Description of States in Quantum Mechanics by Density Matrix and Operator Techniques

Fano, U.

doi:10.1103/revmodphys.29.74

Cited by 1,861 publications

(928 citation statements)

References 29 publications

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“…In the discussion below, we refer to these internal states as "spin states", although the same formalism applies to non-spin degrees of freedom, such as quantized rotational and vibrational states. We extend the Wigner function by combining it with the density operator formalism commonly used in the quantum description of magnetic resonance 8 . The definition of the Wigner function is extended by projecting the density operator onto the spin-state specific position state |x, η⟩, where η = α, β , .…”

Section: Extended Wigner Functionsmentioning

confidence: 99%

Visualisation of quantum evolution in the Stern–Gerlach and Rabi experiments

Utz

Levitt

Cooper

2015

Phys. Chem. Chem. Phys.

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Physical Chemistry Chemical Physics (PCCP) is a high quality journal with a large international readership from many communitiesOnly very important, insightful and high-quality work should be recommended for publication in PCCP.To be accepted in PCCP -a manuscript must report: Very high quality, reproducible new work  Important new physical insights of significant general interest  A novel, stand-alone contribution Routine or incremental work should not be recommended for publication. Purely synthetic work is not suitable for PCCPIf you rate the article as 'routine' yet recommend acceptance, please give specific reasons in your report.Less than 50% of articles sent for peer review are recommended for publication in PCCP. The current PCCP Impact Factor is 4.20.PCCP is proud to be a leading journal. We thank you very much for your help in evaluating this manuscript. Your advice as a referee is greatly appreciated.With our best wishes, Anna Simpson (pccp@rsc.org) Prof Daniella Goldfarb Managing Editor, PCCP Chair, PCCP Editorial Board General Guidance (For further details, see the RSC's Refereeing Procedure and Policy)Referees have the responsibility to treat the manuscript as confidential. Please be aware of our Ethical Guidelines which contain full information on the responsibilities of referees and authors. When preparing your report, please:• Comment on the originality, importance, impact and scientific reliability of the work;• State clearly whether you would like to see the paper accepted or rejected and give detailed comments (with references) that will both help the Editor to make a decision on the paper and the authors to improve it; Please inform the Editor if:• There is a conflict of interest;• There is a significant part of the work which you cannot referee with confidence;• If the work, or a significant part of the work, has previously been published, including online publication, or if the work represents part of an unduly fragmented investigation. When submitting your report, please:• Provide your report rapidly and within the specified deadline, or inform the Editor immediately if you cannot do so. We welcome suggestions of alternative referees. The Stern-Gerlach experiment is a seminal experiment in quantum physics, involving the interaction between a particle with spin and an applied magnetic field gradient. A recent article [Wennerström et al., Phys. Chem. Chem. Phys., 2012, 14, 1677-1684 claimed that a full understanding of the Stern-Gerlach experiment can only be attained if transverse spin relaxation is taken into account, generated by fluctuating magnetic fields originating in the magnetic materials which generate the field gradient. This interpretation is contrary to the standard quantum description of the Stern-Gerlach experiment, which requires no dissipative effects. We present simulations of conventional quantum dynamics in the Stern-Gerlach experiment, using extended Wigner functions to describe the propagation of the quantum state in space and time. No relaxation effects are require...

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Section: Extended Wigner Functionsmentioning

confidence: 99%

Visualisation of quantum evolution in the Stern–Gerlach and Rabi experiments

Utz

Levitt

Cooper

2015

Phys. Chem. Chem. Phys.

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“…First, I( p) and I tot are not unfamiliar expressions. The quantity i (p i − 1/n) 2 is one of the class of measures of the concentration of a probability distribution given by Uffink (1990), and Fano (1957), for example, remarks that Tr(ρ 2 ) can serve as a good measure of information; furthermore, the relation expressed in eqn. (2.5) has previously been employed by Larsen (1990) in discussing exact uncertainty relations.…”

Section: Brukner and Zeilinger's 'Total Information Content'mentioning

confidence: 99%

Quantum Information Theory and the Foundations of Quantum Mechanics

Timpson¹

2013

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of Thesis Submitted for the Degree of Doctor of PhilosophyThis thesis is a contribution to the debate on the implications of quantum information theory for the foundational problems of quantum mechanics. In Part I an attempt is made to shed some light on the nature of information and quantum information theory. It is emphasized that the everyday notion of information is to be firmly distinguished from the technical notions arising in information theory;however it is maintained that in both settings 'information' functions as an abstract noun, hence does not refer to a particular or substance. The popular claim 'Information is Physical' is assessed and it is argued that this proposition faces a destructive dilemma. Accordingly, the slogan may not be understood as an ontological claim, but at best, as a methodological one. A novel argument is provided against Dretske's (1981) attempt to base a semantic notion of information on ideas from information theory.The function of various measures of information content for quantum systems is explored and the applicability of the Shannon information in the quantum context maintained against the challenge of Brukner and Zeilinger (2001). The phenomenon of quantum teleportation is then explored as a case study serving to emphasize the value of recognising the logical status of 'information' as an abstract noun: it is argued that the conceptual puzzles often associated with this phenomenon result from the familiar error of hypostatizing an abstract noun.The approach of Deutsch and Hayden (2000) to the questions of locality and information flow in entangled quantum systems is assessed. It is suggested that the approach suffers from an equivocation between a conservative and an ontological reading; and the differing implications of each is examined. Some results are presented on the characterization of entanglement in the Deutsch-Hayden formalism.Part I closes with a discussion of some philosophical aspects of quantum computation.In particular, it is argued against Deutsch that the Church-Turing hypothesis is not underwritten by a physical principle, the Turing Principle. Some general morals are drawn concerning the nature of quantum information theory.In Part II, attention turns to the question of the implications of quantum information theory for our understanding of the meaning of the quantum formalism. Following some preliminary remarks, two particular information-theoretic approaches to the foundations of quantum mechanics are assessed in detail. It is argued that Zeilinger's (1999) Foundational Principle is unsuccessful as a foundational principle for quantum mechanics. The information-theoretic characterization theorem of Clifton, is assessed more favourably, but the generality of the approach is questioned and it is argued that the implications of the theorem for the traditional foundational problems in quantum mechanics remains obscure.

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“…Если задан один лишь оператор плотности ρ S в от-сутствие дополнительной физической информации (что достаточно для вычисле-ния всех необходимых вероятностей), то невозможно вычленить привилегированное разложение оператора ρ S , коэффициенты которого можно интерпретировать как эпистемические вероятности. В связи с этим некоторые авторы считают, что интер-претация смесей в терминах незнания несостоятельна (см., например, [6]- [9]). Дру-гие авторы, наоборот, считают, что концептуальные неоднозначности, возникающие из неоднозначной разложимости квантовых смесей, появляются за счет ограничен-ных возможностей технического языка описания КМ, на котором невозможно вы-разить некоторые физически значимые особенности рассмотрения (см., например, [10], [11]).…”

Section: Introductionunclassified

Представление И Интерпретация Квантовых Смесей В Модели Развитого Семантического Реализма

Гарола¹,

Garola²,

Соццо³

et al. 2011

ТМФ

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ПРЕДСТАВЛЕНИЕ И ИНТЕРПРЕТАЦИЯ КВАНТОВЫХ СМЕСЕЙ В МОДЕЛИ РАЗВИТОГО СЕМАНТИЧЕСКОГО РЕАЛИЗМАИнтерпретация смесей в квантовой механике в соответствии с этой теори-ей сталкивается с проблемами ввиду необъективности их физических свойств. В этой связи была разработана модель развитого семантического реализма, в которой происходит восстановление объективности в силу того, что квантовые вероятности интерпретируются при детектировании как условные, что позво-ляет ввести математический формализм квантовой механики в более общее неконтекстуальное (а потому локальное) рассмотрение. В этой модели каж-дая обобщенная наблюдаемая представляется в виде семейства положительных операторно-значных мер, параметризованных чистыми состояниями рассмат-риваемой физической системы Ω. В настоящей работе предложено новое дока-зательство утверждения о том, что каждая собственная смесь задается семей-ством операторов плотности, параметризованных макроскопическими характе-ристиками системы Ω. Показано, что некоторые предсказания, вытекающие из этого представления, отличаются от предсказаний квантовой механики, и они оказываются свободными от проблем, возникающих в стандартном представ-лении квантовой механики для собственных смесей. Напоминается, что преоб-разования состояний, вызванные идеальными неразрушающими измерениями, можно получить с помощью нетривиального обобщения постулата Людерса.Ключевые слова: квантовая механика, квантовые смеси, квантовая вероятность, по-стулат Людерса.

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Description of States in Quantum Mechanics by Density Matrix and Operator Techniques

Cited by 1,861 publications

References 29 publications

Visualisation of quantum evolution in the Stern–Gerlach and Rabi experiments

Visualisation of quantum evolution in the Stern–Gerlach and Rabi experiments

Quantum Information Theory and the Foundations of Quantum Mechanics

Представление И Интерпретация Квантовых Смесей В Модели Развитого Семантического Реализма

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