# Conditions for a Class of Entanglement Transformations

@article{Nielsen1999ConditionsFA, title={Conditions for a Class of Entanglement Transformations}, author={Michael A. Nielsen}, journal={Physical Review Letters}, year={1999}, volume={83}, pages={436-439} }

Suppose Alice and Bob jointly possess a pure state, |ψ〉. Using local operations on their respective systems and classical communication it may be possible for Alice and Bob to transform |ψ〉 into another joint state |φ〉. This Letter gives necessary and sufficient conditions for this process of entanglement transformation to be possible. These conditions reveal a partial ordering on the entangled states and connect quantum entanglement to the algebraic theory of majorization. As a consequence, we…

## 79 Citations

Conditions for local transformations between sets of quantum states

- MathematicsPhysical Review A
- 2022

We study the problem of transforming a set of pure bipartite states into another using deterministic LOCC (local operations and classical communication). Necessary conditions for the existence of…

Probabilistic Implementation of Non-Local CNOT Operation and Entanglement Purification

- Physics
- 2004

It is pointed out that the nonlocal CNOT operation can be used as a purification protocol to concentrate entanglement from an ensemble of partially entangled particles into a subensemble of maximally entangled ones.

Character of locally inequivalent classes of states and entropy of entanglement

- Mathematics
- 2008

In this Rapid Communication we have established the physical character of pure bipartite states with the same amount of entanglement in the same Schmidt rank that either they are local unitarily…

A Brief Overview of Bipartite and Multipartite Entanglement Measures

- PhysicsInternational Journal of Theoretical Physics
- 2018

The efficient bipartite and multipartite entanglement measures are reported, which are used for pure and mixed states in quantum computation and quantum information theory.

Entanglement in Quantum Information Theory

- Physics, Philosophy
- 1998

Quantum mechanics has many counter-intuitive consequences which contradict our intuition which is based on classical physics. Here we discuss a special aspect of quantum mechanics, namely the…

Range criterion and classification of true entanglement in a 2×M×N system

- Physics
- 2006

We propose a range criterion that is a sufficient and necessary condition satisfied by two pure states transformable into each other under reversible stochastic local operations assisted by classical…

An Indexed Bibliography of Genetic Algorithms & Quantum Computing

- Computer Science
- 2015

The Communication Value of a Quantum Channel

- Computer Science2022 IEEE International Symposium on Information Theory (ISIT)
- 2022

This work studies the communication value (cv) of channel, which describes the optimal success probability of transmitting a randomly selected classical message over the channel, and proves that any pair of qubit channels have multiplicative cv when used in parallel.

## References

SHOWING 1-10 OF 25 REFERENCES

Physics Today.

- PhysicsApplied optics
- 1966

Using a combination of x-ray diffraction and electron diffraction, the scientists produced a three-dimensional map of the hybridized "orbital hole" bonding copper with neighboring oxygen atoms in cuprite (Cu2O).

Matrix analysis

- MathematicsStatistical Inference for Engineers and Data Scientists
- 2018

This new edition of the acclaimed text presents results of both classic and recent matrix analyses using canonical forms as a unifying theme, and demonstrates their importance in a variety of applications.

Inequalities: Theory of Majorization and Its Applications

- Mathematics
- 1980

Although they play a fundamental role in nearly all branches of mathematics, inequalities are usually obtained by ad hoc methods rather than as consequences of some underlying "theory of…

Elements of Information Theory

- Computer Science
- 1991

The author examines the role of entropy, inequality, and randomness in the design of codes and the construction of codes in the rapidly changing environment.

Probability and Random Processes

- EconomicsTechnometrics
- 2005

This handbook is a very useful handbook for engineers, especially those working in signal processing, and provides real data bootstrap applications to illustrate the theory covered in the earlier chapters.

Phys

- Rev. A 53, 2046
- 1996

Matrix analysis (Springer-Verlag

- New York,
- 1997

Wiss

- Z. Karl-Marx-Univ. Leipzig 20, 633
- 1971