6
votes
Accepted
Understanding the $M$ upper bound in the paper: "Multipartite entanglement and high-precision metrology"
Your conclusion appears correct to me. It seems that Eq.(23), modified with your proposed change to the RHS, can be verified by combining Eq.(3), for the upper bound on the $M$ unentangled particles, ...
- 3,352
5
votes
Accepted
Are entanglement witnesses of this form optimal?
Answer to edited question:
It's still not true for qubit systems. Consider these two unit vectors, both of which are entangled:
$$
|\phi\rangle = \frac{1}{\sqrt{2}} | 00\rangle + \frac{1}{\sqrt{2}} | ...
- 5,083
5
votes
Accepted
How is the expression for the optimal entanglement witness derived?
The idea behind this expression is indeed a fairly general one.
$\newcommand{\bs}[1]{\boldsymbol{#1}}\newcommand{\calS}{\mathcal{S}}$An entanglement witness $\mathcal W$ is defined as an operator ...
glS♦
- 22.9k
3
votes
Accepted
How are witness operators physically implemented?
This is certainly how theorists think of this being done. I don't know if there's an experimental reality to compare this to. Whether they actually decompose it in terms of the eigenvectors, or find ...
- 54.5k
3
votes
Explicit 16⨯16 matrix representations of two-qudit entanglement witnesses
Dariusz Chruscinski has provided me with an example of a particular such entanglement witness. It takes the form
\begin{equation}
\left(
\begin{array}{cccccccccccccccc}
1 & 0 & 0 & 0 &...
- 879
3
votes
Can we characterise the general structure of two-qubit witness operators?
You can try to use the Størmer-Woronowicz theorem for that (it's used to prove the sufficiency of the Peres–Horodecki criterion in $2 \times 2$ and $2 \times 3$ cases).
The theorem states that any ...
- 6,596
2
votes
Entanglement Witnesses close to GHZ states
A partial explanation is motivated by the proof in Theorem 1 (bottom of page 2).
Assuming two locally non-commuting stabilizing operators, using the Cauchy-Schwarz inequality, for pure product states ...
- 747
1
vote
How to prove the following bosonic entanglement expression?
We have,
\begin{equation}
\begin{aligned}
S &= - \operatorname { Tr } \left( \varrho \log _ { 2 } \varrho \right) = \log _ { 2 } \left( \frac { \left| \gamma _ { B } \right| ^ { \left( 2 \left| \...
- 135
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