Contextual advantages and certification for maximum confidence discrimination

• URL: http://arxiv.org/abs/2112.09626v1
• Date: Fri, 17 Dec 2021 16:58:16 GMT
• Title: Contextual advantages and certification for maximum confidence discrimination
• Authors: Kieran Flatt and Hanwool Lee and Carles Roch i Carceller and Jonatan Bohr Brask and Joonwoo Bae
• Abstract summary: We consider a maximum confidence measurement that unifies different strategies of quantum state discrimination. We first show that maximum confidence discrimination, as well as unambiguous discrimination, contains contextual advantages. Our results establish how the advantages of quantum theory over a classical model may appear in a realistic scenario of a discrimination task.
• Score: 1.3124513975412255
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: One of the most fundamental results in quantum information theory is that no measurement can perfectly discriminate between non-orthogonal quantum states. In this work, we investigate quantum advantages for discrimination tasks over noncontextual theories by considering a maximum confidence measurement that unifies different strategies of quantum state discrimination, including minimum-error and unambiguous discrimination. We first show that maximum confidence discrimination, as well as unambiguous discrimination, contains contextual advantages. We then consider a semi-device independent scenario of certifying maximum confidence measurement. The scenario naturally contains undetected events, making it a natural setting to explore maximum confidence measurements. We show that the certified maximum confidence in quantum theory also contains contextual advantages. Our results establish how the advantages of quantum theory over a classical model may appear in a realistic scenario of a discrimination task.

Related papers

• Sequential Quantum Maximum Confidence Discrimination [0.8192907805418583]
  We investigate a sequential scenario of quantum state discrimination with maximum confidence. We show that sequential state discrimination with equally high confidence can be realized only when positive-operator-valued measure elements for a maximum-confidence measurement are linearly independent.
  arXiv  Detail & Related papers  (2024-11-19T15:03:34Z)
• Bounds for Revised Unambiguous Discrimination Tasks of Quantum Resources [0.9790236766474201]
  Quantum state discrimination is a fundamental task that is meaningful in quantum information theory. We show an upper bound of the success probability for a revised discrimination task in the unasymptotic and unambiguous scenarios. We also show the advantage of the quantum by considering a quantifier on a set of semidefinite positive operators.
  arXiv  Detail & Related papers  (2024-10-06T14:52:17Z)
• CLUE: Concept-Level Uncertainty Estimation for Large Language Models [49.92690111618016]
  We propose a novel framework for Concept-Level Uncertainty Estimation for Large Language Models (LLMs) We leverage LLMs to convert output sequences into concept-level representations, breaking down sequences into individual concepts and measuring the uncertainty of each concept separately. We conduct experiments to demonstrate that CLUE can provide more interpretable uncertainty estimation results compared with sentence-level uncertainty.
  arXiv  Detail & Related papers  (2024-09-04T18:27:12Z)
• ConU: Conformal Uncertainty in Large Language Models with Correctness Coverage Guarantees [68.33498595506941]
  We introduce a novel uncertainty measure based on self-consistency theory. We then develop a conformal uncertainty criterion by integrating the uncertainty condition aligned with correctness into the CP algorithm. Empirical evaluations indicate that our uncertainty measure outperforms prior state-of-the-art methods.
  arXiv  Detail & Related papers  (2024-06-29T17:33:07Z)
• Experimental demonstration of Contextual Advantage in minimum error and maximum confidence mirror-state discrimination [2.277447144331876]
  We show the first experimental demonstration of contextual advantage in both minimum error discrimination (MED) and maximum confidence discrimination (MCD) Our experiment agrees well with the result of theoretical simulation, and also shows the great potentiality of leveraging this method to explore a simpler version for the witness of contextuality.
  arXiv  Detail & Related papers  (2024-03-12T20:54:32Z)
• A contextuality witness inspired by optimal state discrimination [0.0]
  We present a witness for preparation contextuality inspired by optimal two-state discrimination. The main idea is based on finding the accessible probabilities averaged success and error in both classical and quantum models. We can then construct a noncontextuality inequality and associated witness which we find to be robust against depolarising noise and loss in the form of inconclusive events.
  arXiv  Detail & Related papers  (2023-10-19T13:18:34Z)
• Discrimination and certification of unknown quantum measurements [45.84205238554709]
  We study the discrimination of von Neumann measurements in the scenario when we are given a reference measurement and some other measurement. We consider the cases when the reference measurement is given without the classical description and when its classical description is known.
  arXiv  Detail & Related papers  (2023-01-12T11:38:24Z)
• Theory of Quantum Generative Learning Models with Maximum Mean Discrepancy [67.02951777522547]
  We study learnability of quantum circuit Born machines (QCBMs) and quantum generative adversarial networks (QGANs) We first analyze the generalization ability of QCBMs and identify their superiorities when the quantum devices can directly access the target distribution. Next, we prove how the generalization error bound of QGANs depends on the employed Ansatz, the number of qudits, and input states.
  arXiv  Detail & Related papers  (2022-05-10T08:05:59Z)
• Quantum vs. noncontextual semi-device-independent randomness certification [1.3124513975412255]
  We study randomness certification based on state discrimination and take noncontextuality as the notion of classicality. For quantum eavesdropppers, quantum devices can certify more randomness than noncontextual ones whenever none of the input states are unambiguously identified.
  arXiv  Detail & Related papers  (2021-12-17T18:46:19Z)
• Experimental multi-state quantum discrimination through a Quantum network [63.1241529629348]
  We have experimentally implemented two discrimination schemes in a minimum-error scenario based on a receiver featured by a network structure and a dynamical processing of information. The first protocol achieves binary optimal discrimination, while the second one provides a novel approach to multi-state quantum discrimination, relying on the dynamical features of the network-like receiver.
  arXiv  Detail & Related papers  (2021-07-21T09:26:48Z)
• Perfect Discrimination in Approximate Quantum Theory of General Probabilistic Theories [51.7367238070864]
  We define larger measurement classes that are smoothly connected with the class of POVMs via a parameter. We give a sufficient condition of perfect discrimination, which shows a significant improvement beyond the class of POVMs.
  arXiv  Detail & Related papers  (2020-04-10T08:45:20Z)

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.