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GHZ-based Quantum Anonymous Transmission: Difference between revisions
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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 traceless, 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| | 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 traceless, 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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==Further Information== | ==Further Information== | ||
* To determine the sender <math>S</math> (Step 1) one can run either a classical collision detection protocol of [[GHZ State based Quantum Anonymous Transmission#References| | * To determine the sender <math>S</math> (Step 1) one can run either a classical collision detection protocol of [[GHZ State based Quantum Anonymous Transmission#References|[4] ]] or a quantum collision detection protocol of [[GHZ State based Quantum Anonymous Transmission#References|[6] ]]. The quantum version of the protocol requires additional <math>(\left\lceil \log n \right\rceil + 1)</math> GHZ states. | ||
* To determine the receiver <math>R</math> during the protocol one can incorporate an additional step using a classical receiver notification protocol of [[GHZ State based Quantum Anonymous Transmission#References| | * To determine the receiver <math>R</math> during the protocol one can incorporate an additional step using a classical receiver notification protocol of [[GHZ State based Quantum Anonymous Transmission#References|[4] ]]. | ||
* To send classical teleportation bits <math>m_0,m_1</math> (Step 5) the players can run a classical logical OR protocol of [[GHZ State based Quantum Anonymous Transmission#References| | * To send classical teleportation bits <math>m_0,m_1</math> (Step 5) the players can run a classical logical OR protocol of [[GHZ State based Quantum Anonymous Transmission#References|[4] ]] or anonymous transmission protocol for classical bits with quantum resources of [[GHZ State based Quantum Anonymous Transmission#References|[6] ]]. The quantum protocol requires one additional GHZ state for transmitting one classical bit. | ||
* The anonymous transmission of quantum states was introduced in [[GHZ State based Quantum Anonymous Transmission#References| | * The anonymous transmission of quantum states was introduced in [[GHZ State based Quantum Anonymous Transmission#References|[6] ]]. | ||
* The problem was subsequently developed to consider the preparation and certification of the GHZ state [[GHZ State based Quantum Anonymous Transmission#References| | * The problem was subsequently developed to consider the preparation and certification of the GHZ state [[GHZ State based Quantum Anonymous Transmission#References|[3], [5] ]]. | ||
* In [[GHZ State based Quantum Anonymous Transmission#References| | * 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| | * 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 utilize solely Bell pairs to create anonymous entanglement [[GHZ State based Quantum Anonymous Transmission#References| | * Other protocols were proposed, which do not make use of multipartite entanglement, but utilize solely Bell pairs to create anonymous entanglement [[GHZ State based Quantum Anonymous Transmission#References|[2] ]]. | ||
==References== | ==References== | ||
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#[https://link.springer.com/chapter/10.1007/11593447_12 Christandl et al (2005)] | #[https://link.springer.com/chapter/10.1007/11593447_12 Christandl et al (2005)] | ||
==Further Information== | ==Further Information== | ||
<div style='text-align: right;'>'' | <div style='text-align: right;'>''contributed by Victoria Lipinska''</div> | ||