implements Entanglement Verification
This protocol [1] implement the task of Multipartite entanglement verification in a multinode quantum network. The protocol uses classical communication and measurements of quantum states to verify whether the parties share a GHZ state. We present here a loss tolerant version of the protocol, which doesn’t assume that the source of the state nor the parties (except one) are trusted.
It has various application in a setting where at each timestep a source shares a state. Most of the time this state will be verified using this protocol and once in a while it will be used to perform some computation or communication protocol (e.g. Anonymous transmission)
This protocol is based on the work in W. McCutcheon, A. Pappa et al.. The goal is for a specific party called the Verifier to check whether the source has shared a GHZ-state among the n-nodes network. It goes as follow:
Network stage: quantum memory network.
Requirements:
Correctness:
If the source shares a GHZ state and every party behaves honestly, the outcome broadcasted by the verifier is $b = 0$.
Statistical Behavior:
The outcome of the protocol depends on the trace distance between the shared state $|\\\psi\\\rangle$ and the ideal GHZ state.
The output $b$ is such that:
$$
b =
\\\begin{cases}
0 & \\\text{with probability } 1 – \\\frac{\\\tau^2}{2} \\\\\\\\\
1 & \\\text{with probability } \\\frac{\\\tau^2}{2}
\\\end{cases}
$$
where
$$
\\\tau = \\\min_U \\\text{TD}(|\\\phi_0^n\\\rangle\\\langle\\\phi_0^n|, U|\\\psi\\\rangle\\\langle\\\psi|U^\\\dagger)
$$
TD is the trace distance. $U$ is a quantum operation acting on $D$, the subspace of dishonest parties (i.e., a tensor product of a unitary on $D$ and the identity on the rest).
This means: the further the shared state is from the GHZ state, the less likely the verifier will accept it, even if dishonest parties apply local quantum operations to approximate the GHZ state.
Robustness:
The protocol still functions in the presence of photon losses.
Security:
Input: $\\\{y_i\\\}_{i=1}^{n}$, 1 qubit, $v$
Output: one Bit in $\\\{0,1\\\}$ and $\\\{\\\theta_i\\\}_{i=1}^{n}$
And for each $i = 1,…,n, i \\\neq v$
Input: 1 angle $\\\theta_i$, 1 qubit and $v$
Output: Bit $y_i$
![]()
Image caption: Abstract Cryptography figure for the MEV protocol for n=3 parties. Each blue box is a converter representing a protocol a party is following and red boxes are the resources used namely: state generation resource, quantum and authenticated classical channels.
The protocol has also been experimentally realised in [1]
This protocol was first introduced in Multipartite Entanglement Verification Resistant against Dishonest Parties [2], in which the authors present an XY version of the protocol where $\\\forall i,\\\theta_i \\\in \\\{0,1\\\}$. It means that each party applies an X or a Z gate on its qubit before measuring in the computational basis. It appeared that when a 50% qubit loss rate is tolerated, there exists a cheating strategy allowing a dishonest party to convince the verifier that the state shared was a GHZ state even when it is not.
This is why in “Experimental verification of multipartite entanglement in quantum networks”[2], the authors present the current version of the protocol which is loss tolerant. They also present an experimental realization of the verification protocol with $n=4$ parties and photonic GHZ states.
In “Anonymity for practical quantum networks” [3], Authors use this verification protocol as a subroutine allowing the parties to be certain to have a GHZ state shared when they perform an anonymous transmission protocol.
implements Entanglement Verification
This protocol [1] implement the task of Multipartite entanglement verification in a multinode quantum network. The protocol uses classical communication and measurements of quantum states to verify whether the parties share a GHZ state. We present here a loss tolerant version of the protocol, which doesn’t assume that the source of the state nor the parties (except one) are trusted.
It has various application in a setting where at each timestep a source shares a state. Most of the time this state will be verified using this protocol and once in a while it will be used to perform some computation or communication protocol (e.g. Anonymous transmission)
This protocol is based on the work in W. McCutcheon, A. Pappa et al.. The goal is for a specific party called the Verifier to check whether the source has shared a GHZ-state among the n-nodes network. It goes as follow:
Network stage: quantum memory network.
Requirements:
Correctness:
If the source shares a GHZ state and every party behaves honestly, the outcome broadcasted by the verifier is $b = 0$.
Statistical Behavior:
The outcome of the protocol depends on the trace distance between the shared state $|\\\psi\\\rangle$ and the ideal GHZ state.
The output $b$ is such that:
$$
b =
\\\begin{cases}
0 & \\\text{with probability } 1 – \\\frac{\\\tau^2}{2} \\\\\\\\\
1 & \\\text{with probability } \\\frac{\\\tau^2}{2}
\\\end{cases}
$$
where
$$
\\\tau = \\\min_U \\\text{TD}(|\\\phi_0^n\\\rangle\\\langle\\\phi_0^n|, U|\\\psi\\\rangle\\\langle\\\psi|U^\\\dagger)
$$
TD is the trace distance. $U$ is a quantum operation acting on $D$, the subspace of dishonest parties (i.e., a tensor product of a unitary on $D$ and the identity on the rest).
This means: the further the shared state is from the GHZ state, the less likely the verifier will accept it, even if dishonest parties apply local quantum operations to approximate the GHZ state.
Robustness:
The protocol still functions in the presence of photon losses.
Security:
Input: $\\\{y_i\\\}_{i=1}^{n}$, 1 qubit, $v$
Output: one Bit in $\\\{0,1\\\}$ and $\\\{\\\theta_i\\\}_{i=1}^{n}$
And for each $i = 1,…,n, i \\\neq v$
Input: 1 angle $\\\theta_i$, 1 qubit and $v$
Output: Bit $y_i$

Image caption: Abstract Cryptography figure for the MEV protocol for n=3 parties. Each blue box is a converter representing a protocol a party is following and red boxes are the resources used namely: state generation resource, quantum and authenticated classical channels.
The protocol has also been experimentally realised in [1]
This protocol was first introduced in Multipartite Entanglement Verification Resistant against Dishonest Parties [2], in which the authors present an XY version of the protocol where $\\\forall i,\\\theta_i \\\in \\\{0,1\\\}$. It means that each party applies an X or a Z gate on its qubit before measuring in the computational basis. It appeared that when a 50% qubit loss rate is tolerated, there exists a cheating strategy allowing a dishonest party to convince the verifier that the state shared was a GHZ state even when it is not.
This is why in “Experimental verification of multipartite entanglement in quantum networks”[2], the authors present the current version of the protocol which is loss tolerant. They also present an experimental realization of the verification protocol with $n=4$ parties and photonic GHZ states.
In “Anonymity for practical quantum networks” [3], Authors use this verification protocol as a subroutine allowing the parties to be certain to have a GHZ state shared when they perform an anonymous transmission protocol.
implements Entanglement Verification
This protocol [1] implement the task of Multipartite entanglement verification in a multinode quantum network. The protocol uses classical communication and measurements of quantum states to verify whether the parties share a GHZ state. We present here a loss tolerant version of the protocol, which doesn’t assume that the source of the state nor the parties (except one) are trusted.
It has various application in a setting where at each timestep a source shares a state. Most of the time this state will be verified using this protocol and once in a while it will be used to perform some computation or communication protocol (e.g. Anonymous transmission)
This protocol is based on the work in W. McCutcheon, A. Pappa et al.. The goal is for a specific party called the Verifier to check whether the source has shared a GHZ-state among the n-nodes network. It goes as follow:
Network stage: quantum memory network.
Requirements:
Correctness:
If the source shares a GHZ state and every party behaves honestly, the outcome broadcasted by the verifier is $b = 0$.
Statistical Behavior:
The outcome of the protocol depends on the trace distance between the shared state $|\\\psi\\\rangle$ and the ideal GHZ state.
The output $b$ is such that:
$$
b =
\\\begin{cases}
0 & \\\text{with probability } 1 – \\\frac{\\\tau^2}{2} \\\\\\\\\
1 & \\\text{with probability } \\\frac{\\\tau^2}{2}
\\\end{cases}
$$
where
$$
\\\tau = \\\min_U \\\text{TD}(|\\\phi_0^n\\\rangle\\\langle\\\phi_0^n|, U|\\\psi\\\rangle\\\langle\\\psi|U^\\\dagger)
$$
TD is the trace distance. $U$ is a quantum operation acting on $D$, the subspace of dishonest parties (i.e., a tensor product of a unitary on $D$ and the identity on the rest).
This means: the further the shared state is from the GHZ state, the less likely the verifier will accept it, even if dishonest parties apply local quantum operations to approximate the GHZ state.
Robustness:
The protocol still functions in the presence of photon losses.
Security:
Input: $\\\{y_i\\\}_{i=1}^{n}$, 1 qubit, $v$
Output: one Bit in $\\\{0,1\\\}$ and $\\\{\\\theta_i\\\}_{i=1}^{n}$
And for each $i = 1,…,n, i \\\neq v$
Input: 1 angle $\\\theta_i$, 1 qubit and $v$
Output: Bit $y_i$

Image caption: Abstract Cryptography figure for the MEV protocol for n=3 parties. Each blue box is a converter representing a protocol a party is following and red boxes are the resources used namely: state generation resource, quantum and authenticated classical channels.
The protocol has also been experimentally realised in [1]
This protocol was first introduced in Multipartite Entanglement Verification Resistant against Dishonest Parties [2], in which the authors present an XY version of the protocol where $\\\forall i,\\\theta_i \\\in \\\{0,1\\\}$. It means that each party applies an X or a Z gate on its qubit before measuring in the computational basis. It appeared that when a 50% qubit loss rate is tolerated, there exists a cheating strategy allowing a dishonest party to convince the verifier that the state shared was a GHZ state even when it is not.
This is why in “Experimental verification of multipartite entanglement in quantum networks”[2], the authors present the current version of the protocol which is loss tolerant. They also present an experimental realization of the verification protocol with $n=4$ parties and photonic GHZ states.
In “Anonymity for practical quantum networks” [3], Authors use this verification protocol as a subroutine allowing the parties to be certain to have a GHZ state shared when they perform an anonymous transmission protocol.
implements Entanglement verification
This protocol [1] implement the task of Multipartite entanglement verification in a multinode quantum network. The protocol uses classical communication and measurements of quantum states to verify whether the parties share a GHZ state. We present here a loss tolerant version of the protocol, which doesn’t assume that the source of the state nor the parties (except one) are trusted.
It has various application in a setting where at each timestep a source shares a state. Most of the time this state will be verified using this protocol and once in a while it will be used to perform some computation or communication protocol (e.g. Anonymous transmission)
This protocol is based on the work in W. McCutcheon, A. Pappa et al.. The goal is for a specific party called the Verifier to check whether the source has shared a GHZ-state among the n-nodes network. It goes as follow:
Network stage: quantum memory network.
Requirements:
Correctness:
If the source shares a GHZ state and every party behaves honestly, the outcome broadcasted by the verifier is $b = 0$.
Statistical Behavior:
The outcome of the protocol depends on the trace distance between the shared state $|psirangle$ and the ideal GHZ state.
The output $b$ is such that:
$$
b =
begin{cases}
0 & text{with probability } 1 – frac{tau^2}{2} \\\\\\\\\
1 & text{with probability } frac{tau^2}{2}
end{cases}
$$
where
$$
tau = min_U text{TD}(|phi_0^nranglelanglephi_0^n|, U|psiranglelanglepsi|U^dagger)
$$
TD is the trace distance. $U$ is a quantum operation acting on $D$, the subspace of dishonest parties (i.e., a tensor product of a unitary on $D$ and the identity on the rest).
This means: the further the shared state is from the GHZ state, the less likely the verifier will accept it, even if dishonest parties apply local quantum operations to approximate the GHZ state.
Robustness:
The protocol still functions in the presence of photon losses.
Security:
Input: ${y_i}_{i=1}^{n}$, 1 qubit, $v$
Output: one Bit in ${0,1}$ and ${theta_i}_{i=1}^{n}$
And for each $i = 1,…,n, i neq v$
Input: 1 angle $theta_i$, 1 qubit and $v$
Output: Bit $y_i$

Image caption: Abstract Cryptography figure for the MEV protocol for n=3 parties. Each blue box is a converter representing a protocol a party is following and red boxes are the resources used namely: state generation resource, quantum and authenticated classical channels.
The protocol has also been experimentally realised in [1]
This protocol was first introduced in Multipartite Entanglement Verification Resistant against Dishonest Parties [2], in which the authors present an XY version of the protocol where $forall i,theta_i in {0,1}$. It means that each party applies an X or a Z gate on its qubit before measuring in the computational basis. It appeared that when a 50% qubit loss rate is tolerated, there exists a cheating strategy allowing a dishonest party to convince the verifier that the state shared was a GHZ state even when it is not.
This is why in “Experimental verification of multipartite entanglement in quantum networks”[2], the authors present the current version of the protocol which is loss tolerant. They also present an experimental realization of the verification protocol with $n=4$ parties and photonic GHZ states.
In “Anonymity for practical quantum networks” [3], Authors use this verification protocol as a subroutine allowing the parties to be certain to have a GHZ state shared when they perform an anonymous transmission protocol.
implements (Symmetric) Private Information Retrieval
This protocol [1] implement the task of Multipartite entanglement verification in a multinode quantum network. The protocol uses classical communication and measurements of quantum states to verify whether the parties share a GHZ state. We present here a loss tolerant version of the protocol, which doesn’t assume that the source of the state nor the parties (except one) are trusted.
It has various application in a setting where at each timestep a source shares a state. Most of the time this state will be verified using this protocol and once in a while it will be used to perform some computation or communication protocol (e.g. Anonymous transmission)
This protocol is based on the work in W. McCutcheon, A. Pappa et al.. The goal is for a specific party called the Verifier to check whether the source has shared a GHZ-state among the n-nodes network. It goes as follow:
Network stage: quantum memory network.
Requirements:
Correctness:
If the source shares a GHZ state and every party behaves honestly, the outcome broadcasted by the verifier is $b = 0$.
Statistical Behavior:
The outcome of the protocol depends on the trace distance between the shared state $|\\\psi\\\rangle$ and the ideal GHZ state.
The output $b$ is such that:
$$
b =
\\\begin{cases}
0 & \\\text{with probability } 1 – \\\frac{\\\tau^2}{2} \\\\\\\\\
1 & \\\text{with probability } \\\frac{\\\tau^2}{2}
\\\end{cases}
$$
where
$$
\\\tau = \\\min_U \\\text{TD}(|\\\phi_0^n\\\rangle\\\langle\\\phi_0^n|, U|\\\psi\\\rangle\\\langle\\\psi|U^\\\dagger)
$$
TD is the trace distance. $U$ is a quantum operation acting on $D$, the subspace of dishonest parties (i.e., a tensor product of a unitary on $D$ and the identity on the rest).
This means: the further the shared state is from the GHZ state, the less likely the verifier will accept it, even if dishonest parties apply local quantum operations to approximate the GHZ state.
Robustness:
The protocol still functions in the presence of photon losses.
Security:
Input: $\\\{y_i\\\}_{i=1}^{n}$, 1 qubit, $v$
Output: one Bit in $\\\{0,1\\\}$ and $\\\{\\\theta_i\\\}_{i=1}^{n}$
And for each $i = 1,…,n, i \\\neq v$
Input: 1 angle $\\\theta_i$, 1 qubit and $v$
Output: Bit $y_i$

Image caption: Abstract Cryptography figure for the MEV protocol for n=3 parties. Each blue box is a converter representing a protocol a party is following and red boxes are the resources used namely: state generation resource, quantum and authenticated classical channels.
The protocol has also been experimentally realised in [1]
This protocol was first introduced in Multipartite Entanglement Verification Resistant against Dishonest Parties [2], in which the authors present an XY version of the protocol where $\\\forall i,\\\theta_i \\\in \\\{0,1\\\}$. It means that each party applies an X or a Z gate on its qubit before measuring in the computational basis. It appeared that when a 50% qubit loss rate is tolerated, there exists a cheating strategy allowing a dishonest party to convince the verifier that the state shared was a GHZ state even when it is not.
This is why in “Experimental verification of multipartite entanglement in quantum networks”[2], the authors present the current version of the protocol which is loss tolerant. They also present an experimental realization of the verification protocol with $n=4$ parties and photonic GHZ states.
In “Anonymity for practical quantum networks” [3], Authors use this verification protocol as a subroutine allowing the parties to be certain to have a GHZ state shared when they perform an anonymous transmission protocol.
implements Entanglement verification
This protocol [1] implement the task of Multipartite entanglement verification in a multinode quantum network. The protocol uses classical communication and measurements of quantum states to verify whether the parties share a GHZ state. We present here a loss tolerant version of the protocol, which doesn’t assume that the source of the state nor the parties (except one) are trusted.
It has various application in a setting where at each timestep a source shares a state. Most of the time this state will be verified using this protocol and once in a while it will be used to perform some computation or communication protocol (e.g. Anonymous transmission)
This protocol is based on the work in W. McCutcheon, A. Pappa et al.. The goal is for a specific party called the Verifier to check whether the source has shared a GHZ-state among the n-nodes network. It goes as follow:
Network stage: quantum memory network.
Requirements:
Correctness:
If the source shares a GHZ state and every party behaves honestly, the outcome broadcasted by the verifier is $b = 0$.
Statistical Behavior:
The outcome of the protocol depends on the trace distance between the shared state $|psirangle$ and the ideal GHZ state.
The output $b$ is such that:
$$
b =
begin{cases}
0 & text{with probability } 1 – frac{tau^2}{2} \\\\\\\\\
1 & text{with probability } frac{tau^2}{2}
end{cases}
$$
where
$$
tau = min_U text{TD}(|phi_0^nranglelanglephi_0^n|, U|psiranglelanglepsi|U^dagger)
$$
TD is the trace distance. $U$ is a quantum operation acting on $D$, the subspace of dishonest parties (i.e., a tensor product of a unitary on $D$ and the identity on the rest).
This means: the further the shared state is from the GHZ state, the less likely the verifier will accept it, even if dishonest parties apply local quantum operations to approximate the GHZ state.
Robustness:
The protocol still functions in the presence of photon losses.
Security:
Input: ${y_i}_{i=1}^{n}$, 1 qubit, $v$
Output: one Bit in ${0,1}$ and ${theta_i}_{i=1}^{n}$
And for each $i = 1,…,n, i neq v$
Input: 1 angle $theta_i$, 1 qubit and $v$
Output: Bit $y_i$

Image caption: Abstract Cryptography figure for the MEV protocol for n=3 parties. Each blue box is a converter representing a protocol a party is following and red boxes are the resources used namely: state generation resource, quantum and authenticated classical channels.
The protocol has also been experimentally realised in [1]
This protocol was first introduced in Multipartite Entanglement Verification Resistant against Dishonest Parties [2], in which the authors present an XY version of the protocol where $forall i,theta_i in {0,1}$. It means that each party applies an X or a Z gate on its qubit before measuring in the computational basis. It appeared that when a 50% qubit loss rate is tolerated, there exists a cheating strategy allowing a dishonest party to convince the verifier that the state shared was a GHZ state even when it is not.
This is why in “Experimental verification of multipartite entanglement in quantum networks”[2], the authors present the current version of the protocol which is loss tolerant. They also present an experimental realization of the verification protocol with $n=4$ parties and photonic GHZ states.
In “Anonymity for practical quantum networks” [3], Authors use this verification protocol as a subroutine allowing the parties to be certain to have a GHZ state shared when they perform an anonymous transmission protocol.
implements Entanglement verification
This protocol [1] implement the task of Multipartite entanglement verification in a multinode quantum network. The protocol uses classical communication and measurements of quantum states to verify whether the parties share a GHZ state. We present here a loss tolerant version of the protocol, which doesn’t assume that the source of the state nor the parties (except one) are trusted.
It has various application in a setting where at each timestep a source shares a state. Most of the time this state will be verified using this protocol and once in a while it will be used to perform some computation or communication protocol (e.g. Anonymous transmission)
This protocol is based on the work in W. McCutcheon, A. Pappa et al.. The goal is for a specific party called the Verifier to check whether the source has shared a GHZ-state among the n-nodes network. It goes as follow:
Network stage: quantum memory network.
Requirements:
Correctness:
If the source shares a GHZ state and every party behaves honestly, the outcome broadcasted by the verifier is $b = 0$.
Statistical Behavior:
The outcome of the protocol depends on the trace distance between the shared state $|psirangle$ and the ideal GHZ state.
The output $b$ is such that:
$$
b =
begin{cases}
0 & text{with probability } 1 – frac{tau^2}{2} \\\\\\\\\
1 & text{with probability } frac{tau^2}{2}
end{cases}
$$
where
$$
tau = min_U text{TD}(|phi_0^nranglelanglephi_0^n|, U|psiranglelanglepsi|U^dagger)
$$
TD is the trace distance. $U$ is a quantum operation acting on $D$, the subspace of dishonest parties (i.e., a tensor product of a unitary on $D$ and the identity on the rest).
This means: the further the shared state is from the GHZ state, the less likely the verifier will accept it, even if dishonest parties apply local quantum operations to approximate the GHZ state.
Robustness:
The protocol still functions in the presence of photon losses.
Security:
Input: ${y_i}_{i=1}^{n}$, 1 qubit, $v$
Output: one Bit in ${0,1}$ and ${theta_i}_{i=1}^{n}$
And for each $i = 1,…,n, i neq v$
Input: 1 angle $theta_i$, 1 qubit and $v$
Output: Bit $y_i$

Image caption: Abstract Cryptography figure for the MEV protocol for n=3 parties. Each blue box is a converter representing a protocol a party is following and red boxes are the resources used namely: state generation resource, quantum and authenticated classical channels.
The protocol has also been experimentally realised in [1]
This protocol was first introduced in Multipartite Entanglement Verification Resistant against Dishonest Parties [2], in which the authors present an XY version of the protocol where $forall i,theta_i in {0,1}$. It means that each party applies an X or a Z gate on its qubit before measuring in the computational basis. It appeared that when a 50% qubit loss rate is tolerated, there exists a cheating strategy allowing a dishonest party to convince the verifier that the state shared was a GHZ state even when it is not.
This is why in “Experimental verification of multipartite entanglement in quantum networks”[2], the authors present the current version of the protocol which is loss tolerant. They also present an experimental realization of the verification protocol with $n=4$ parties and photonic GHZ states.
In “Anonymity for practical quantum networks” [3], Authors use this verification protocol as a subroutine allowing the parties to be certain to have a GHZ state shared when they perform an anonymous transmission protocol.