Quantum and Classical Correlations in Quantum Measurement

Xi, Zhengjun; Li, Yongming

doi:10.1007/s10701-012-9686-0

Cited by 3 publications

(3 citation statements)

References 13 publications

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“…27 For example, Ahluwalia (1994) links that series of de-coherent states in the process of quantum measurement and the fundamental Planck constant by the rejection of locality; an analogical viewpoint to measurement by entanglement (Cerf, Adami 1998) as well as the resolution of the measurement problem through decoherence of the quantum state (Dieks 1989) or investigating quantum and classical correlations in quantum measurement (Xi, Li 2013); analogically, by "many Hilbert spaces" (Namiki, Pascazio 1993). An anticipation can be discovered after de Broglie's interpretation of quantum mechanics in relation to measurement as by Andrade e Silva (1982).…”

Section: The Interpretation Of Wave Function By the Probability Distr...mentioning

confidence: 99%

Gentzen’s ‘Cut Rule’ and Quantum Measurement in Terms of Hilbert Arithmetic. Metaphor and Understanding Modeled Formally

Пенчев

2022

SSRN Journal

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Section: The Interpretation Of Wave Function By the Probability Distr...mentioning

confidence: 99%

Gentzen’s ‘Cut Rule’ and Quantum Measurement in Terms of Hilbert Arithmetic. Metaphor and Understanding Modeled Formally

Пенчев

2022

SSRN Journal

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“…Schroeck 1997). 27 For example, Ahluwalia (1994) links that series of de-coherent states in the process of quantum measurement and the fundamental Planck constant by the rejection of locality; an analogical viewpoint to measurement by entanglement (Cerf, Adami 1998) as well as the resolution of the measurement problem through decoherence of the quantum state (Dieks 1989) or investigating quantum and classical correlations in quantum measurement (Xi, Li 2013); analogically, by "many Hilbert spaces" (Namiki, Pascazio 1993). An anticipation can be discovered after de Broglie's interpretation of quantum mechanics in relation to measurement as by Andrade e Silva (1982).…”

Section: The Interpretation Of Wave Function By the Probability Distr...mentioning

confidence: 99%

Gentzen’s “Cut Rule” and Quantum Measurement in Terms of Hilbert Arithmetic. Metaphor and Understanding Modeled Formally

Пенчев¹

2022

Preprint

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Hilbert arithmetic in a wide sense, including Hilbert arithmetic in a narrow sense consisting by two dual and anti-isometric Peano arithmetics, on the one hand, and the qubit Hilbert space (originating for the standard separable complex Hilbert space of quantum mechanics), on the other hand, allows for an arithmetic version of Gentzen’s cut elimination and quantum measurement to be described uniformy as two processes occurring accordingly in those two branches. A philosophical reflection also justifying that unity by quantum neo-Pythagoreanism links it to the opposition of propositional logic, to which Gentzen’s cut rule refers immediately, on the one hand, and the linguistic and mathematical theory of metaphor therefore sharing the same structure borrowed from Hilbert arithmetic in a wide sense. An example by hermeneutical circle modeled as a dual pair of a syllogism (accomplishable also by a Turing machine) and a relevant metaphor (being a formal and logical mistake and thus fundamentally inaccessible to any Turing machine) visualizes human understanding corresponding also to Gentzen’s cut elimination and the Gödel dichotomy about the relation of arithmetic to set theory: either incompleteness or contradiction. The metaphor as the complementing “half” of any understanding of hermeneutical circle is what allows for that Gödel-like incompleteness to be overcome in human thought.

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“…Though, information gain as well as information loss in a measurement process, have been studied in the past [4,[16][17][18][19], they are far from being complete. One may think that the more entangled the apparatus and system are, the more will be the information gain.…”

Section: Introductionmentioning

confidence: 99%

Quantum coherence, coherent information and information gain in quantum measurement

Sharma

Sazim

Pati

2019

EPL

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A measurement is deemed successful, if one can maximize the information gain by the measurement apparatus. Here, we ask if quantum coherence of the system imposes a limitation on the information gain during quantum measurement. First, we argue that the information gain in a quantum measurement is nothing but the coherent information or the distinct quantum information that one can send from the system to apparatus. We prove that the maximum information gain from a pure state, using a mixed apparatus is upper bounded by the initial coherence of the system. Further, we illustrate the measurement scenario in the presence of environment. We argue that the information gain is upper bounded by the entropy exchange between the system and the apparatus. Also, to maximize the information gain, both the initial coherence of the apparatus, and the final entanglement between the system and apparatus should be maximum. Moreover, we find that for a fixed amount of coherence in the final apparatus state the more robust apparatus is, the more will be the information gain. *

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Quantum and Classical Correlations in Quantum Measurement

Cited by 3 publications

References 13 publications

Gentzen’s ‘Cut Rule’ and Quantum Measurement in Terms of Hilbert Arithmetic. Metaphor and Understanding Modeled Formally

Gentzen’s ‘Cut Rule’ and Quantum Measurement in Terms of Hilbert Arithmetic. Metaphor and Understanding Modeled Formally

Gentzen’s “Cut Rule” and Quantum Measurement in Terms of Hilbert Arithmetic. Metaphor and Understanding Modeled Formally

Quantum coherence, coherent information and information gain in quantum measurement

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