Quantum Random Access Codes using Single $d$-level Systems

TL;DR

Random access codes ask how Alice can communicate limited information while letting Bob recover any bit he requests. This paper studies classical and quantum codes using d-level communication, derives average classical performance, and constructs high-level QRAC families; it reports larger quantum advantages and a four-level experiment exceeding the classical bound.

• Problem

  In a random access code, Alice must encode her information in restricted communication so Bob can recover whichever bit he requests.

  Source: p. 1

• Method

  The paper derives average success probabilities for classical d-level RACs and constructs families of quantum d-level RACs.

  Source: p. 1

• Results

  For 3(d) →1 QRACs, the quantum-to-classical success-probability ratio reaches approximately 1.224, versus approximately 1.052 for 3(2) →1; experimentally, the average quantum success probability is 0.754±0.038 against the classical bound 0.625.

  Source: pp. 4–5

• Takeaways & Limitations

  The reported high-level QRACs have larger advantages over corresponding RACs than two-level QRACs, and the four-level experiment agrees well with quantum-mechanical predictions.

  Source: pp. 4, 6

  The optimality of the proposed 3(3) →1 QRAC remains an open problem.

  Source: p. 6