# Quantitative entanglement witnesses

@article{Eisert2006QuantitativeEW, title={Quantitative entanglement witnesses}, author={Jens Eisert and Fernando G. S. L. Brand{\~a}o and Koenraad M. R. Audenaert}, journal={New Journal of Physics}, year={2006}, volume={9}, pages={46 - 46} }

Entanglement witnesses provide tools to detect entanglement in experimental situations without the need of having full tomographic knowledge about the state. If one estimates in an experiment an expectation value smaller than zero, one can directly infer that the state has been entangled, or specifically multi-partite entangled, in the first place. In this paper, we emphasize that all these tests—based on the very same data—give rise to quantitative estimates in terms of entanglement measures…

## 142 Citations

### The structure of ultrafine entanglement witnesses

- Physics, PhilosophyJournal of Physics A: Mathematical and Theoretical
- 2018

An entanglement witness is an observable with the property that a negative expectation value signals the presence of entanglement. The question arises how a witness can be improved if the expectation…

### Entanglement Quantification in Atomic Ensembles.

- PhysicsPhysical review letters
- 2021

This work analytically derives the lower bounds of broad families of entanglement criteria based on variances of arbitrary operators and lower bounding the best separable approximation and the generalized robustness only from measurements of first and second moments of the collective spin operator.

### Witnessing bipartite entanglement sequentially by multiple observers

- PhysicsPhysical Review A
- 2018

We investigate sharing of bipartite entanglement in a scenario where half of an entangled pair is possessed and projectively measured by one observer, called Alice, while the other half is subjected…

### Reliable and robust entanglement witness

- Computer Science
- 2016

This work employs a recently proposed measurement-device-independent entanglement witness, in which the correctness of the conclusion is independent of the implemented measurement devices, and optimize the EW to draw a better conclusion given certain experimental data.

### Design and experimental performance of local entanglement witness operators

- Computer SciencePhysical Review A
- 2020

This work proposes and analyzes a class of entanglement witnesses that detect the presence ofEntanglement in subsystems of experimental multi-qubit stabilizer states and theoretically establishes the noise tolerance of the proposed witnesses and benchmark their practical performance by analyzing the local entangled structure of an experimental seven-qu bit quantum error correction code.

### Lower bounds on entanglement measures from incomplete information

- Computer Science, Physics
- 2008

A simple algorithm is presented for the estimation of the concurrence and extensions of entanglement measures via Legendre transforms, if the diagonal elements of the quantum state in a certain basis are known.

### Detection and quantification of entanglement with measurement-device-independent and universal entanglement witness

- Physics
- 2020

This study experimentally design and realize an MDI UEW for two-qubit entangled states that is able to quantify entanglement by comparing it with concurrence estimated through state tomography and ensures that the UEW is MDI.

### Estimating localizable entanglement from witnesses

- PhysicsNew Journal of Physics
- 2018

Computing localizable entanglement for noisy many-particle quantum states is difficult due to the optimization over all possible sets of local projection measurements. Therefore, it is crucial to…

### Optimal estimation of entanglement

- Physics
- 2008

Entanglement does not correspond to an observable, and its evaluation always corresponds to an estimation procedure where the amount of entanglement is inferred from the measurements of one or more…

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