https://arxiv.org/pdf/2002.12400.pdf
A. Entanglement witness games
In this section, we will recap entanglement witness
games from the literature. We will start from the assumption that a choice of witness W has been made.
The quantum system under investigation is decomposed
into m subsystems on which local measurements can be
performed (e.g., m = 2 for bipartite entanglement witnessing). The witness operator then admits a decomposition into locally measurable observables of the form
W = cI +
X
x
wxM(1)
x ⊗ · · · ⊗ M(m)
x
, (3)
5
where each M
(j)
x is a locally measurable observable on
subsystem j and where x runs over the terms in the decomposition. Note that such a decomposition is always
possible. A decomposition is minimal if the number of
terms over which x runs is minimal. In practice, the
locally measurable observables M
(j)
x will often be Pauli
observables. The decomposition in Eq. (3) is chosen such
that each locally measurable observable can be easily
measured in the experiment. Measurement of M
(j)
x yields
one of the possible outcomes labeled by aj (in the case of
Pauli observables, the outcomes are simply ±1). We shall
denote the vector of all outcomes of the m subsystems as