Questions tagged [entanglement-witness]
For questions about the use of functionals to detect the entanglement of a given quantum state.
11
questions
10
votes
1
answer
254
views
Understanding the $M$ upper bound in the paper: "Multipartite entanglement and high-precision metrology"
This paper is a paper in 2012 and cited by a lot of papers. And there does not exist comment in arxiv or error statement in PRA. But when I reading this paper, I think the right part of the eq(23) ...
- 2,852
5
votes
0
answers
95
views
Finding a class $C$ of bipartite PPT states such that entanglement of $\rho \in C$ implies entanglement of $\rho + \rho^{\Gamma}$
Consider an entangled bipartite quantum state $\rho \in \mathcal{M}_d(\mathbb{C}) \otimes \mathcal{M}_{d'}(\mathbb{C})$ which is positive under partial transposition, i.e., $\rho^\Gamma \geq 0$. As ...
- 309
4
votes
1
answer
252
views
Are entanglement witnesses of this form optimal?
One can make an entanglement witness by taking the partial transpose of any pure entangled state.
Consider $|\phi \rangle $ as any pure entangled state.
Then $W = | \phi \rangle \langle \phi |^{T_2} ...
- 1,611
4
votes
1
answer
231
views
How is the expression for the optimal entanglement witness derived?
In the Bertlmann 2009 paper in the Annals of Physics (here), an optimal witness operator for an entangled state $\rho$, given that the closest separable state to it is $\rho_0$ is given by:
$$A_{\...
- 1,611
4
votes
1
answer
143
views
Can we characterise the general structure of two-qubit witness operators?
Consider a two-qubit space, and a Hermitian operator $R\in\mathrm{Herm}(\mathbb{C}^2\otimes\mathbb{C}^2)$ in this space.
The operator is positive semidefinite iff $\langle u,Ru\rangle\ge0$ for all $u\...
glS♦
- 22.9k
4
votes
1
answer
342
views
How are witness operators physically implemented?
Let's take an example of an entanglement witness of the form $W = | \phi \rangle \langle \phi | ^{T_2}$ where $ | \phi \rangle $ is some pure entangled state.
If I wanted to test some state $\rho$, I ...
- 1,611
4
votes
1
answer
79
views
Explicit 16⨯16 matrix representations of two-qudit entanglement witnesses
I have a set of $16 \times 16$ two-qudit density matrices. I would like to study the bound-entanglement for this set, making use of entanglement witnesses for which explicit matrix representations are ...
- 879
4
votes
1
answer
133
views
Entanglement Witnesses close to GHZ states
Consider page 2 of Toth's paper 'Entanglement detection in the stabilizer formalism (2005)'. To detect entanglement close to GHZ states, they construct entanglement witnesses of the form $$\mathcal{W} ...
- 747
4
votes
0
answers
82
views
Is there a two-qudit Choi entanglement witness $W^{(+)}$?
Example 2 in arXiv:1811.09896 states that the "Choi EW (entanglement witness) $W^{(+)}$ obtained from the Choi map in $d=3$ $\ldots$ is given by
\begin{equation}
W^{(+)} = \frac{1}{6} \left( \...
- 879
2
votes
1
answer
48
views
How to prove the following bosonic entanglement expression?
Based on the article given by J. L. Ball, I. Fuentes-Schuller, and F. P. Schuller, Phys. Lett. A 359, 550 (2006)
had used the following expression of von-Neumann entropy
\begin{equation}
S = - \...
- 135
2
votes
0
answers
195
views
What it means to say that SWAP gate has maximum operator entanglement entropy?
In this (freely available) article, just below equation 14, it says
The SWAP operator has the maximum operator entanglement entropy...
The operator entanglement entropy, denoted by $E(U)$ for an ...
- 598