Editing GHZ-based Quantum Anonymous Transmission
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The GHZ-based quantum anonymous transmission protocol implements the task of [[anonymous transmission]] in a <math>n</math>-node quantum network. The protocol uses <math>n</math>-partite [[GHZ state]] to enable two nodes, sender <math>S</math> and receiver <math>R</math>, to establish a link which they use to transmit a quantum message. Importantly, the quantum message is transmitted in a way that the identity of <math>S</math> is unknown to every other node, and the identity of <math>R</math> is known only to <math>S</math>. | |||
'''Tags:''' [[:Category: Quantum Enhanced Classical Functionality|Quantum Enhanced Classical Functionality]][[Category: Quantum Enhanced Classical Functionality]], [[:Category: Multi Party Protocols|Multi Party Protocols]] [[Category: Multi Party Protocols]], [[:Category:Specific Task|Specific Task]][[Category:Specific Task]], GHZ state, anonymous transmission | '''Tags:''' [[:Category: Quantum Enhanced Classical Functionality|Quantum Enhanced Classical Functionality]][[Category: Quantum Enhanced Classical Functionality]], [[:Category: Multi Party Protocols|Multi Party Protocols]] [[Category: Multi Party Protocols]], [[:Category:Specific Task|Specific Task]][[Category:Specific Task]], GHZ state, anonymous transmission | ||
==Assumptions== | ==Assumptions== | ||
* '''Network:''' The network consists of <math>n</math> nodes that are fully identified and completely connected with pairwise [[authenticated]] classical channels. Additionally, there is a secure classical [ | * '''Network:''' The network consists of <math>n</math> nodes that are fully identified and [[completely connected]] with pairwise [[authenticated]] classical channels. Additionally, there is a secure classical [[broadcast]] channel. | ||
* '''Source:''' [[Trusted]] [[multipartite]] state source. | * '''Source:''' [[Trusted]] [[multipartite]] state source. | ||
* '''Adversarial model:''' [[active adversary]] who does not control the source. | * '''Adversarial model:''' [[active adversary]] who does not control the source. | ||
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* <math>R</math>: the receiver of the quantum message | * <math>R</math>: the receiver of the quantum message | ||
==Requirements== | ==Hardware Requirements== | ||
*Network stage: [[:Category: Quantum Memory Network Stage|quantum memory network]][[Category:Quantum Memory Network Stage]]. | *Network stage: [[:Category: Quantum Memory Network Stage|quantum memory network]][[Category:Quantum Memory Network Stage]]. | ||
* Relevant parameters to establish one anonymous link: <math>k=1</math> round of quantum communication per node, circuit depth <math>m=1</math>, <math>q=1</math> physical qubits per node. | * Relevant parameters to establish one anonymous link: <math>k=1</math> round of quantum communication per node, circuit depth <math>m=1</math>, <math>q=1</math> physical qubits per node. | ||
* Quantum memories, single-qubit Pauli gates and single-qubit measurements at the end nodes. | * Quantum memories, single-qubit Pauli gates and single-qubit measurements at the end nodes. | ||
==Properties== | ==Properties== | ||
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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]]]. | 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== | ||
Receiver <math>R</math> is determined before the start of the protocol. <math>S</math> holds a message qubit <math>|\psi\rangle</math>. | Receiver <math>R</math> is determined before the start of the protocol. <math>S</math> holds a message qubit <math>|\psi\rangle</math>. | ||
# Nodes run a collision detection protocol and determine a single sender <math>S</math>. | # Nodes run a collision detection protocol and determine a single sender <math>S</math>. | ||
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* 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. | * 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|[6] ]]. | * 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|[3], [5 | * 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|[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 | * 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 utilise solely Bell pairs to create anonymous entanglement [[GHZ State based Quantum Anonymous Transmission#References|[2] ]]. | * 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] ]]. | ||
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#[https://ieeexplore.ieee.org/document/4077005 Bouda et al (2007)] | #[https://ieeexplore.ieee.org/document/4077005 Bouda et al (2007)] | ||
#[https://arxiv.org/abs/0706.2010 Broadbent et al (2007)] | #[https://arxiv.org/abs/0706.2010 Broadbent et al (2007)] | ||
#[https://arxiv.org/abs/ | #[https://arxiv.org/abs/quant-ph/9901035 Brassard et al (2007)] | ||
#[https:// | #[https://link.springer.com/chapter/10.1007/11593447_12 Christandl et al (2005)] | ||
<div style='text-align: right;'>''contributed by Victoria Lipinska''</div> | <div style='text-align: right;'>''contributed by Victoria Lipinska''</div> |