Incorporating Zero-Probability Constraints to Device-Independent Randomness Expansion

• URL: http://arxiv.org/abs/2401.08452v1
• Date: Tue, 16 Jan 2024 15:57:17 GMT
• Title: Incorporating Zero-Probability Constraints to Device-Independent Randomness Expansion
• Authors: Chun-Yu Chen, Kai-Siang Chen, Kai-Min Chung, Min-Hsiu Hsieh, Yeong-Cherng Liang, and Gelo Noel M. Tabia
• Abstract summary: We explore various forms of randomness that are certifiable in the so-called device-independent (DI) paradigm. In this work, we determine the certifiable randomness when zero-probability constraints are incorporated into the task of DI randomness expansion.
• Score: 11.765274200974774
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: One of the distinguishing features of quantum theory is that its measurement outcomes are usually unpredictable or, equivalently, random. Moreover, this randomness is certifiable with minimal assumptions in the so-called device-independent (DI) paradigm, where a device's behavior does not need to be presupposed but can be verified through the statistics it produces. In this work, we explore various forms of randomness that are certifiable in this setting, where two users can perform two binary-outcome measurements on their shared entangled state. In this case, even though the Clauser-Horne-Shimony-Holt (CHSH) Bell-inequality violation is a pre-requisite for the generation of DI certifiable randomness, the CHSH value alone does not generally give a tight bound on the certifiable randomness. Here, we determine the certifiable randomness when zero-probability constraints are incorporated into the task of DI randomness expansion for the standard local and global randomness and the so-called "blind" randomness. Asymptotically, we observe consistent improvements in the amount of DI certifiable randomness (of all kinds) as we increase the number zero constraints for a wide range of given CHSH Bell violations. However, if we further optimize over the allowed CHSH values, then benefits of these additional constraints over the standard CHSH-based protocol are only found in the case of global and blind randomness. In contrast, in the regimes of finite data, these zero constraints only give a slight improvement in the local randomness rate when compared with all existing protocols.

Related papers

• The Rate-Distortion-Perception Trade-off: The Role of Private Randomness [53.81648040452621]
  We show that private randomness is not useful if the compression rate is lower than the entropy of the source. We characterize the corresponding rate-distortion trade-off and show that private randomness is not useful if the compression rate is lower than the entropy of the source.
  arXiv  Detail & Related papers  (2024-04-01T13:36:01Z)
• Improvements on Device Independent and Semi-Device Independent Protocols of Randomness Expansion [0.0]
  Device Independent (DI) and Semi-Device Independent (semi-DI) protocols of randomness expansion are discussed. We introduce enhanced DI and semi-DI protocols that surpass existing ones in terms of output randomness rate, security, or in some instances, both. A notable contribution is the introduction of randomness expansion protocols that recycle input randomness, significantly enhancing finite round randomness rates for DI protocols based on the CHSH inequality violation.
  arXiv  Detail & Related papers  (2023-11-22T17:03:04Z)
• Certification of unbounded randomness without nonlocality [0.0]
  We provide a scheme to certify unbounded randomness in a semi-device-independent way based on the maximal violation of Leggett-Garg inequalities. The scheme is independent of the choice of the quantum state, and consequently even "quantum" noise could be utilized to self-test quantum measurements.
  arXiv  Detail & Related papers  (2023-07-03T20:11:08Z)
• Shortcomings of Top-Down Randomization-Based Sanity Checks for Evaluations of Deep Neural Network Explanations [67.40641255908443]
  We identify limitations of model-randomization-based sanity checks for the purpose of evaluating explanations. Top-down model randomization preserves scales of forward pass activations with high probability.
  arXiv  Detail & Related papers  (2022-11-22T18:52:38Z)
• 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)
• Tight analytic bound on the trade-off between device-independent randomness and nonlocality [1.7188280334580197]
  Two parties sharing entangled quantum systems can generate correlations that cannot be produced using only shared classical resources. These nonlocal correlations are a fundamental feature of quantum theory but also have practical applications. The amount of certifiable randomness that can be generated from some given non-local correlations is a key quantity of interest.
  arXiv  Detail & Related papers  (2022-04-30T01:40:15Z)
• Dense Uncertainty Estimation via an Ensemble-based Conditional Latent Variable Model [68.34559610536614]
  We argue that the aleatoric uncertainty is an inherent attribute of the data and can only be correctly estimated with an unbiased oracle model. We propose a new sampling and selection strategy at train time to approximate the oracle model for aleatoric uncertainty estimation. Our results show that our solution achieves both accurate deterministic results and reliable uncertainty estimation.
  arXiv  Detail & Related papers  (2021-11-22T08:54:10Z)
• Sampling-Based Robust Control of Autonomous Systems with Non-Gaussian Noise [59.47042225257565]
  We present a novel planning method that does not rely on any explicit representation of the noise distributions. First, we abstract the continuous system into a discrete-state model that captures noise by probabilistic transitions between states. We capture these bounds in the transition probability intervals of a so-called interval Markov decision process (iMDP)
  arXiv  Detail & Related papers  (2021-10-25T06:18:55Z)
• Improved device-independent randomness expansion rates using two sided randomness [3.4376560669160394]
  A device-independent randomness expansion protocol aims to take an initial random string and generate a longer one. We investigate the possible improvement that could be gained using the two-sided randomness. We also consider a modified protocol in which the input randomness is recycled.
  arXiv  Detail & Related papers  (2021-03-12T19:49:17Z)
• Certified Randomness From Steering Using Sequential Measurements [0.0]
  A single entangled two-qubit pure state can be used to produce arbitrary amounts of certified randomness. Motivated by these difficulties in the device-independent setting, we consider the scenario of one-sided device independence. We show how certain aspects of previous work can be adapted to this scenario and provide theoretical bounds on the amount of randomness which can be certified.
  arXiv  Detail & Related papers  (2020-08-03T08:18:29Z)
• Using Randomness to decide among Locality, Realism and Ergodicity [91.3755431537592]
  An experiment is proposed to find out, or at least to get an indication about, which one is false. The results of such experiment would be important not only to the foundations of Quantum Mechanics.
  arXiv  Detail & Related papers  (2020-01-06T19:26:32Z)

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.