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:quant-ph/0504095 · Physical Review A

Infinite number of conditions for local mixed-state manipulations

Gilad Gour

Published Aug 18, 2005• 20 citations
arXivHTMLPDF

Abstract

It is shown that a finite number of conditions are not sufficient to determine the locality of transformations between two probability distributions of pure states as well as the locality of transformations between two $d\ifmmode\times\else\texttimes\fi{}d$ mixed states with $d\ensuremath{\geqslant}4$. As an example, an infinite, but minimal, set of necessary and sufficient conditions for the existence of a local procedure that converts one probability distribution of two pure pair of qubits into another one is found.

DOI
10.1103/physreva.72.022323

Related papers

Conditions for Local Entanglement Manipulation from Pure States to Mixed States

Lin-Mei Liang, Ping‐Xing Chen, Cheng-Zu Li +1 more

We discuss the transformation from pure states to mixed states in a bipartite system H A ⊗ H B and provide the sufficient condition for this transformation. We also provide a necessary and sufficient condition for one class of this transformation. Meanwhile, the method of realization for the transformation from pure states to mixed states is also present. Furthermore, we briefly discuss the application.

Chinese Physics Letters•Feb 1, 2002•0 citations

Minimal Conditions for Local Pure-State Entanglement Manipulation

Daniel Jonathan, Martin Bodo Plenio

We find a minimal set of necessary and sufficient conditions for the existence of a local procedure that converts a finite pure state into one of a set of possible final states. This result provides a powerful method for obtaining optimal local entanglement manipulation protocols for pure initial states. As an example, we determine analytically the optimal distillable entanglement for arbitrary finite pure states. We also construct an explicit protocol achieving this bound.

arXiv:quant-ph/9903054•Physical Review Letters•Aug 16, 1999•217 citations

Coherence convertibility for mixed states

Xiaofei Qi, Zhaofang Bai, Shuanping Du

In this paper, by providing a class of coherence measures in finite dimensional systems, a sufficient and necessary condition for the existence of coherence transformations that convert one probability distribution of any pure states into another one is obtained.

arXiv:1505.07387•May 27, 2015•7 citations

Conditions for Local Entanglement Manipulation from Pure States to Mixed States

梁林梅, 黄明球

We discuss the transformation from pure states to mixed states in a bipartite system HA×HB and provide the sufficient condition for this transformation.We also provide a necessary and sufficient condition for one chass of this transformation.Meanwhile,the method of realization for the transformation from pure states to mixed states is also present.Furthermore,we briefly discuss the application.

Chinese Physics Letters•Jan 1, 2002•0 citations

Purification of two-qubit mixed states

E. Jan\'e

We find the necessary and sufficient condition under which two two-qubit mixed states can be purified into a pure maximally entangled state by local operations and classical communication. The optimal protocol for such transformation is obtained. This result leads to a necessary and sufficient condition for the exact purification of $n$ copies of a two-qubit state.

Quantum Information and Computation•Aug 1, 2002•7 citations

Purification of two-qubit mixed states

E. Jané

We find the necessary and sufficient condition under which two two-qubit mixed states can be purified into a pure maximally entangled state by local operations and classical communication. The optimal protocol for such transformation is obtained. This result leads to a necessary and sufficient condition for the exact purification of $n$ copies of a two-qubit state.

arXiv:quant-ph/0205107•Quantum Information and Computation•May 17, 2002•7 citations
It is shown that a finite number of conditions are not sufficient to determine the locality of transformations between two probability distributions of pure states as well as the locality of transformations between two d\ifmmode×\else\texttimes\fidd\ifmmode\times\else\texttimes\fi{}dd\ifmmode×\else\texttimes\fid mixed states with d\ensuremath⩾4d\ensuremath{\geqslant}4d\ensuremath⩾4. As an example, an infinite, but minimal, set of necessary and sufficient conditions for the existence of a local procedure that converts one probability distribution of two pure pair of qubits into another one is found.
We find the necessary and sufficient condition under which two two-qubit mixed states can be purified into a pure maximally entangled state by local operations and classical communication. The optimal protocol for such transformation is obtained. This result leads to a necessary and sufficient condition for the exact purification of nnn copies of a two-qubit state.
We find the necessary and sufficient condition under which two two-qubit mixed states can be purified into a pure maximally entangled state by local operations and classical communication. The optimal protocol for such transformation is obtained. This result leads to a necessary and sufficient condition for the exact purification of nnn copies of a two-qubit state.