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

Journal of Xuzhou Normal University

Calculating the Compact Relative Entropy of Entanglement of 3-Qubit Pure State

Siping Liu

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

From Linden-Popescu-Schlienz standard form and canonical form,the compact relative entropy of entanglement of 3-qubit pure state and the compact relative entropy of entanglement of W state are calculated.The fact that the compact relative entropy of entanglement is not invariant under LU transformation is pointed out,and the relation between the compact relative entropy of entanglement and the relative entropy of entanglement of Partovi is discussed.

Related papers

Closed formula for the relative entropy of entanglement

Adam Miranowicz, Satoshi Ishizaka

The long-standing problem of finding a closed formula for the relative entropy of entanglement (REE) for two qubits is addressed. A compact-form solution to the inverse problem, which characterizes an entangled state for a given closest separable state, is obtained. Analysis of the formula for a large class of entangled states strongly suggests that a compact analytical solution of the original problem, which corresponds to finding the closest separable state for a given entangled state, can be given only in some special cases. A few applications of the compact-form formula are given to show additivity of the REE, to relate the REE with the Rains upper bound for distillable entanglement, and to show that a Bell state does not have a unique closest separable state.

arXiv:0805.3134•Physical Review A•Sep 8, 2008•48 citations

Relative entropy of entanglement of two-qubit ‘X’ states

黄接辉, 刘念华, 刘江涛 +2 more

Two closest single-qubit states could be diagonalised by the same unitary matrix, which helps to find the relative entropy of entanglement of a two-qubit 'X' state. We formulate two binary equations for the relative entropy of entanglement and the corresponding closest separable state of a given two-qubit 'X' state. This approach can be applied to get the relative entropy of entanglement of many widely-discussed two-qubit states, such as pure states, Werner states, and so on.

Chinese Physics B•Nov 1, 2010•6 citations

Modification of relative entropy of Entanglement

An Min Wang

We present the modified relative entropy of entanglement (MRE) in order to both improve the computability for the relative entropy of entanglement and avoid the problem that the entanglement of formation seems to be greater than entanglement of distillation. For two qubit system we derive out an explicit and "weak" closed expression of MRE that depends on the pure state decompositions in the case of mixed states. For more qubit system, we obtain an algorithm to calculate MRE in principle. MRE significantly improves the computability of relative entropy of entanglement and decreases the dependence and sensitivity on the pure state decompositions. Moreover it is able to inherit most of the important physical features of the relative entropy of entanglement. In addition, a kind of states, as an extension of Werner's states, is discussed constructively.

arXiv:quant-ph/0001023•Jan 10, 2000•0 citations

LU Invariants and Canonical Forms and SLOCC Classification of Pure 3-Qubit States

Di Yao-Min, Ya Cao

In this paper the entanglement of pure 3-qubit states is discussed. The local unitary (LU) polynomial invariants that are closely related to the canonical forms are constructed and the relations of the coefficients of the canonical forms are given. Then the stochastic local operations and classical communication (SLOCC) classification of the states are discussed on the basis of the canonical forms, and the symmetric canonical form of the states without 3-tangle is discussed. Finally, we give the relation between the LU polynomial invariants and SLOCC classification.

Communications in Theoretical Physics•Apr 1, 2006•3 citations

Two Theorems on Calculating the Relative Entropy of Entanglement

Shengjun Wu, Wu Qiang, Zhang Yong-De

We present two theorems on calculating the relative entropy of entanglement. Theorem 1 is an extension of Vedral and Plenio's theorem (Phys. Rev. A 57 (1998) 1619) for pure states, which is useful for calculating the relative entropy of entanglement for all pure states as well as for a class of mixed states. Theorem 2 gives the relative entropy of entanglement for any bipartite state whose tripartite purification has two separable reduced bipartite states.

arXiv:quant-ph/0004018•Chinese Physics Letters•Feb 1, 2001•12 citations

The relation between tangle and local unitary invariants for pure three and four-qubit states

Xin-Wei Zha, Yunguang Zhang, Jianxia Qi +1 more

A new form of local unitary (LU) transformation invariant is given for multi-qubit states . The general relation between tangle and the LU transformation invariant of pure three and four-qubit states is given. We find that the tangle actually is a special LU transformation invariant. Furthermore, the tangle is a important local unitary (LU) transformation invariant which is a nessesary condition for maximally multi-qubit entangled state.

arXiv:1404.4912•Apr 19, 2014•0 citations
From Linden-Popescu-Schlienz standard form and canonical form,the compact relative entropy of entanglement of 3-qubit pure state and the compact relative entropy of entanglement of W state are calculated.The fact that the compact relative entropy of entanglement is not invariant under LU transformation is pointed out,and the relation between the compact relative entropy of entanglement and the relative entropy of entanglement of Partovi is discussed.
The long-standing problem of finding a closed formula for the relative entropy of entanglement (REE) for two qubits is addressed. A compact-form solution to the inverse problem, which characterizes an entangled state for a given closest separable state, is obtained. Analysis of the formula for a large class of entangled states strongly suggests that a compact analytical solution of the original problem, which corresponds to finding the closest separable state for a given entangled state, can be given only in some special cases. A few applications of the compact-form formula are given to show additivity of the REE, to relate the REE with the Rains upper bound for distillable entanglement, and to show that a Bell state does not have a unique closest separable state.
We present the modified relative entropy of entanglement (MRE) in order to both improve the computability for the relative entropy of entanglement and avoid the problem that the entanglement of formation seems to be greater than entanglement of distillation. For two qubit system we derive out an explicit and "weak" closed expression of MRE that depends on the pure state decompositions in the case of mixed states. For more qubit system, we obtain an algorithm to calculate MRE in principle. MRE significantly improves the computability of relative entropy of entanglement and decreases the dependence and sensitivity on the pure state decompositions. Moreover it is able to inherit most of the important physical features of the relative entropy of entanglement. In addition, a kind of states, as an extension of Werner's states, is discussed constructively.
In this paper the entanglement of pure 3-qubit states is discussed. The local unitary (LU) polynomial invariants that are closely related to the canonical forms are constructed and the relations of the coefficients of the canonical forms are given. Then the stochastic local operations and classical communication (SLOCC) classification of the states are discussed on the basis of the canonical forms, and the symmetric canonical form of the states without 3-tangle is discussed. Finally, we give the relation between the LU polynomial invariants and SLOCC classification.