by Rudy Raymond, IBM Research
Quantum Random Access Coding (QRAC) is an encoding protocol to encode n bits of information into m qubits so that any 1 out of n bits can be extracted with non-trivial success probabilities when n > m. For convenience, a (n, m, p)-QRAC denotes such encoding scheme where p > 1/2 denotes the success probability (which can be defined as the worst-case success probability, or the average-case success probability).
There are tutorials of QRACs on qiskit-tutorial as here and here. QRACs are related to PR boxes and are known useful to generate random numbers with quantum devices.
This repository is a companion to Constructions of Quantum Random Access Codes presented at AQIS 2018 in Nagoya, Japan.
This repository is aimed to gather information of QRACs, and will be updated accordingly.
You need to install qiskit and qiskit-tutorial repositories to run the codes.
Please follow the installation steps here.
Below are two-qubit QRACs that are known to be better than those found in Improved Classical and Quantum Random Access Codes. The results are (n,2,p)-QRACs with n and p summarized as follows:
| n | 3 | 5 | 7 | 8 | 9 |
|---|---|---|---|---|---|
| p here | 0.908 | 0.811 | 0.702 | 0.690 | 0.671 |
| p prev | 0.853 | 0.788 | 0.684 | 0.652 | 0.621 |
Here is the list the two-qubit QRACs:
- The (3,2)-QRAC: encoding 3 bits into 2 qubits. The classical RAC has success probability 2/3.
- The (5,2)-QRAC: encoding 5 bits into 2 qubits. No classical RACs can perform this with 2 bits.
- The (7,2)-QRAC: encoding 7 bits into 2 qubits. No classical RACs can perform this with 2 bits.
- The (8,2)-QRAC: encoding 8 bits into 2 qubits. No classical RACs can perform this with 2 bits.
- The (9,2)-QRAC: encoding 9 bits into 2 qubits. No classical RACs can perform this with 2 bits.
Special thanks to Keita Takeuchi of Univ. of Tokyo for preparing the states and measurements of the (5,2)-QRACs.