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[[Category: Quantum Memory Network Stage]] | [[Category: Quantum Memory Network Stage]] | ||
* GHZ-based protocol is deterministic, whereas W-based protocol is probabilistic, but the W-based protocol tolerates more noise. | * GHZ-based protocol is deterministic, whereas W-based protocol is probabilistic, but the W-based protocol tolerates more noise. | ||
* Entanglement relay protocol does not require a | * Entanglement relay protocol does not require a pre-shared multipartite state, but it creates a 4-partite GHZ state during the protocol. | ||
==Properties== | ==Properties== | ||
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*'''Guessing probability''' Let <math>\mathcal{A}</math> be a subset of adversaries among <math>n</math> nodes. Let <math>C</math> be the register that contains all classical and quantum side information accessible to the adversaries. Then, the probability of adversaries guessing the sender is given by | *'''Guessing probability''' Let <math>\mathcal{A}</math> be a subset of adversaries among <math>n</math> nodes. Let <math>C</math> be the register that contains all classical and quantum side information accessible to the adversaries. Then, the probability of adversaries guessing the sender is given by | ||
<math> P_{\text{guess}}[S|C, S\notin \mathcal{A}] = \max_{\{M^i\}} \sum_{i \in [n]} P[S=i|S\notin \mathcal{A}] \text{Tr}[M^i \cdot \rho_{C|S=i} ],</math></br> | <math> P_{\text{guess}}[S|C, S\notin \mathcal{A}] = \max_{\{M^i\}} \sum_{i \in [n]} P[S=i|S\notin \mathcal{A}] \text{Tr}[M^i \cdot \rho_{C|S=i} ],</math></br> | ||
where the | where the maximisation is taken over the set of POVMs <math>{\{M^i\}}</math> for the adversaries and <math>\rho_{C|S=i}</math> is the state of the adversaries at the end of the protocol, given that node <math>i</math> is the sender | ||
*'''Sender-security''' We say that an anonymous transmission protocol is ''sender-secure'' if, given that the sender is honest, the probability of the adversary guessing the sender is </br> | *'''Sender-security''' We say that an anonymous transmission protocol is ''sender-secure'' if, given that the sender is honest, the probability of the adversary guessing the sender is </br> | ||
<math>P_{\text{guess}}[S|C,S\notin \mathcal{A}] \leq \max_{i\in[n]} P[S=i|S\notin \mathcal{A}].</math></br> | <math>P_{\text{guess}}[S|C,S\notin \mathcal{A}] \leq \max_{i\in[n]} P[S=i|S\notin \mathcal{A}].</math></br> | ||
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==Further Information== | ==Further Information== | ||
* The definitions above guarantee information-theoretic security of the protocol when the resource states are both trusted [[Quantum Anonymous Transmission#References|[4], [1], [2] ]] and | * The definitions above guarantee information-theoretic security of the protocol when the resource states are both trusted [[Quantum Anonymous Transmission#References|[4], [1], [2] ]] and not trusted [[Quantum Anonymous Transmission#References|[3] ]]. | ||
==References== | ==References== | ||
#[https://journals.aps.org/pra/abstract/10.1103/PhysRevA.98.052320 Lipinska et al (2018)] | #[https://journals.aps.org/pra/abstract/10.1103/PhysRevA.98.052320 Lipinska et al (2018)] | ||