Abstract
A random access code (RAC) is a strategy to encode a message into a shorter one in a way that any bit of the original can still be recovered with nontrivial probability. Encoding with quantum bits rather than classical ones can improve this probability, but has an important limitation: due to the disturbance caused by standard quantum measurements, qubits cannot be used more than once. However, as recently shown by Mohan, Tavakoli, and Brunner [New J. Phys. 21 083034, (2019)], weak measurements can alleviate this problem, allowing two sequential decoders to perform better than with the best classical RAC. We use single photons to experimentally show that these weak measurements are feasible and nonclassical success probabilities are achievable by two decoders. We prove this for different values of the measurement strength and use our experimental results to put tight bounds on them, certifying the accuracy of our setting. This proves the feasibility of using sequential quantum RACs for quantum information tasks such as the self-testing of untrusted devices.
Highlights
A random access code (RAC) is a communication protocol that requires a transmitter (Alice) to encode a n-bit long random sequence into a shorter m-bit message, and a receiver (Bob) to be able to decode any of the n bits with nontrivial probability p > 1/2
A random access code (RAC) is a strategy to encode a message into a shorter one in a way that any bit of the original can still be recovered with nontrivial probability
All the results that we report here are extracted from the same experimental data
Summary
A random access code (RAC) is a communication protocol that requires a transmitter (Alice) to encode a n-bit long random sequence into a shorter m-bit message, and a receiver (Bob) to be able to decode any of the n bits with nontrivial probability p > 1/2. These parameters are often grouped in expression n −→p m that describes the task. A quantum random access code (QRAC) is the very similar situation in which Alice sends m qubits rather than bits. Applications include communication complexity [10], network coding [11], locally decodable codes [12], dimension witnessing of quantum states [13], self-testing of quantum devices [14,15], semi-device-independent quantum randomness extraction (SDI-QRE) [16,17,18], and semi-device-independent key distribution (SDI-QKD) [19,20]
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