Anonymous transmission in a noisy quantum network using the W state

The protocol allows a sender Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle S} to transmit an arbitrary quantum state $|\psi \rangle$ to a receiver Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle R} in an anonymous way and uses the Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle N} -partite Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle W} state as a quantum resource.

Assumptions

The protocol relies on a set of classical subroutines (collision detection, receiver notification, veto and logical OR). Their proposed implementation [1] has been shown to be information-theoretically secure in the classical regime, even with an arbitrary number of corrupted participants, assuming the parties share pairwise authenticated private channels and a broadcast channel.

The protocol assumes that the implementations listed above remain secure even in the presence of a quantum adversary.

Outline

The $N$ nodes first ensure that a single one is willing to send information. They go on with notifying the receiver of its role. They use a trusted source of Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle W} states to share entanglement between the Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle N} nodes. This is done via a measurement performed by all nodes except the sender and receiver. Entanglement is only established probabilistically, but when it is successful, it can be used to teleport an arbitrary quantum state chosen by $S$. The classical communication for teleporting the state is performed anonymously.

Properties

The protocol is sender and receiver secure in the semi-active scenario. It is able to retain its security in the presence of noise affecting the Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle W} state distribution under the assumption that each qubit experiences the same noise map.

Protocol Description

Collision detection

Nodes run the classical collision detection protocol [9] to determine a single sender $S$. All nodes input 1 if they do wish to be the sender and 0 otherwise. If a single node wants to be the sender, continue.

Receiver notification

Nodes run the classical receiver notification protocol [9], where the receiver $R$ is notified of her role.

State distribution

A trusted source distributes the $N$-partite Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle W} state.

Measurement

All nodes except for $S$ and $R$ measure in the {|0〉,|1〉} basis.

Anonymous announcement of outcomes

Nodes use the classical veto protocol [9] which outputs 0 if all the $N-2$ measurement outcomes are 0, and 1 otherwise. If the output is 0 then anonymous entanglement is established, else abort.

Teleportation

Sender $S$ teleports the message state |ψ〉 to the receiver $R$. Classical messagemassociated with teleportationis sent anonymously. The communication is carried outusing the classical logical OR protocol [9] which computes $m\oplus rand$, where Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle rand} is a random 2-bit string input by the receiver $R$.

References

1. A. Broadbent and A. Tapp, inAdvances in Cryptology– ASIACRYPT 2007, edited by K. Kurosawa (Springer Berlin Heidelberg, Berlin, Heidelberg, 2007) pp. 410–426.