Measurement-Based Quantum Foundations

Rau, Jochen

doi:10.1007/s10701-010-9427-1

Cited by 11 publications

(21 citation statements)

References 48 publications

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“…This contention is motivated by the intuition expressed by Rovelli, that "the unease (in the interpretation of quantum theory) may derive from the use of a concept which is inappropriate to describe the world at the quantum level" ( [19] p. 1638). On the basis of this intuition, Rovelli rejects the assumption of observer-independent quantum states, an assumption also rejected by quantum Bayesians [36,37,39,40]. The present paper rejects an equally-deep assumption: The assumption of a "Galilean" observer, an observer that is simply "a quantum system interacting with the observed system" without further information-theoretic constraints.…”

Section: Introductionmentioning

confidence: 53%

“…Quantum theory does not, therefore, require more than these assumptions. The unmotivated and ad hoc nature of the formal postulates that have been employed to axiomatize quantum theory both traditionally [59] and more recently (e.g., [34,39]) can be seen as a side-effect of the assumption of Galilean observers and the compensatory, generally tacit assumption of "axiom(o)".…”

Section: Discussionmentioning

confidence: 99%

“…Responses in the first category treat decoherence as a fundamental physical process and derive an account of measurement from it; examples include traditional relative-state (i.e., many-worlds or many-minds) interpretations [11,[20][21][22][23][24], the consistent histories formulation [25][26][27] and quantum Darwinism [12,[28][29][30][31][32]. Those in the second treat measurement as a fundamental physical process; they are distinguished by whether they treat information and hence probabilities as objective [33][34][35] or subjective [19,[36][37][38][39][40].…”

Section: Introductionmentioning

confidence: 99%

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If Physics Is an Information Science, What Is an Observer?

Fields

2012

Information

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Abstract:Interpretations of quantum theory have traditionally assumed a "Galilean" observer, a bare "point of view" implemented physically by a quantum system. This paper investigates the consequences of replacing such an informationally-impoverished observer with an observer that satisfies the requirements of classical automata theory, i.e., an observer that encodes sufficient prior information to identify the system being observed and recognize its acceptable states. It shows that with reasonable assumptions about the physical dynamics of information channels, the observations recorded by such an observer will display the typical characteristics predicted by quantum theory, without requiring any specific assumptions about the observer's physical implementation.

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Section: Introductionmentioning

confidence: 53%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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If Physics Is an Information Science, What Is an Observer?

Fields

2012

Information

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“…Another set of axioms using tomographic locality was given by Marco Zaopo [45]. There has been much work recently by many people along less related lines (Fuchs [17], Goyal [19], Wilce [42], Rau [38,39], Fivel [13], . .…”

Section: A Personal History Of Reconstructionmentioning

confidence: 99%

Reconstructing Quantum Theory

Hardy

2015

Fundamental Theories of Physics

190

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I provide operational postulates for quantum theory. These involve certain operational notions. Systems come in different types, a, b, c, . . .. A maximal set of distinguishable states is any set containing the maximum number, Na, of states for which there exists some measurement, called a maximal measurement, which can identify which state from the set we have in a single shot. A maximal effect is associated with each result of a maximal measurement. An informational face is the full set of states that give rise only to some subset of outcomes of some maximal measurements (it corresponds to constraining the system to have some reduced information carrying capacity). States are represented by vectors whose Ka entries are probabilities. A set of states is said to be non-flat if it is a spanning subset of some informational face. A filter is a transformation that passes unchanged those states in a given informational face while blocking those states in the complement informational face (that would give rise only to outcomes in the complement outcome set of the maximal measurement). Classical probability theory and quantum theory are the only two theories consistent with the following set of postulates.P1 Logical sharpness. There is a one-to-one map between pure states and maximal effects such that we get unit probability.P2 Information locality. A maximal measurement is effected on a composite system if we perform maximal measurements on each of the components (or, equivalently, N ab = NaN b ).P3 Tomographic locality. The state of a composite system can be determined from the statistics collected by making measurements on the components (or, equivalently, K ab = KaK b ). P4′ Permutability. There exists a reversible transformation on any system effecting any given permutation of any given maximal set of distinguishable states for that system. P5 Sturdiness. Filters are non-flattening.To single out quantum theory we need only add any requirement that is inconsistent with classical probability theory and consistent with quantum theory.

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“…These theories share with quantum mechanics its non-classical features such as randomness of individual results, the impossibility of copying unknown states [21,22], violation of Bellʼs inequalities [2], uncertainty relations [18,19] or interference [20]. Recent progress in reconstructions of quantum formalism give a variety of choices for postulates on which quantum theory can be singled out from the class of generalized probabilistic theories [16,17,[23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Density cubes and higher-order interference theories

2014

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Can quantum theory be seen as a special case of a more general probabilistic theory, as classical theory is a special case of the quantum one? We study here the class of generalized probabilistic theories defined by the order of interference they exhibit as proposed by Sorkin. A simple operational argument shows that the theories require higher-order tensors as a representation of physical states. For the third-order interference we derive an explicit theory of 'density cubes' and show that quantum theory, i.e. theory of density matrices, is naturally embedded in it. We derive the genuine non-quantum class of states and nontrivial dynamics for the case of a three-level system and show how one can construct the states of higher dimensions. Additionally to genuine third-order interference, the density cubes are shown to violate the Leggett-Garg inequality beyond the quantum Tsirelson bound for temporal correlations.

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Measurement-Based Quantum Foundations

Cited by 11 publications

References 48 publications

If Physics Is an Information Science, What Is an Observer?

If Physics Is an Information Science, What Is an Observer?

Reconstructing Quantum Theory

Density cubes and higher-order interference theories

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