# Clifford Code for Quantum Authentication

The *Clifford Authentication Scheme* is a non-interactive protocol for quantum authentication and was introduced in the paper Interactive Proofs For Quantum Computations by Aharanov et al.. It applies a random Clifford operator to the quantum message and an auxiliary register and then measures the auxiliary register to decide whether or not a eavesdropper has tampered the original quantum message.

**Tags:** Two Party Protocol, Quantum Functionality, Specific Task, Building Block

## Outline[edit]

The *Clifford code* encodes a quantum message by appending an auxiliary register with each qubit in state and then applying a random Clifford operator on all qubits. The authenticator then measures only the auxiliary register. If all qubits in the auxiliary register are still in state , the authenticator accepts and decodes the quantum message. Otherwise, the original quantum message was tampered by a third party and the authenticator aborts the process.

## Notations[edit]

- : suppliant (sender)
- : authenticator (prover)
- : -qubit state to be transmitted
- : security parameter defining the number of qubits in the auxiliary register
- : set of Clifford operations on qubits labelled by a classical key

## Properties[edit]

- The Clifford code makes use of qubits
- The Clifford code is quantum authentication scheme with security
- The qubit registers used can be divided into a message register with qubits, an auxiliary register with qubits, and a flag register with qubit.

## Protocol Description[edit]

**Input:** , ,

**Output:** Quantum state if the protocol accepts; fixed quantum state if the protocol aborts

**Encoding:**

- appends an auxiliary register of qubits in state to the quantum message , which results in .
- then applies for a uniformly random on the total state.
- sends the result to .

**Mathematical Encoding Description:**

Mathematically, the encoding process can be described by**Decoding:**

- applies the inverse Clifford to the received state, which is denoted by .
- measures the auxiliary register in the computational basis.

a. If all auxiliary qubits are 0, the state is accepted and an additional flag qubit in state is appended.

b. Otherwise, the remaining system is traced out and replaced with a fixed -qubit state and an additional flag qubit in state is appended.

**Mathematical Decoding Description:**

Mathematically, the decoding process is described byIn the above, is the trace over the auxiliary register only, and is the trace over the quantum message system and the auxiliary system. Furthermore, and refer to the measurement projectors that determine whether the protocol accepts or aborts the received quantum message. It isand

## References[edit]

*Contributed by Isabel Nha Minh Le and Shraddha Singh*

*This page was created within the QOSF Mentorship Program Cohort 4*