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Information complementarity: A new paradigm for decoding quantum incompatibility.

ABSTRACT: The existence of observables that are incompatible or not jointly measurable is a characteristic feature of quantum mechanics, which lies at the root of a number of nonclassical phenomena, such as uncertainty relations, wave--particle dual behavior, Bell-inequality violation, and contextuality. However, no intuitive criterion is available for determining the compatibility of even two (generalized) observables, despite the overarching importance of this problem and intensive efforts of many researchers. Here we introduce an information theoretic paradigm together with an intuitive geometric picture for decoding incompatible observables, starting from two simple ideas: Every observable can only provide limited information and information is monotonic under data processing. By virtue of quantum estimation theory, we introduce a family of universal criteria for detecting incompatible observables and a natural measure of incompatibility, which are applicable to arbitrary number of arbitrary observables. Based on this framework, we derive a family of universal measurement uncertainty relations, provide a simple information theoretic explanation of quantitative wave--particle duality, and offer new perspectives for understanding Bell nonlocality, contextuality, and quantum precision limit.

SUBMITTER: Zhu H

PROVIDER: S-EPMC4585721 | biostudies-literature | 2015 Sep

REPOSITORIES: biostudies-literature

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Information complementarity: A new paradigm for decoding quantum incompatibility.

Zhu Huangjun H

Scientific reports 20150922

The existence of observables that are incompatible or not jointly measurable is a characteristic feature of quantum mechanics, which lies at the root of a number of nonclassical phenomena, such as uncertainty relations, wave--particle dual behavior, Bell-inequality violation, and contextuality. However, no intuitive criterion is available for determining the compatibility of even two (generalized) observables, despite the overarching importance of this problem and intensive efforts of many resea ...[more]

PMID: 26392075

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Project description:Making predictions about the world and responding appropriately to unexpected events are essential functions of the healthy brain. In neurodegenerative disorders, such as frontotemporal dementia and Alzheimer's disease, impaired processing of 'surprise' may underpin a diverse array of symptoms, particularly abnormalities of social and emotional behaviour, but is challenging to characterize. Here, we addressed this issue using a novel paradigm: music. We studied 62 patients (24 female; aged 53-88) representing major syndromes of frontotemporal dementia (behavioural variant, semantic variant primary progressive aphasia, non-fluent-agrammatic variant primary progressive aphasia) and typical amnestic Alzheimer's disease, in relation to 33 healthy controls (18 female; aged 54-78). Participants heard famous melodies containing no deviants or one of three types of deviant note-acoustic (white-noise burst), syntactic (key-violating pitch change) or semantic (key-preserving pitch change). Using a regression model that took elementary perceptual, executive and musical competence into account, we assessed accuracy detecting melodic deviants and simultaneously recorded pupillary responses and related these to deviant surprise value (information-content) and carrier melody predictability (entropy), calculated using an unsupervised machine learning model of music. Neuroanatomical associations of deviant detection accuracy and coupling of detection to deviant surprise value were assessed using voxel-based morphometry of patients' brain MRI. Whereas Alzheimer's disease was associated with normal deviant detection accuracy, behavioural and semantic variant frontotemporal dementia syndromes were associated with strikingly similar profiles of impaired syntactic and semantic deviant detection accuracy and impaired behavioural and autonomic sensitivity to deviant information-content (all P < 0.05). On the other hand, non-fluent-agrammatic primary progressive aphasia was associated with generalized impairment of deviant discriminability (P < 0.05) due to excessive false-alarms, despite retained behavioural and autonomic sensitivity to deviant information-content and melody predictability. Across the patient cohort, grey matter correlates of acoustic deviant detection accuracy were identified in precuneus, mid and mesial temporal regions; correlates of syntactic deviant detection accuracy and information-content processing, in inferior frontal and anterior temporal cortices, putamen and nucleus accumbens; and a common correlate of musical salience coding in supplementary motor area (all P < 0.05, corrected for multiple comparisons in pre-specified regions of interest). Our findings suggest that major dementias have distinct profiles of sensory 'surprise' processing, as instantiated in music. Music may be a useful and informative paradigm for probing the predictive decoding of complex sensory environments in neurodegenerative proteinopathies, with implications for understanding and measuring the core pathophysiology of these diseases.

Dataset Information

Information complementarity: A new paradigm for decoding quantum incompatibility.

Publications

Information complementarity: A new paradigm for decoding quantum incompatibility.

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