Editing Multipartite Entanglement Verification
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\tau=\min_{U}\mbox{TD}(|\phi_{0}^{n} \rangle\langle \phi_{0}^{n}|, U|\psi \rangle \langle \psi | U^{\dagger} ) | \tau=\min_{U}\mbox{TD}(|\phi_{0}^{n} \rangle\langle \phi_{0}^{n}|, U|\psi \rangle \langle \psi | U^{\dagger} ) | ||
</math> | </math> | ||
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 protocol still works in the presence of photon losses. | * 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. | |||
* This protocol is secure for one round against any coalition of dishonest parties, including the source. | * This protocol is secure for one round against any coalition of dishonest parties, including the source. |