Constructions of Quantum Random Access Codes
Quantum Random Access Codes (QRACs) are coding schemes that allow to encode n bits into m qubits, for n > m, so that any one of the bits can be extracted with success probability at least p > 1/2. QRAC is one of examples that demonstrate the advantage of quantum communication systems. It is also used in various quantum computation models, such as, quantum finite automata and state learning. Several approaches to derive the construction of QRACs with few qubits have been proposed, but they are mostly not optimal. Here, we investigate the construction of QRACs by heuristics based on semidefinite programming (SDP). The construction allows us to find QRACs on two qubits whose success probabilities are better than those previously known. We also demonstrate the QRACs on the real quantum devices of IBM Q Systems using the open source QISKit.