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Quantum evolution

About: Quantum evolution is a research topic. Over the lifetime, 472 publications have been published within this topic receiving 7135 citations.


Papers
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Journal ArticleDOI
TL;DR: In this paper, the authors present the fundamental notions of quantum metrology, such as shot-noise scaling, Heisenberg scaling, the quantum Fisher information and the Cramer-Rao bound.
Abstract: We summarize important recent advances in quantum metrology, in connection to experiments in cold gases, trapped cold atoms and photons. First we review simple metrological setups, such as quantum metrology with spin squeezed states, with Greenberger–Horne–Zeilinger states, Dicke states and singlet states. We calculate the highest precision achievable in these schemes. Then, we present the fundamental notions of quantum metrology, such as shot-noise scaling, Heisenberg scaling, the quantum Fisher information and the Cramer–Rao bound. Using these, we demonstrate that entanglement is needed to surpass the shot-noise scaling in very general metrological tasks with a linear interferometer. We discuss some applications of the quantum Fisher information, such as how it can be used to obtain a criterion for a quantum state to be a macroscopic superposition. We show how it is related to the speed of a quantum evolution, and how it appears in the theory of the quantum Zeno effect. Finally, we explain how uncorrelated noise limits the highest achievable precision in very general metrological tasks.This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to '50 years of Bell's theorem'.

532 citations

Journal Article
Nicolas Gisin1
TL;DR: In this article, the Schroedinger dynamics and the projection postulate are unified and a non deterministic generalization of the Schröter equation compatible with relativity is presented. And a symmetry preserving generalisation of the Ghirardi-Rimini-Weber model is presented for quantum dynamical semigroups, including the damped harmonic oscillator and spin relaxation.
Abstract: Our aim is to unify the Schroedinger dynamics and the projection postulate. We first prove that the Schroedinger evolution is the only quantum evolution that is deterministic and compatible with relativity. Next we present a non deterministic generalization of the Schroedinger equation compatible with relativity. This time continuous pure state valued stochastic process covers the whole class of quantum dynamical semigroups, as exemplified by the damped harmonic oscillator and spin relaxation. Finally a symmetry preserving generalization of the Ghirardi-Rimini-Weber model is presented. (orig.).

513 citations

Journal ArticleDOI
TL;DR: This work explores the ultimate limit in paradigmatic cases of optimal control theory, and demonstrates that it coincides with the maximum speed limit allowed by quantum evolution.
Abstract: Optimal control theory is a promising candidate for a drastic improvement of the performance of quantum information tasks. We explore its ultimate limit in paradigmatic cases, and demonstrate that it coincides with the maximum speed limit allowed by quantum evolution.

404 citations

Journal ArticleDOI
TL;DR: In this paper, a new approach to the theory of the geometric phase in quantum mechanics, based entirely on kinematic ideas, is developed, and it is shown that a gauge and reparametrization invariant phase can be naturally associated with any smooth open curve of unit vectors in Hilbert space.

398 citations

Journal ArticleDOI
TL;DR: This work proposes a new characterization of non-Markovian quantum evolution based on the concept ofnon- Markovianity degree, which provides an analog of a Schmidt number in the entanglement theory and reveals the formal analogy between quantum evolution and the entangled state.
Abstract: We propose a new characterization of non-Markovian quantum evolution based on the concept of non-Markovianity degree. It provides an analog of a Schmidt number in the entanglement theory and reveals the formal analogy between quantum evolution and the entanglement theory: Markovian evolution corresponds to a separable state and the non-Markovian one is further characterized by its degree. It enables one to introduce a non-Markovianity witness-an analog of an entanglement witness, and a family of measures-an analog of Schmidt coefficients, and finally to characterize maximally non-Markovian evolution being an analog of the maximally entangled state. Our approach allows us to classify the non-Markovianity measures introduced so far in a unified rigorous mathematical framework.

295 citations

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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20221
202143
202067
201941
201840
201720