6 votes

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, ...
Jonathan Trousdale's user avatar
5 votes

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}} | ...
John Watrous's user avatar
  • 5,083
5 votes

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's user avatar
  • 22.9k
3 votes

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 ...
DaftWullie's user avatar
  • 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 &...
Paul B. Slater's user avatar
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 ...
Danylo Y's user avatar
  • 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 ...
John Doe's user avatar
  • 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| \...
EnthusiastiC's user avatar

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