Statistical structure of quantum theory

By Alexander S. Holevo. 2001

691 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/084cf0ddaf8446c317490f9911172ff41567f64a

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In Artificial Intelligence

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Citations in the corpus

Fundamentals of quantum information theory (2002, neutral): “[125,83].”
Feedback control of quantum state reduction (2004, background): “ly similar to classical probability: the spectrum of X plays the role of the probability space, the projectors Pi generate a σ-algebra andρ can be used to deﬁne an appropriate probability measure [8]–[11]. However, two quantum observables X and Y which do not commute do not have the same spectrum, h”
Concepts of quantum non-Markovianity: A hierarchy (2017, background): “the form of Qt i+1 t i ). Finally, to avoid possible confusion, it is worth mentioning that divisibility of the dynamical map should be distinguished from the related property of innite divisibility [110,111]: a CPTP map Mis innitely divisible if and only if for every positive integer nit has the fo”
Dividing Quantum Channels (2006, methodology): “Following the terminology used in classical probability theory one calls a channel T infinitely divisible [ 1 ,4 ]i f for alln ∈ N there is another channel Tn such that T = T n n .”
Quantum Stochastic Processes and Quantum non-Markovian Phenomena (2020, neutral): “[223, 224]).”
On quantum statistical inference (2003, background): “The interested reader is referred to Davies and Lewis (1970), Davies (1976), Kraus (1983), Ozawa (1985), Nielsen and Chuang (2000), Loubenets (2001) and Holevo (2001a).”
Geometry of Quantum States: Index (2007, background): “14 For an interesting discussion of hidden variables from this point of view, see Holevo [447].”
Introduction to decoherence theory (2006, background): “tum system to the information it reveals to the environment. Since the formulation is based on the notion of an indirect measurement it is necessary to ﬁrst collect some aspects of measurement theory [10, 11]. (a) Elements of general measurement theory Projective measurements This is the type of mea”
An Introduction to Quantum Filtering (2006, background): “One also finds in the literature generalizations of the projection postulate, called instruments, which implement different types of probes [25, 40].”