Inaccessible information in probabilistic models of quantum systems, non-contextuality inequalities and noise thresholds for contextuality

• URL: http://arxiv.org/abs/2003.05984v1
• Date: Thu, 12 Mar 2020 19:23:14 GMT
• Title: Inaccessible information in probabilistic models of quantum systems, non-contextuality inequalities and noise thresholds for contextuality
• Authors: Iman Marvian
• Abstract summary: We quantify the inaccessible information of a model in terms of the maximum distinguishability of probability distributions. These bounds can be interpreted as a new class of robust preparation non-contextuality inequalities.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Classical probabilistic models of (noisy) quantum systems are not only relevant for understanding the non-classical features of quantum mechanics, but they are also useful for determining the possible advantage of using quantum resources for information processing tasks. A common feature of these models is the presence of inaccessible information, as captured by the concept of preparation contextuality: There are ensembles of quantum states described by the same density operator, and hence operationally indistinguishable, and yet in any probabilistic (ontological) model, they should be described by distinct probability distributions. In this work, we quantify the inaccessible information of a model in terms of the maximum distinguishability of probability distributions associated to any pair of ensembles with identical density operators, as quantified by the total variation distance of the distributions. We obtain a family of lower bounds on this maximum distinguishability in terms of experimentally measurable quantities. In the case of an ideal qubit this leads to a lower bound of, approximately, 0.07. These bounds can also be interpreted as a new class of robust preparation non-contextuality inequalities. Our non-contextuality inequalities are phrased in terms of generalizations of max-relative entropy and trace distance for general operational theories, which could be of independent interest. Under sufficiently strong noise any quantum system becomes preparation non-contextual, i.e., can be described by models with zero inaccessible information. Using our non-contextuality inequalities, we show that this can happen only if the noise channel has the average gate fidelity less than or equal to 1/D(1+1/2+...+1/D), where D is the dimension of the Hilbert space.

Related papers

• Compatibility of Quantum Measurements and the Emergence of Classical Objectivity [0.0]
  We consider the KDQ distributions describing arbitrary collections of measurements on disjoint components of some generic multipartite system. We show that the system dynamics ensures that these distributions are classical if and only if the Hamiltonian supports Quantum Darwinism.
  arXiv  Detail & Related papers  (2024-11-16T19:01:30Z)
• The probabilistic world II : Quantum mechanics from classical statistics [0.0]
  A simple neuromorphic computer based on neurons in an active or quiet state within a probabilistic environment can learn the unitary transformations of an entangled two-qubit system. Our explicit constructions constitute a proof that no-go theorems for the embedding of quantum mechanics in classical statistics are circumvented.
  arXiv  Detail & Related papers  (2024-08-09T14:02:55Z)
• Form of Contextuality Predicting Probabilistic Equivalence between Two Sets of Three Mutually Noncommuting Observables [0.0]
  We introduce a contextual quantum system comprising mutually complementary observables organized into two or more collections of pseudocontexts with the same probability sums of outcomes. These pseudocontexts constitute non-orthogonal bases within the Hilbert space, featuring a state-independent sum of probabilities. The measurement contextuality in this setup arises from the quantum realizations of the hypergraph, which adhere to a specific bound on the linear combination of probabilities.
  arXiv  Detail & Related papers  (2023-09-22T08:51:34Z)
• An entropic uncertainty principle for mixed states [0.0]
  We provide a family of generalizations of the entropic uncertainty principle. Results can be used to certify entanglement between trusted parties, or to bound the entanglement of a system with an untrusted environment.
  arXiv  Detail & Related papers  (2023-03-20T18:31:53Z)
• 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)
• Improved Quantum Algorithms for Fidelity Estimation [77.34726150561087]
  We develop new and efficient quantum algorithms for fidelity estimation with provable performance guarantees. Our algorithms use advanced quantum linear algebra techniques, such as the quantum singular value transformation. We prove that fidelity estimation to any non-trivial constant additive accuracy is hard in general.
  arXiv  Detail & Related papers  (2022-03-30T02:02:16Z)
• Shannon theory beyond quantum: information content of a source [68.8204255655161]
  We extend the definition of information content to operational probabilistic theories. We prove relevant properties as the subadditivity, and the relation between purity and information content of a state.
  arXiv  Detail & Related papers  (2021-12-23T16:36:06Z)
• On the properties of the asymptotic incompatibility measure in multiparameter quantum estimation [62.997667081978825]
  Incompatibility (AI) is a measure which quantifies the difference between the Holevo and the SLD scalar bounds. We show that the maximum amount of AI is attainable only for quantum statistical models characterized by a purity larger than $mu_sf min = 1/(d-1)$.
  arXiv  Detail & Related papers  (2021-07-28T15:16:37Z)
• Non-equilibrium stationary states of quantum non-Hermitian lattice models [68.8204255655161]
  We show how generic non-Hermitian tight-binding lattice models can be realized in an unconditional, quantum-mechanically consistent manner. We focus on the quantum steady states of such models for both fermionic and bosonic systems.
  arXiv  Detail & Related papers  (2021-03-02T18:56:44Z)
• Gaussian Process States: A data-driven representation of quantum many-body physics [59.7232780552418]
  We present a novel, non-parametric form for compactly representing entangled many-body quantum states. The state is found to be highly compact, systematically improvable and efficient to sample. It is also proven to be a universal approximator' for quantum states, able to capture any entangled many-body state with increasing data set size.
  arXiv  Detail & Related papers  (2020-02-27T15:54:44Z)
• Symmetric Informationally Complete Measurements Identify the Irreducible Difference between Classical and Quantum Systems [0.0]
  We describe a general procedure for associating a minimal informationally-complete quantum measurement (or MIC) with a set of linearly independent post-measurement quantum states. We prove that the representation of the Born Rule obtained from a symmetric informationally-complete measurement (or SIC) minimizes this distinction in at least two senses.
  arXiv  Detail & Related papers  (2018-05-22T16:27:27Z)

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.