Symmetric Informationally Complete Measurements Identify the Irreducible Difference between Classical and Quantum Systems

• URL: http://arxiv.org/abs/1805.08721v4
• Date: Sat, 16 Dec 2023 15:43:00 GMT
• Title: Symmetric Informationally Complete Measurements Identify the Irreducible Difference between Classical and Quantum Systems
• Authors: John B. DeBrota, Christopher A. Fuchs, Blake C. Stacey
• Abstract summary: 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We describe a general procedure for associating a minimal informationally-complete quantum measurement (or MIC) and a set of linearly independent post-measurement quantum states with a purely probabilistic representation of the Born Rule. Such representations are motivated by QBism, where the Born Rule is understood as a consistency condition between probabilities assigned to the outcomes of one experiment in terms of the probabilities assigned to the outcomes of other experiments. In this setting, the difference between quantum and classical physics is the way their physical assumptions augment bare probability theory: Classical physics corresponds to a trivial augmentation -- one just applies the Law of Total Probability (LTP) between the scenarios -- while quantum theory makes use of the Born Rule expressed in one or another of the forms of our general procedure. To mark the irreducible difference between quantum and classical, one should seek the representations that minimize the disparity between the expressions. 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 -- the first to do with unitarily invariant distance measures between the rules, and the second to do with available volume in a reference probability simplex (roughly speaking a new kind of uncertainty principle). Both of these arise from a significant majorization result. This work complements recent studies in quantum computation where the deviation of the Born Rule from the LTP is measured in terms of negativity of Wigner functions.

Related papers

• What is "quantum" about quantum gravity? [0.0]
  We argue that if both the equivalence principle and quantum mechanics continue to survive experimental tests, that this favors epistemic'' interpretations of quantum mechanics.
  arXiv  Detail & Related papers  (2024-05-13T21:19:50Z)
• Quantification of Entanglement and Coherence with Purity Detection [16.01598003770752]
  Entanglement and coherence are fundamental properties of quantum systems, promising to power near future quantum technologies. Here, we demonstrate quantitative bounds to operationally useful entanglement and coherence. Our research offers an efficient means of verifying large-scale quantum information processing.
  arXiv  Detail & Related papers  (2023-08-14T11:03:40Z)
• Measurement and Probability in Relativistic Quantum Mechanics [0.0]
  This paper provides a relativistic model of measurement, in which the state of the universe is decomposed into decoherent histories of measurements recorded within it. The wave functions that we actually use for such experiments are local reductions of very coarse-grained superpositions of universal eigenstates.
  arXiv  Detail & Related papers  (2022-09-26T04:21:52Z)
• Generalized Gleason theorem and finite amount of information for the context [0.0]
  Quantum processes cannot be reduced to classical processes without specifying the context in the description of a measurement procedure. We consider a class of hidden variable theories by assuming that the amount of information about the measurement context is finite.
  arXiv  Detail & Related papers  (2022-06-23T16:55:50Z)
• Experimental Test of Contextuality based on State Discrimination with a Single Qubit [16.530085733940528]
  We extend the scope of experimental test of contextuality to a minimal quantum system of only two states (qubit) We observe a substantial violation of a no-go inequality derived by assuming non-contextuality. We also quantify the contextual advantage of state discrimination and the tolerance against quantum noises.
  arXiv  Detail & Related papers  (2022-06-22T04:03:04Z)
• Demonstrating Quantum Microscopic Reversibility Using Coherent States of Light [58.8645797643406]
  We propose and experimentally test a quantum generalization of the microscopic reversibility when a quantum system interacts with a heat bath. We verify that the quantum modification for the principle of microscopic reversibility is critical in the low-temperature limit.
  arXiv  Detail & Related papers  (2022-05-26T00:25:29Z)
• Entanglement and Quantum Correlation Measures from a Minimum Distance Principle [0.0]
  Entanglement, and quantum correlation, are precious resources for quantum technologies implementation based on quantum information science. We derive an explicit measure able to quantify the degree of quantum correlation for pure or mixed multipartite states. We prove that our entanglement measure is textitfaithful in the sense that it vanishes only on the set of separable states.
  arXiv  Detail & Related papers  (2022-05-14T22:18:48Z)
• Stochastic approximate state conversion for entanglement and general quantum resource theories [41.94295877935867]
  An important problem in any quantum resource theory is to determine how quantum states can be converted into each other. Very few results have been presented on the intermediate regime between probabilistic and approximate transformations. We show that these bounds imply an upper bound on the rates for various classes of states under probabilistic transformations. We also show that the deterministic version of the single copy bounds can be applied for drawing limitations on the manipulation of quantum channels.
  arXiv  Detail & Related papers  (2021-11-24T17:29:43Z)
• Quantum indistinguishability through exchangeable desirable gambles [69.62715388742298]
  Two particles are identical if all their intrinsic properties, such as spin and charge, are the same. Quantum mechanics is seen as a normative and algorithmic theory guiding an agent to assess her subjective beliefs represented as (coherent) sets of gambles. We show how sets of exchangeable observables (gambles) may be updated after a measurement and discuss the issue of defining entanglement for indistinguishable particle systems.
  arXiv  Detail & Related papers  (2021-05-10T13:11:59Z)
• Symmetric distinguishability as a quantum resource [21.071072991369824]
  We develop a resource theory of symmetric distinguishability, the fundamental objects of which are elementary quantum information sources. We study the resource theory for two different classes of free operations: $(i)$ $rmCPTP_A$, which consists of quantum channels acting only on $A$, and $(ii)$ conditional doubly (CDS) maps acting on $XA$.
  arXiv  Detail & Related papers  (2021-02-24T19:05:02Z)
• Entanglement detection in quantum many-body systems using entropic uncertainty relations [0.0]
  We study experimentally accessible lower bounds on entanglement measures based on entropic uncertainty relations. We derive an improved entanglement bound for bipartite systems, which requires measuring joint probability distributions in only two different measurement settings per subsystem.
  arXiv  Detail & Related papers  (2021-01-21T20:50:11Z)

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.