieved at the standard entangl ement, the true quantum entanglement, coinciding with a d-entanglement only in the commutative case. The q-capacity of a quantum noiseless channel, defi ned as the supremum over all entanglements, is given as the logarithm of the dimensionality of the input von Neumann algebra. It can double the classical capacity, achieved as the supremum over all semi-quantum couplings (d-entang lements, or encodings), which is bounded by the logarithm of the dimensional ity of a maximal Abelian subalgebra.

arXiv:quant-ph/0004069•Apr 18, 2000•4 citations

QUANTUM ENTANGLED STATES

Zheng Y. Zhou

Entanglement is one of the intriguing characteristics of quantum mechanics. We review the history of quantum entangled states and the main advances in the measure of entanglement, the distinguishing of entangled states from separable states and the classification of entangled states.

•Jan 1, 2000•2 citations

On positive maps in quantum information

W. A. Majewski

Using the Grothendieck approach to the tensor product of locally convex spaces, we review a characterization of positive maps as well as Belavkin-Ohya characterization of PPT states. Moreover, within this scheme, a generalization of the idea of Choi matrices for genuine quantum systems will be presented.

arXiv:1405.3415•Russian Journal of Mathematical Physics•Jul 1, 2014•8 citations

Geometric Characterization and Feasible Region Analysis of Bipartite Qutrit Bound Entanglement

Mazhar Ali

We characterize bound entanglement in bipartite qutrit systems by combining the Positive Partial Transpose (PPT) criterion with a structural, non-completely positive map. Focusing on a comprehensive three-parameter bipartite qutrit family $ρ_{a,b,c}$, we present an exact analytical and geometric partitioning of the physical state space simplex. We derive the closed-form quadratic boundary governing the leaf-like PPT region $(a^2+ab+b^2-b \leq 0)$ over the domain $0 < a \leq \frac{1}{3}$, and identify the exact linear threshold $(a > c)$ that characterizes the PPT bound entangled sub-region. This family strictly generalizes the well-known Horodecki bound entangled states, which appear as a single slice of the three-dimensional leaf. Applying the structural map to this decomposition, we show that it certifies bound entanglement throughout the entire threshold region, accounting for $14.76\%$ of the total PPT leaf area.

quant-pharXiv:2609.39141•Oct 1, 2026•0 citations
The mathematical structure of quantum entanglement is studied and classified from the point of view of quantum compound states. We show that t he classical-quantum correspondences such as encodings can be treated as dia gonal (d-) entanglements. The mutual entropy of the d-compound and entangled states lead to two different types of entropies for a given quantum state: t he von Neumann entropy, which is achieved as the supremum of the information over all d-entanglements, and the dimensional entropy, which is achieved at the standard entanglement, the true quantum entanglement, coinciding with a d-entanglement only in the case of pure marginal states. The q-capacity of a quantum noiseless channel, defined as the supremum over all entanglements, i s given by the logarithm of the dimensionality of the input algebra. It doub les the classical capacity, achieved as the supremum over all d-entanglement s (encodings), which is bounded by the logarithm of the dimensionality of a maximal Abelian subalgebra.
Quantum entanglements, describing truly quantum couplings, are stu died and classified from the point of view of quantum compound states. We show that c lassical-quantum correspondences such as quantum encodings can be treated as d-entanglements leading to a special class of the separable compound states. The mutual information of the d-compound and entangled states lead to two di fferent types of entropies for a given quantum state: the von Neumann entrop y, which is achieved as the supremum of the information over all d-entanglem ents, and the dimensional entropy, which is achieved at the standard entangl ement, the true quantum entanglement, coinciding with a d-entanglement only in the commutative case. The q-capacity of a quantum noiseless channel, defi ned as the supremum over all entanglements, is given as the logarithm of the dimensionality of the input von Neumann algebra. It can double the classical capacity, achieved as the supremum over all semi-quantum couplings (d-entang lements, or encodings), which is bounded by the logarithm of the dimensional ity of a maximal Abelian subalgebra.
We characterize bound entanglement in bipartite qutrit systems by combining the Positive Partial Transpose (PPT) criterion with a structural, non-completely positive map. Focusing on a comprehensive three-parameter bipartite qutrit family ρa,b,cρ_{a,b,c}ρa,b,c​, we present an exact analytical and geometric partitioning of the physical state space simplex. We derive the closed-form quadratic boundary governing the leaf-like PPT region (a2+ab+b2−b≤0)(a^2+ab+b^2-b \leq 0)(a2+ab+b2−b≤0) over the domain 0<a≤130 < a \leq \frac{1}{3}0<a≤31​, and identify the exact linear threshold (a>c)(a > c)(a>c) that characterizes the PPT bound entangled sub-region. This family strictly generalizes the well-known Horodecki bound entangled states, which appear as a single slice of the three-dimensional leaf. Applying the structural map to this decomposition, we show that it certifies bound entanglement throughout the entire threshold region, accounting for 14.76%14.76\%14.76% of the total PPT leaf area.