Quantum entanglement

By Ryszard Horodecki, Pawel Horodecki, Michal Horodecki, Karol Horodecki. 2007

3,892 citations recorded by the source corpus.

All our former experience with application of quantum theory seems to say: {\it what is predicted by quantum formalism must occur in laboratory}. But the essence of quantum formalism - entanglement, recognized by Einstein, Podolsky, Rosen and Schr\"odinger - waited over 70 years to enter to laboratories as a new resource as real as energy. This holistic property of compound quantum systems, which involves nonclassical correlations between subsystems, is a potential for many quantum processes, including ``canonical'' ones: quantum cryptography, quantum teleportation and dense coding. However, it appeared that this new resource is very complex and difficult to detect. Being usually fragile to environment, it is robust against conceptual and mathematical tools, the task of which is to decipher its rich structure. This article reviews basic aspects of entanglement including its characterization, detection, distillation and quantifying. In particular, the authors discuss various manifestations of entanglement via Bell inequalities, entropic inequalities, entanglement witnesses, quantum cryptography and point out some interrelations. They also discuss a basic role of entanglement in quantum communication within distant labs paradigm and stress some peculiarities such as irreversibility of entanglement manipulations including its extremal form - bound entanglement phenomenon. A basic role of entanglement witnesses in detection of entanglement is emphasized.

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

View Paper: https://www.semanticscholar.org/paper/b2b81503312bbd4f77acb21ea04019f30e060f78

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In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

Description of quantum coherence in thermodynamic processes requires constraints beyond free energy (2014, methodology): “The approach most suited to our needs in this work is the one followed in refs 21,25,27,28, which has emerged from the theory of entanglement 20 .”
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Circuit complexity for coherent states (2018, background): “ht think of the coordinates in eq. (2.24). In the following, we focus on a family of pure states j ()i and then we can consider the quantum delity as the inner product between two such states, e.g., [67,68], F(;0) = jh ()j (0)ij: (5.1) The quantum information metric then measures the distance betwee”
Harnessing the Power of the Second Quantum Revolution (2020, background): “This new understanding grew out of a series of new (and/or re-examined) concepts including entanglement [2,3,13–16], contextuality [17–19], negativity of quasiprobabilities [20–22], deco-herence [4], no-cloning [23], and quantum trajectories [11,12,24,25].”
Characterizing Quantum Gates via Randomized Benchmarking (2011, methodology): “The average gate fidelity is obtained by integrating FE,U over CP d−1 using the Fubini-Study measure μFS [43], FE,U = FΛ,I = ∫”
On the Bures–Wasserstein distance between positive definite matrices (2017, background): “we have seen a curve for which the two sides of this inequality are equal. Thus the metric (32) leads to the distance function d(A,B) by a direct computation. The material in this section is based on [5, 20, 33, 34]. Takatsu [33] also discusses the metric geometry of the spaces of psd matrices of ra”
Expressibility and Entangling Capability of Parameterized Quantum Circuits for Hybrid Quantum‐Classical Algorithms (2019, background): “Past studies have shown that the first t frame potentials of an ensemble achieve their minimum values (Welch bounds) if and only if the ensemble is a state t-design [27– 29], motivating frame potentials as “probe[s] of randomness” [25].”
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