2011
DOI: 10.1017/cbo9781139031103
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The Mathematical Language of Quantum Theory

Abstract: For almost every student of physics, the first course on quantum theory raises a lot of puzzling questions and creates a very uncertain picture of the quantum world. This book presents a clear and detailed exposition of the fundamental concepts of quantum theory: states, effects, observables, channels and instruments. It introduces several up-to-date topics, such as state discrimination, quantum tomography, measurement disturbance and entanglement distillation. A separate chapter is devoted to quantum entangle… Show more

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Cited by 264 publications
(487 citation statements)
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“…Let us analyze the probabilistic evolutions resulting from the requirement of zero energy cost. According to quantum measurement theory [52,[61][62][63], the measurement of O induces a stochastic evolution of the state of the system, described by a quantum instrument, namely a collection of quantum operations (completely positive trace non-increasing maps) {M x } x∈X subject to the normalization condition…”
Section: Energy-preserving Instrumentsmentioning
confidence: 99%
“…Let us analyze the probabilistic evolutions resulting from the requirement of zero energy cost. According to quantum measurement theory [52,[61][62][63], the measurement of O induces a stochastic evolution of the state of the system, described by a quantum instrument, namely a collection of quantum operations (completely positive trace non-increasing maps) {M x } x∈X subject to the normalization condition…”
Section: Energy-preserving Instrumentsmentioning
confidence: 99%
“…Once we know what generalized effect modules are, it is easy to see that 'homming into [0, 1]' yields the adjunction in (9). Moreover, this diagram (9) is enriched over Conv ≤1 , so that weakest precondition wp preserves subconvex sums of Kleisli maps (programs).…”
Section: Linear and (Sub)convex Computationmentioning
confidence: 99%
“…[9]. In certain cases the adjunction forms -or may be restricted to -an equivalence of categories, yielding a duality situation.…”
Section: Introductionmentioning
confidence: 99%
“…E(̺) = Tr M [U(ξ ⊗ ̺)], where ξ is the initial state of the memory and U : S(M ⊗ H) → S(H ⊗ M) (for more details see for instance Ref. [2]). …”
Section: Preliminariesmentioning
confidence: 99%