Randomness in quantum mechanics: philosophy, physics and technology

Bera, Manabendra Nath; Acín, Antonio; Kuś, Marek; Mitchell, Morgan W.; Lewenstein, Maciej

doi:10.1088/1361-6633/aa8731

Cited by 105 publications

(115 citation statements)

References 150 publications

(202 reference statements)

Supporting

Mentioning

115

Contrasting

Order By: Relevance

“…Increasingly Carmichael numbers become "rare". 5 In what follows we thus present four different tests based on the Chaitin-Schwartz Theorem and the Solovay-Strassen test. Since the proposed tests rely directly on the algorithmic randomness of a string, they can potentially give direct empirical evidence of incomputability, in stark contrast to most tests of randomness.…”

Section: Chaitin-schwartz-solovay-strassen Testsmentioning

confidence: 99%

Experimentally probing the algorithmic randomness and incomputability of quantum randomness

et al. 2019

View full text Add to dashboard Cite

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 generated by QRNGs, despite the absence of empirical tests supporting this. Nonetheless, one may expect sequences of bits generated by QRNGs to have properties that pseudo-random sequences do not; indeed, pseudorandom sequences are necessarily computable, a highly nontypical property of sequences.In this paper, we discuss the differences between QRNGs and PRNGs and the challenges involved in certifying the quality of QRNGs theoretically and testing their output experimentally. While QRNGs are often tested with standard suites of statistical tests, such tests are designed for PRNGs and only verify statistical properties of a QRNG, but are insensitive to many supposed advantages of QRNGs. We discuss the ability to test the incomputability and algorithmic complexity of QRNGs. While such properties cannot be directly verified with certainty, we show how one can construct indirect tests that may provide evidence for the incomputability of QRNGs. We use these tests to compare various PRNGs to a QRNG, based on superconducting transmon qutrits and certified by the Kochen-Specker Theorem, to see whether such evidence can be found in practice.While our tests fail to observe a strong advantage of the quantum random sequences due to algorithmic properties, the results are nonetheless informative: some of the test results are ambiguous and require further study, while others highlight difficulties that can guide the development of future tests of algorithmic randomness and incomputability.1 An example is the discovery in 2012 of a weakness in the encryption system used worldwide for online shopping, banking and email; the flaw was traced to the numbers a PRNG had produced [1]. As of 2018, Java still relies on a linear congruential generator, a low quality PRNG.arXiv:1806.08762v2 [quant-ph]

show abstract

Section: Chaitin-schwartz-solovay-strassen Testsmentioning

confidence: 99%

Experimentally probing the algorithmic randomness and incomputability of quantum randomness

et al. 2019

View full text Add to dashboard Cite

show abstract

“…However, entanglement is not a unique measure of quantum correlation because separable states can have nonclassical correlations. The concept of quantum coherence has recently seen a surge of popularity since it serves as a resource in quantum information tasks [1], similar to other well-studied quantum resource such as the entanglement [2], quantum correlations [3], and the randomness [4]. Baumgratz et al [5] introduced a rigorous framework for the quantification of coherence based on resource theory and identified easily computable measures of coherence.…”

Section: Introductionmentioning

confidence: 99%

Quantum coherence in a compass chain under an alternating magnetic field

You

Wang

et al. 2018

Phys. Rev. B

View full text Add to dashboard Cite

We investigate quantum phase transitions and quantum coherence in a quantum compass chain under an alternating transverse magnetic field. The model can be analytically solved by the Jordan-Wigner transformation and this solution shows that it is equivalent to a two-component one-dimensional (1D) Fermi gas on a lattice. We explore mutual effects of the staggered magnetic interaction and multi-site interactions on the energy spectra and analyze the ground state phase diagram. We use quantum coherence measures to identify the quantum phase transitions. Our results show that l1 norm of coherence fails to detect faithfully the quantum critical points separating a gapped phase from a gapless phase, which can be pinpointed exactly by relative entropy of coherence. Jensen-Shannon divergence is somewhat obscure at exception points. We also propose an experimental realization of such a 1D system using superconducting quantum circuits. arXiv:1806.03337v1 [cond-mat.str-el]

show abstract

“…The second is to use chaotic systems, whose long-time behaviour is essentially impossible to predict without perfect knowledge of the initial conditions. Quantum theory, as a fundamentally non-deterministic theory, provides an alternative route [1][2][3]. As a simple example, which way a photon takes after passing through a balanced beam splitter is a fundamentally probabilistic event, and thus serves as a basic quantum random number generator.…”

mentioning

confidence: 99%

Maximal Randomness Generation from Steering Inequality Violations Using Qudits

Skrzypczyk

Cavalcanti

2018

Phys. Rev. Lett.

View full text Add to dashboard Cite

We consider the generation of randomness based upon the observed violation of an Einstein-Podolsky-Rosen (EPR) steering inequality, known as one-sided device-independent randomness generation. We show that in the simplest scenario-involving only two parties and two measurements for the uncharacterised party with d outcomes-that there exist EPR steering inequalities whose maximal violation certifies maximal randomness generation, equal to log(d) bits. We further show that all pure partially entangled full-Schmidt-rank states in all dimensions can achieve maximal violation of these inequalities, and thus lead to maximal randomness generation in the one-sided device-independent setting. More generally, the amount of randomness that can be generated is given by a semidefinite program, which we use to study the behavior for nonmaximal violations of the inequalities.

show abstract

Randomness in quantum mechanics: philosophy, physics and technology

Cited by 105 publications

References 150 publications

Experimentally probing the algorithmic randomness and incomputability of quantum randomness

Experimentally probing the algorithmic randomness and incomputability of quantum randomness

Quantum coherence in a compass chain under an alternating magnetic field

Maximal Randomness Generation from Steering Inequality Violations Using Qudits

Contact Info

Product

Resources

About