13,151 research outputs found
Quantum Randomness Certified by the Uncertainty Principle
We present an efficient method to extract the amount of true randomness that
can be obtained by a Quantum Random Number Generator (QRNG). By repeating the
measurements of a quantum system and by swapping between two mutually unbiased
bases, a lower bound of the achievable true randomness can be evaluated. The
bound is obtained thanks to the uncertainty principle of complementary
measurements applied to min- and max- entropies. We tested our method with two
different QRNGs, using a train of qubits or ququart, demonstrating the
scalability toward practical applications.Comment: 10 page
Recommendations and illustrations for the evaluation of photonic random number generators
The never-ending quest to improve the security of digital information
combined with recent improvements in hardware technology has caused the field
of random number generation to undergo a fundamental shift from relying solely
on pseudo-random algorithms to employing optical entropy sources. Despite these
significant advances on the hardware side, commonly used statistical measures
and evaluation practices remain ill-suited to understand or quantify the
optical entropy that underlies physical random number generation. We review the
state of the art in the evaluation of optical random number generation and
recommend a new paradigm: quantifying entropy generation and understanding the
physical limits of the optical sources of randomness. In order to do this, we
advocate for the separation of the physical entropy source from deterministic
post-processing in the evaluation of random number generators and for the
explicit consideration of the impact of the measurement and digitization
process on the rate of entropy production. We present the Cohen-Procaccia
estimate of the entropy rate as one way to do this. In order
to provide an illustration of our recommendations, we apply the Cohen-Procaccia
estimate as well as the entropy estimates from the new NIST draft standards for
physical random number generators to evaluate and compare three common optical
entropy sources: single photon time-of-arrival detection, chaotic lasers, and
amplified spontaneous emission
On privacy amplification, lossy compression, and their duality to channel coding
We examine the task of privacy amplification from information-theoretic and
coding-theoretic points of view. In the former, we give a one-shot
characterization of the optimal rate of privacy amplification against classical
adversaries in terms of the optimal type-II error in asymmetric hypothesis
testing. This formulation can be easily computed to give finite-blocklength
bounds and turns out to be equivalent to smooth min-entropy bounds by Renner
and Wolf [Asiacrypt 2005] and Watanabe and Hayashi [ISIT 2013], as well as a
bound in terms of the divergence by Yang, Schaefer, and Poor
[arXiv:1706.03866 [cs.IT]]. In the latter, we show that protocols for privacy
amplification based on linear codes can be easily repurposed for channel
simulation. Combined with known relations between channel simulation and lossy
source coding, this implies that privacy amplification can be understood as a
basic primitive for both channel simulation and lossy compression. Applied to
symmetric channels or lossy compression settings, our construction leads to
proto- cols of optimal rate in the asymptotic i.i.d. limit. Finally, appealing
to the notion of channel duality recently detailed by us in [IEEE Trans. Info.
Theory 64, 577 (2018)], we show that linear error-correcting codes for
symmetric channels with quantum output can be transformed into linear lossy
source coding schemes for classical variables arising from the dual channel.
This explains a "curious duality" in these problems for the (self-dual) erasure
channel observed by Martinian and Yedidia [Allerton 2003; arXiv:cs/0408008] and
partly anticipates recent results on optimal lossy compression by polar and
low-density generator matrix codes.Comment: v3: updated to include equivalence of the converse bound with smooth
entropy formulations. v2: updated to include comparison with the one-shot
bounds of arXiv:1706.03866. v1: 11 pages, 4 figure
Monte Carlo Simulation of Laser Diodes Sub-Poissonian Light Generation
When laser diodes are driven by high-impedance electrical sources the
variance of the number of photo-detection events counted over large time
durations is less than the average number of events (sub-Poissonian light). The
paper presents a Monte Carlo simulation that keeps track of each level
occupancy (0 or 1) in the conduction and valence bands, and of the number of
light quanta in the optical cavity. When there is good electron-lattice thermal
contact the electron and hole temperatures remain equal to that of the lattice.
In that case, elementary laser-diode noise theory results are accurately
reproduced by the simulation. But when the thermal contact is poor (or, almost
equivalently, at high power levels) new effects occur (spectral-hole burning,
temperature fluctuations, statistical fluctuations of the optical gain) that
are difficult to handle theoretically. Our numerical simulation shows that the
frequency domain over which the photo-current spectral density is below the
shot-noise level becomes narrower as the optical power increases.Comment: 22 pages, 3 figures, 1 table, submitted to Optical and Quantum
Electronic
Does gravity have to be quantized? Lessons from non-relativistic toy models
It is often argued that gravity has to be a quantum theory simply because a
fundamentally semiclassical approach would necessarily be inconsistent. Here I
review recent Newtonian toy models of (stochastic) semiclassical gravity. They
provide one option to implement a force semiclassically without getting into
the known problems associated with mean-field. These models are not complete
theories and should not be considered too seriously, but their consistency
shows that semiclassical gravity is hard to dismiss on purely theoretical
grounds.Comment: 16 pages -- written for the proceedings of the DICE 2018 workshop in
Castiglioncello -- provides a more detailed account of the technical
arguments in arXiv:1802.0329
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