Journal ArticleDOI
Fidelity for Mixed Quantum States
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TLDR
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.Abstract:
We propose a definition of fidelity for mixed quantum states in terms of Uhlmann's ‘transition probability’ formula F(ϱ1, ϱ2) = {trace [(√ϱ1ϱ2 × √ϱ1)1/2]}2 and give new elementary proofs of its essential properties.read more
Citations
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Quantum Computation and Quantum Information
TL;DR: This chapter discusses quantum information theory, public-key cryptography and the RSA cryptosystem, and the proof of Lieb's theorem.
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
Mixed State Entanglement and Quantum Error Correction
Charles H. Bennett,Charles H. Bennett,Charles H. Bennett,David P. DiVincenzo,David P. DiVincenzo,David P. DiVincenzo,John A. Smolin,John A. Smolin,John A. Smolin,William K. Wootters,William K. Wootters,William K. Wootters +11 more
TL;DR: It is proved that an EPP involving one-way classical communication and acting on mixed state M (obtained by sharing halves of Einstein-Podolsky-Rosen pairs through a channel) yields a QECC on \ensuremath{\chi} with rate Q=D, and vice versa, and it is proved Q is not increased by adding one- way classical communication.
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.
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.
References
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Book
Elements of information theory
Thomas M. Cover,Joy A. Thomas +1 more
TL;DR: The author examines the role of entropy, inequality, and randomness in the design of codes and the construction of codes in the rapidly changing environment.
Journal ArticleDOI
Statistical distance and the geometry of quantum states
TL;DR: By finding measurements that optimally resolve neighboring quantum states, this work uses statistical distinguishability to define a natural Riemannian metric on the space of quantum-mechanical density operators and to formulate uncertainty principles that are more general and more stringent than standard uncertainty principles.
Journal ArticleDOI
The “transition probability” in the state space of a ∗-algebra
TL;DR: 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.
Journal ArticleDOI
Statistical distance and Hilbert space
TL;DR: In this article, the authors define statistical distance between different preparations of the same quantum system, or in other words, between different rays in the same Hilbert space, and find that these two kinds of distance are in fact the same, a result which depends on certain peculiarities of quantum mechanics.