The Quantum Theory of Measurement

Busch, Paul; Lahti, Pekka; Mittelstaedt, Peter

doi:10.1007/978-3-662-13844-1_3

Cited by 245 publications

(535 citation statements)

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“…In the framework of the quantum theory of measurement, this result is in fact a consequence of the calibration condition [3]. Moreover, adapting arguments initially developed in the context of the relative-state interpretation of Quantum Mechanics, Peter Mittelstaedt has shown that the quantum mechanical probability emerges as an approximately definite property of a large ensemble of identically prepared systems represented by the same state [13].…”

Section: 4mentioning

confidence: 97%

“…Owing to the stronger premise, this result is found to hold also for Hilbert spaces of dimension two. 2 In [3] the term objective is introduced to characterize a property that is either actual or absent in a general quantum state represented by a density operator. In the present paper we consider mostly pure states and in this context use both determinate or definite as synonym to objective, and likewise for the negations.…”

Section: 2mentioning

confidence: 99%

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Unsharp Quantum Reality

Busch

Jaeger

2010

Found Phys

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ABSTRACT. The positive operator (valued) measures (POMs) allow one to generalize the notion of observable beyond the traditional one based on projection valued measures (PVMs). Here, we argue that this generalized conception of observable enables a consistent notion of unsharp reality and with it a concept of joint properties. A property manifests itself as an element of unsharp reality by its power, or tendency, of becoming actual or actualizing a specific measurement outcome, where this tendency of actualization is quantified by the associated quantum probability. The resulting single-case interpretation of probability as a degree of reality will be explained in detail and its role in addressing the tensions between quantum and classical accounts of the physical world will be elucidated. It will be shown that potentiality can be viewed as a causal agency that evolves in a well-defined way.

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Section: 4mentioning

confidence: 97%

Section: 2mentioning

confidence: 99%

Unsharp Quantum Reality

Busch

Jaeger

2010

Found Phys

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“…The outcome statistics of a quantum measurement are described by a positive-operatorvalued measure (POVM) [80] on a set X of measurement outcomes. When X is countable the POVM is completely characterized by a set of positive operators, {F (x)} x∈X , called the "POVM elements," which together satisfy the normalization constraint x∈X F (x) = I.…”

Section: Weighted 2-designs As Informationally Complete Povmsmentioning

confidence: 99%

Weighted complex projective 2-designs from bases: Optimal state determination by orthogonal measurements

Roy

Scott

2007

Journal of Mathematical Physics

121

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We introduce the problem of constructing weighted complex projective 2-designs from the union of a family of orthonormal bases. If the weight remains constant across elements of the same basis, then such designs can be interpreted as generalizations of complete sets of mutually unbiased bases, being equivalent whenever the design is composed of d + 1 bases in dimension d. We show that, for the purpose of quantum state determination, these designs specify an optimal collection of orthogonal measurements. Using highly nonlinear functions on abelian groups, we construct explicit examples from d + 2 orthonormal bases whenever d + 1 is a prime power, covering dimensions d = 6, 10, and 12, for example, where no complete sets of mutually unbiased bases have thus far been found.

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“…In the now-standard quantum theory of measurement (cf., e.g., [17], p. 28), contrary to Heisenberg, the process of measurement and its elements are typically treated via a two-component joint system form, as follows. A system S is initially prepared through a series of physical interactions, such as filtering, in some well-defined quantum state |η , after which it is measured through interaction with a measurement apparatus A.…”

Section: Measurement Without the "Cut"mentioning

confidence: 99%

“Wave-Packet Reduction” and the Quantum Character of the Actualization of Potentia

Jaeger

2017

Entropy

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Werner Heisenberg introduced the notion of quantum potentia in order to accommodate the indeterminism associated with quantum measurement. Potentia captures the capacity of the system to be found to possess a property upon a corresponding sharp measurement in which it is actualized. The specific potentiae of the individual system are represented formally by the complex amplitudes in the measurement bases of the eigenstate in which it is prepared. All predictions for future values of system properties can be made by an experimenter using the probabilities which are the squared moduli of these amplitudes that are the diagonal elements of the density matrix description of the pure ensemble to which the system, so prepared, belongs. Heisenberg considered the change of the ensemble attribution following quantum measurement to be analogous to the classical change in Gibbs' thermodynamics when measurement of the canonical ensemble enables a microcanonical ensemble description. This analogy, presented by Heisenberg as operating at the epistemic level, is analyzed here. It has led some to claim not only that the change of the state in measurement is classical mechanical, bringing its quantum character into question, but also that Heisenberg held this to be the case. Here, these claims are shown to be incorrect, because the analogy concerns the change of ensemble attribution by the experimenter upon learning the result of the measurement, not the actualization of the potentia responsible for the change of the individual system state which-in Heisenberg's interpretation of quantum mechanics-is objective in nature and independent of the experimenter's knowledge.

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The Quantum Theory of Measurement

Cited by 245 publications

References 0 publications

Unsharp Quantum Reality

Unsharp Quantum Reality

Weighted complex projective 2-designs from bases: Optimal state determination by orthogonal measurements

“Wave-Packet Reduction” and the Quantum Character of the Actualization of Potentia

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