Journal ArticleDOI
The “transition probability” in the state space of a ∗-algebra
TLDR
In this paper, the authors derived properties of this straightforward generalization of the quantum mechanical transition probability and gave, in some important cases, an explicit expression for the transition probability P(ω,ϱ) in terms of the spectrum of all the numbers |(x,y)|2 taken over all such realizations.About:
This article is published in Reports on Mathematical Physics.The article was published on 1976-04-01. It has received 1555 citations till now. The article focuses on the topics: State space (physics) & Spectrum (functional analysis).read more
Citations
More filters
Journal ArticleDOI
Quantum entanglement
TL;DR: In this article, the basic aspects of entanglement including its characterization, detection, distillation, and quantification are discussed, and a basic role of entonglement in quantum communication within distant labs paradigm is discussed.
Journal ArticleDOI
Gaussian quantum information
Christian Weedbrook,Stefano Pirandola,Raúl García-Patrón,Nicolas J. Cerf,Timothy C. Ralph,Jeffrey H. Shapiro,Seth Lloyd +6 more
TL;DR: This review focuses on continuous-variable quantum information processes that rely on any combination of Gaussian states, Gaussian operations, and Gaussian measurements, including quantum communication, quantum cryptography, quantum computation, quantum teleportation, and quantum state and channel discrimination.
Journal ArticleDOI
Fidelity for Mixed Quantum States
TL;DR: In this article, the authors propose a definition of fidelity for mixed quantum states in terms of Uhlmann's transition probability formula F(ϱ1, ϱ2) = {trace [(√ϱ 1ϱ2 × √ ϱ 1)1/2]}2 and give new elementary proofs of its essential properties.
Gaussian quantum information
Christian Weedbrook,Stefano Pirandola,Raúl García-Patrón,Nicolas J. Cerf,Timothy C. Ralph,Jeffrey H. Shapiro,Seth Lloyd +6 more
TL;DR: In this article, a review of the state of the art in continuous-variable quantum information processing can be found, ranging from the basic theoretical tools and landmark experimental realizations to the most recent successful developments.
Journal ArticleDOI
Quantum estimation for quantum technology
TL;DR: Several quantities of interest in quantum information, including entanglement and purity, are nonlinear functions of the density matrix and cannot, even in principle, correspond to proper quantum information as discussed by the authors.
References
More filters
Book
C[*]-algebras and W[*]-algebras
TL;DR: The Representation Theorems for C *-Algebras and W*-Algebra are given in this paper, where the authors define C*-algebra as an algebra of all compact linear operators on a Hilbert space.
Journal ArticleDOI
An extension of Kakutani’s theorem on infinite product measures to the tensor product of semifinite *-algebras
TL;DR: Theorem 4.1 as discussed by the authors states that a normal state of a von Neumann algebra exists on the set of normal states of a w*-algebra X if and only if P(ip(, vi) converges.