Multipartite Entanglement Verification: Difference between revisions

Multipartite Entanglement Verification (edit)

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      \tau=\min_{U}\mbox{TD}(|\phi_{0}^{n} \rangle\langle \phi_{0}^{n}|, U|\psi \rangle \langle \psi | U^{\dagger} )
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-and where TD is the trace distance and <math>U</math> is a quantum operation acting on <math>D</math> the subspace of dishonest parties involved in the protocol (ie a tensor product of an  unitary operator on <math>D</math> and the identity operator on the rest).
+and where TD is the trace distance and <math>U</math> is a quantum operation acting on <math>D</math> the subspace of dishonest parties involved in the protocol (ie a tensor product of an  unitary operator on <math>D</math> and the identity operator on the rest). This means that the further the shared state is from the GHZ state, the less likely the verifier is going to accept it conditioned on any quantum operation that the dishonest party can locally perform to get closer to the GHZ state.
 * This protocol still works in the presence of photon losses.
-* This protocol is composably secure meaning that it can be used as a subroutine in a bigger protocol. A direct application of this protocol is to perform it sequentially many times with a source sending state at each round and to randomly use the shared state at some point if the protocol has output 0 at each round. We then are sure up to a certain threshold that the shared state is a GHZ state.
 ==Pseudo Code==