Verifiable Quantum Anonymous Transmission: Difference between revisions

This verified GHZ-based quantum anonymous transmission protocol is based on the work of \cite{Unnikrishnan}, which uses the following subroutines from [[Verifiable Quantum Anonymous Transmission#References|[6]]] \cite{Wehner}, \cite{Broadbent}, \cite{Pappa}, \cite{McCutcheon}:

* <span style="font-variant:small-caps">Parity</span> \cite{Broadbent}: privately computes the parity of an input string.

* <span style="font-variant:small-caps">LogicalOR</span> \cite{Broadbent}: privately computes the logical OR of an input string, using a modified version of <span style="font-variant:small-caps">Parity</span>.

* <span style="font-variant:small-caps">Notification</span> \cite{Broadbent}: allows one player to anonymously notify another player, using <span style="font-variant:small-caps">LogicalOR</span>.

* <span style="font-variant:small-caps">RandomBit</span> \cite{Unnikrishnan}: allows one player to anonymously choose a bit according to a probability distribution, using <span style="font-variant:small-caps">LogicalOR</span>.

* <span style="font-variant:small-caps">Verification</span> \cite{Pappa, McCutcheon}: allows one player (the Verifier) to run a test to check if the shared state is the GHZ state. The Verifier instructs each player to measure their qubit in a particular basis and checks the parity of the measurement outcomes.  

* <span style="font-variant:small-caps">Anonymous Entanglement</span> \cite{Wehner}: <math>n-2</math> nodes (all except for <math>\mathcal{S}</math> and <math>\mathcal{R}</math>) measure in the <math>X</math> basis and broadcast their measurement outcome. <math>\mathcal{S}</math> and <math>\mathcal{R}</math> broadcast random dummy bits. The parity of measurement outcomes allows the establishment of an entangled link between <math>\mathcal{S}</math> and <math>\mathcal{R}</math> which is called anonymous entanglement.

* The protocol assumes there is only one Sender for simplicity. However, if this is not the case, the players can run a classical \cite{Broadbent} or quantum \cite{Wehner} collision detection protocol to deal with multiple Senders.  

* To send classical teleportation bits <math>m_0, m_1</math>, the players can run <span style="font-variant:small-caps">Fixed Role Anonymous Message Transmission</span> from \cite{Broadbent}, or the anonymous transmission protocol for classical bits with quantum resources from \cite{Wehner}.

* <span style="font-variant:small-caps">Verification</span> was experimentally demonstrated for 3- and 4-party GHZ states in \cite{McCutcheon}.

* The Broadbent-Tapp protocol \cite{Broadbent} implements classical anonymous transmission. It requires pairwise authenticated classical channels and a classical broadcast channel.  

* The Christandl-Wehner protocol \cite{Wehner} implements both classical and quantum anonymous transmission. However, this protocol assumes the nodes share a perfect, trusted GHZ state.

* The Brassard et. al. protocol \cite{Brassard} implements verified quantum anonymous transmission. While their protocol includes a verification stage, it requires each player to perform a size-<math>n</math> quantum circuit and to have access to quantum communication with all other agents.

* The Lipinska et. al. protocol \cite{Lipinska} implements quantum anonymous transmission with a trusted W state instead of a GHZ state. While this is beneficial in terms of robustness to noise, the protocol proceeds to create anonymous entanglement only probabilistically, whereas GHZ-based anonymous entanglement proceeds deterministically.