Parity-based, bias-free optical quantum random number generation with min-entropy estimation

Abstract

We describe the generation of sequences of random bits from the parity of photon counts produced by polarization measurements on a polarization-entangled state. The resulting sequences are bias free, pass the applicable tests in the NIST battery of statistical randomness tests, and are shown to be Borel normal, without the need for experimental calibration stages or postprocessing of the output. Because the photon counts are produced in the course of a measurement of the violation of the Clauser-Horne-Shimony-Holt inequality, we are able to concurrently verify the nonclassical nature of the photon statistics and estimate a lower bound on the min-entropy of the bit-generating source. The rate of bit production in our experiment is around 13 bits/s.

Self-consistent state and measurement tomography with fewer measurements

“…For example, by examining Eqs. ( 4) and (5) we see that if we simultaneously make the substitutions w → − w and p → − p, the probabilities are unchanged. As such, the two solutions ( w, p) and (− w, − p) are equivalent, but represent different gauges and we must choose one.…”

“…Quantum tomography is an important tool for characterizing quantum systems and is useful for a diverse range of quantum information processing applications. It is useful not only for characterizing quantum gates [1,2], but also for tasks such as detecting errors in quantum key distribution [3,4] and quantifying the randomness or privacy of quantum-random-number generators [5,6].…”

Searching for evidence of algorithmic randomness and incomputability in the output of quantum random number generators

“…For details on our experiment, we refer the reader to Ref. [40]. The random bits are generated in the course of a measurement of the Bell-CHSH inequality [41].…”

“…Nevertheless, one may take the observed violations as an indication of the nonclassical nature of the measured photon statistics used to generate the random output, which is thus suggestive of the presence of quantum randomness. The output from our QRNG is not postprocessed in any way, and this raw output has previously been shown to pass all applicable statistical randomness tests in the NIST suite and to be Borel normal [40].…”

“…For the ANU QRNG, nearuniformity of the output arises from postprocessing. For the Parity QRNG, it is due to the use of the parity variable to generate the bits, which tends to wash out any experimentally introduced bias caused by factors such as imperfect state preparation, beam splitter crosstalk, and imbalanced detectors [13,40].…”