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GHZ-based Quantum Anonymous Transmission: Difference between revisions
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==Outline== | ==Outline== | ||
The presented GHZ-based quantum | The presented GHZ-based quantum anonymous transmission protocol is based on the work of [[GHZ State based Quantum Anonymous Transmission#References|[6]]]. The goal of the protocol is to transmit a quantum state <math>|\psi \rangle</math> from the sender <math>S</math> to the receiver <math>R</math>, while keeping the identities of <math>S</math> and <math>R</math> anonymous. We assume that there is exactly one receiver which is determined before the start of the protocol. The protocol consists of the following steps: | ||
* ''Collision detection:'' Nodes run a collision detection protocol to determine a single sender <math>S</math>. | * ''Collision detection:'' Nodes run a collision detection protocol to determine a single sender <math>S</math>. | ||
* ''State distribution:'' A trusted source distributes the <math>n</math>-partite GHZ state. | * ''State distribution:'' A trusted source distributes the <math>n</math>-partite GHZ state. | ||
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<math>P_{\text{guess}}[S|C,S\notin \mathcal{A}] \leq \max_{i\in[n]} P[S=i|S\notin \mathcal{A}] = \frac{1}{n-t},</math></br> | <math>P_{\text{guess}}[S|C,S\notin \mathcal{A}] \leq \max_{i\in[n]} P[S=i|S\notin \mathcal{A}] = \frac{1}{n-t},</math></br> | ||
<math>P_{\text{guess}}[R|C,S\notin \mathcal{A}] \leq \max_{i\in[n]} P[R=i|S\notin \mathcal{A}] = \frac{1}{n-t},</math></br> | <math>P_{\text{guess}}[R|C,S\notin \mathcal{A}] \leq \max_{i\in[n]} P[R=i|S\notin \mathcal{A}] = \frac{1}{n-t},</math></br> | ||
where <math>\mathcal{A}</math> is the subset of <math>t</math> adversaries among <math>n</math> nodes and <math>C</math> is the register that contains all classical and quantum side information accessible to the adversaries. Note that this implies that the protocol is also | where <math>\mathcal{A}</math> is the subset of <math>t</math> adversaries among <math>n</math> nodes and <math>C</math> is the register that contains all classical and quantum side information accessible to the adversaries. Note that this implies that the protocol is also trace-less, since even if the adversary hijacks any <math>t\leq n-2</math> players and gains access to all of their classical and quantum information after the end of the protocol, she cannot learn the identities of <math>S</math> and <math>R</math>. For a formal argument see [[GHZ State based Quantum Anonymous Transmission#References|[6]]]. | ||
==Pseudocode== | ==Pseudocode== | ||
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* In [[GHZ State based Quantum Anonymous Transmission#References|[5] ]], it was first shown that the proposed protocol is information-theoretically secure against an active adversary. | * In [[GHZ State based Quantum Anonymous Transmission#References|[5] ]], it was first shown that the proposed protocol is information-theoretically secure against an active adversary. | ||
* In [[GHZ State based Quantum Anonymous Transmission#References|[1] ]] a protocol using another multipartite state, the W state, was introduced. The reference discusses noise robustness of both GHZ-based and W-based protocols and compares the performance of both protocols. | * In [[GHZ State based Quantum Anonymous Transmission#References|[1] ]] a protocol using another multipartite state, the W state, was introduced. The reference discusses noise robustness of both GHZ-based and W-based protocols and compares the performance of both protocols. | ||
* Other protocols were proposed, which do not make use of multipartite entanglement, but | * Other protocols were proposed, which do not make use of multipartite entanglement, but utilise solely Bell pairs to create anonymous entanglement [[GHZ State based Quantum Anonymous Transmission#References|[2] ]]. | ||
==References== | ==References== | ||