Increased certification of semi-device independent random numbers using many inputs and more post-processing

Abstract

Quantum communication with systems of dimension larger than two provides advantages in information processing tasks. Examples include higher rates of key distribution and random number generation. The main disadvantage of using such multi-dimensional quantum systems is the increased complexity of the experimental setup. Here, we analyze a not-so-obvious problem: the relation between randomness certification and computational requirements of the post-processing of experimental data. In particular, we consider semi-device independent randomness certification from an experiment using a four dimensional quantum system to violate the classical bound of a random access code. Using state-of-the-art techniques, a smaller quantum violation requires more computational power to demonstrate randomness, which at some point becomes impossible with today's computers although the randomness is (probably) still there. We show that by dedicating more input settings of the experiment to randomness certification, then by more computational postprocessing of the experimental data which corresponds to a quantum violation, one may increase the amount of certified randomness. Furthermore, we introduce a method that significantly lowers the computational complexity of randomness certification. Our results show how more randomness can be generated without altering the hardware and indicate a path for future semi-device independent protocols to follow.

Focus on device independent quantum information

“…[40] studies the security of BB84 under the even weaker assumption that the dimension of only one of the systems is constrained to be a qubit. [20] shows that considering higher-dimensional systems (still in the SDI model, where a bound on the dimension of the devices is given a priori) can lead to improve rates, albeit at a higher computational cost. [7] consider the task of RNG in the 'measurement-device independent' MDI) setting, where the source, but not the detector, are trusted; their analysis allows them to handle high losses at the untrusted detector and leads to a more practical protocol which (in contrast to fully DI protocols) does not require the generation of entangled states.…”

Semi-Device-Independent Framework Based on Restricted Distrust in Prepare-and-Measure Experiments

“…The most thoroughly researched semi-DI setting is that in which only the Hilbert space dimension is known. This has led to protocols for quantum key distribution [1,2], random number generation [3,4], random access coding [5][6][7], numerous quantum certification protocols [8][9][10][11][12][13][14][15][16][17][18] and several experiments [18][19][20][21][22][23][24]. More recently, also alternative settings have been investigated, based on a bound on the overlap [25][26][27], energy [28][29][30][31] and information content [32,33] of the states.…”

Self-testing of binary Pauli measurements requiring neither entanglement nor any dimensional restriction

“…Apart from the above schemes of self-testing of measurements based on the use of quantum correlations in entangled states, some certification methods for self-testing have been proposed that do not require entanglement [37][38][39][40]. A pair of anticommuting Pauli observables have been self-tested in the prepare and measure scenario [41], employing the quantum advantage of 2 → 1 random access code (RAC) [42,43].…”