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Randomness is a valuable resource in science, cryptography, engineering, and information technology. Quantum-mechanical sources of randomness are attractive because of the indeterminism of individual quantum processes. Here we consider the production of random bits from polarization measurements on photons. We first present a pedagogical discussion of how the quantum randomness inherent in such measurements is connected to quantum coherence, and how it can be quantified in terms of the quantum state and an associated entropy value known as min-entropy. We then explore these concepts by performing a series of single-photon experiments that are suitable for the undergraduate laboratory. We prepare photons in different nonentangled and entangled states, and measure these states tomographically. We use the information about the quantum state to determine, in terms of the min-entropy, the minimum amount of randomness produced from a given photon state by different bit-generating measurements. This is helpful in assessing the presence of quantum randomness and in ensuring the quality and security of the random-bit source.
A crucial subroutine for various quantum computing and communication algorithms is to efficiently extract different classical properties of quantum states. In a notable recent theoretical work by Huang, Kueng, and Preskill~cite{huang2020predicting},
The advantages of quantum random number generators (QRNGs) over pseudo-random number generators (PRNGs) are normally attributed to the nature of quantum measurements. This is often seen as implying the superiority of the sequences of bits themselves
In a measurement-device-independent or quantum-refereed protocol, a referee can verify whether two parties share entanglement or Einstein-Podolsky-Rosen (EPR) steering without the need to trust either of the parties or their devices. The need for tru
Nonlocality is the most characteristic feature of quantum mechanics. John Bell, in his seminal 1964 work, proved that local-realism imposes a bound on the correlations among the measurement statistics of distant observers. Surpassing this bound rules
We study the optimization of any quantum process by minimizing the randomness in the measurement result at the output of that quantum process. We conceptualize and propose a measure of such randomness and inquire whether an optimization of the quantu