Quantum randomness beyond projective measurements

• URL: http://arxiv.org/abs/2605.18291v1
• Date: Mon, 18 May 2026 12:17:11 GMT
• Title: Quantum randomness beyond projective measurements
• Abstract summary: We prove that $2 log d$ bits of randomness, the maximal amount, can be generated device-dependently in any dimension in which there exists a SIC measurement.<n>We also present the skewed SIC family of measurements, and use them to partially solve an open problem.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The unpredictability of quantum physics gives rise to intrinsic randomness. In an adversarial scenario, any additional degrees of freedom must be attributed to an eavesdropper with correlations to the measurement set-up. The true randomness is then quantified by the probability that she correctly guesses the measurement outcomes, optimised over all possible strategies. Extremal measurements are appealing here, since they do not allow information to leak to such an eavesdropper. Beyond projective measurements, however, a simple question remains open: how much intrinsic randomness can be generated by a given extremal measurement? In a step towards solving it, we characterise the randomness generated by any unbiased extremal rank-one measurement acting on any state, solving the problem explicitly in dimension two. Four-outcome qubit measurements of this type are tomographic, so these results hold for fully source-device-dependent randomness too. The tetrahedral symmetric informationally complete (SIC) measurement, we find, has the least intrinsic randomness within this class. We also present the skewed SIC family of measurements, and use them to partially solve an open problem: we prove that $2 \log d$ bits of randomness, the maximal amount, can be generated device-dependently (or source-device-independently) in any dimension in which there exists a SIC measurement.

Related papers

• Distributionally Faithful Imputation via Positive Semi-Definite Kernel Density Estimation [55.47411235954028]
  We recast imputation under missing completely at random as density estimation from masked observations.<n>We obtain a convex empirical risk problem with closed form marginals, solvable by a Newton interior point method.<n>The resulting PSD Impute model yields both single and multiple imputations from the same fitted density.
  arXiv  Detail & Related papers  (2026-07-08T15:51:05Z)
• Unambiguous randomness from a quantum state [0.0]
  Intrinsic randomness is generated when a quantum state is measured in any basis in which it is not diagonal.<n>In adversarial scenario, we quantify this randomness by the probability that a correlated eavesdropper could correctly guess the measurement outcomes.<n>Inspired by analogous concepts in quantum state discrimination, we introduce the unambiguous randomness of a quantum state and measurement.
  arXiv  Detail & Related papers  (2026-01-22T21:57:54Z)
• Multidimensional Uncertainty Quantification via Optimal Transport [87.97146725546502]
  We take a multidimensional view on uncertainty quantification (UQ) by stacking complementary UQ measures into a vector.<n>VecUQ-OT shows high efficiency even when individual measures fail.
  arXiv  Detail & Related papers  (2025-09-26T14:09:03Z)
• Maximal intrinsic randomness of noisy quantum measurements [1.4913052010438639]
  Given a quantum measurement, how much randomness can be generated from it?<n>In this work, we consider the following question: Given a quantum measurement, how much randomness can be generated from it?
  arXiv  Detail & Related papers  (2025-06-27T15:05:15Z)
• SVTest: general purpose software for testing weakly random sources with exemplary application to seismic data analysis enabling quantum amplification [34.82692226532414]
  Quantum devices can amplify the privacy of a weak source of randomness.<n>One of the theoretical models of such weak sources are the so-called Santha-Vazirani (SV) sources.<n>We develop software to estimate the parameter characterizing the source's randomness.
  arXiv  Detail & Related papers  (2025-04-09T13:58:34Z)
• Is the Born rule a result of measurement noise? [0.0]
  The Born rule asserts the distribution of eigenstates observed in unbiased quantum measurements, but the reason it holds remains elusive. This manuscript discusses how the Born rule might be explained by Schrodinger equation dynamics.
  arXiv  Detail & Related papers  (2024-07-03T14:20:11Z)
• The role of shared randomness in quantum state certification with unentangled measurements [36.19846254657676]
  We study quantum state certification using unentangled quantum measurements. $Theta(d2/varepsilon2)$ copies are necessary and sufficient for state certification. We develop a unified lower bound framework for both fixed and randomized measurements.
  arXiv  Detail & Related papers  (2024-01-17T23:44:52Z)
• The signaling dimension in generalized probabilistic theories [48.99818550820575]
  The signaling dimension of a given physical system quantifies the minimum dimension of a classical system required to reproduce all input/output correlations of the given system. We show that it suffices to consider extremal measurements with rayextremal effects, and we bound the number of elements of any such measurement in terms of the linear dimension. For systems with a finite number of extremal effects, we recast the problem of characterizing the extremal measurements with ray-extremal effects.
  arXiv  Detail & Related papers  (2023-11-22T02:09:16Z)
• Quantum Conformal Prediction for Reliable Uncertainty Quantification in Quantum Machine Learning [47.991114317813555]
  Quantum models implement implicit probabilistic predictors that produce multiple random decisions for each input through measurement shots. This paper proposes to leverage such randomness to define prediction sets for both classification and regression that provably capture the uncertainty of the model.
  arXiv  Detail & Related papers  (2023-04-06T22:05:21Z)
• Testing randomness of series generated in Bell's experiment [62.997667081978825]
  We use a toy fiber optic based setup to generate binary series, and evaluate their level of randomness according to Ville principle. Series are tested with a battery of standard statistical indicators, Hurst, Kolmogorov complexity, minimum entropy, Takensarity dimension of embedding, and Augmented Dickey Fuller and Kwiatkowski Phillips Schmidt Shin to check station exponent. The level of randomness of series obtained by applying Toeplitz extractor to rejected series is found to be indistinguishable from the level of non-rejected raw ones.
  arXiv  Detail & Related papers  (2022-08-31T17:39:29Z)
• Intrinsic randomness under general quantum measurements [2.8101673772585736]
  When measuring a state with von Neumann measurements, the intrinsic randomness can be quantified by the quantum coherence of the state on the measurement basis. We propose an adversary scenario for general measurements with arbitrary input states, based on which, we characterize the intrinsic randomness. Our results show that intrinsic randomness can quantify coherence under general measurements, which generalizes the result in the standard resource theory of state coherence.
  arXiv  Detail & Related papers  (2022-03-16T13:53:20Z)
• Experimental Test of Sequential Weak Measurements for Certified Quantum Randomness Extraction [0.0]
  We study the feasibility of weak measurements to extract randomness from a single state. We show that the weak measurements are real, but can improve the performance of randomness generation only in close-to-ideal conditions.
  arXiv  Detail & Related papers  (2021-01-28T15:46:58Z)
• The Generalized Lasso with Nonlinear Observations and Generative Priors [63.541900026673055]
  We make the assumption of sub-Gaussian measurements, which is satisfied by a wide range of measurement models. We show that our result can be extended to the uniform recovery guarantee under the assumption of a so-called local embedding property.
  arXiv  Detail & Related papers  (2020-06-22T16:43:35Z)
• Generalized Sliced Distances for Probability Distributions [47.543990188697734]
  We introduce a broad family of probability metrics, coined as Generalized Sliced Probability Metrics (GSPMs) GSPMs are rooted in the generalized Radon transform and come with a unique geometric interpretation. We consider GSPM-based gradient flows for generative modeling applications and show that under mild assumptions, the gradient flow converges to the global optimum.
  arXiv  Detail & Related papers  (2020-02-28T04:18:00Z)
• Distributed, partially collapsed MCMC for Bayesian Nonparametrics [68.5279360794418]
  We exploit the fact that completely random measures, which commonly used models like the Dirichlet process and the beta-Bernoulli process can be expressed as, are decomposable into independent sub-measures. We use this decomposition to partition the latent measure into a finite measure containing only instantiated components, and an infinite measure containing all other components. The resulting hybrid algorithm can be applied to allow scalable inference without sacrificing convergence guarantees.
  arXiv  Detail & Related papers  (2020-01-15T23:10:13Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.