Pairing in fermionic systems: A quantum-information perspective

Kraus, Christina V.; Wolf, Michael M.; Cirac, J. I.; Giedke, G.

doi:10.1103/physreva.79.012306

Cited by 72 publications

(89 citation statements)

References 62 publications

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“…This, as far as we know, has never been shown and constitutes an interesting motivation for future projects. Also, a generalization of this proof to LMEs for fermionic systems [56] is apparently possible and interesting. The purpose of this Appendix is to present a self-contained derivation of the Heisenberg uncertainty principle for density operators.…”

Section: Discussionmentioning

confidence: 90%

Lindblad model of quantum Brownian motion

et al. 2016

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The theory of quantum Brownian motion describes the properties of a large class of open quantum systems. Nonetheless, its description in terms of a Born-Markov master equation, widely used in the literature, is known to violate the positivity of the density operator at very low temperatures. We study an extension of existing models, leading to an equation in the Lindblad form, which is free of this problem. We study the dynamics of the model, including the detailed properties of its stationary solution, for both constant and position-dependent coupling of the Brownian particle to the bath, focusing in particular on the correlations and the squeezing of the probability distribution induced by the environment.

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Section: Discussionmentioning

confidence: 90%

Lindblad model of quantum Brownian motion

et al. 2016

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“…Hence, we have to compare pairing with entanglement of particles. As we have shown in [22], there exist states that are entangled according to Def. 2.2, but which are not paired.…”

Section: Pairing and Entanglementmentioning

confidence: 92%

“…Next, one might think that pairing implies entanglement of the twoparticle reduced density-matrix. However, we have proven in [22] that there exist certain classes of BCS-states (which are always paired) that have a two-particle reduced density-matrix that is paired but not entangled in four appropriately chosen modes.…”

Section: Pairing and Entanglementmentioning

confidence: 97%

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Fermionic Quantum Many-Body Systems: A Quantum Information Approach

Kraus

2013

Complex Quantum Systems

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These lecture notes show how Quantum Information Theory can help us to gain deeper insight into the physics of fermionic quantum many-body systems. In the first part, we start from fermionic correlations as they appear in recent experiments with cold gases and develop a pairing theory for fermionic particles applicable to the current experimental setups. In the second part we introduce and discuss a new class of variational states, the fermionic Projected Entangled Pair States (fPEPS) that allow for an efficient approximation of ground and thermal states of local fermionic Hamiltonians.

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“…known from the BCS theory of superconductivity 67,68 . These states look similar to GHZstates coming from combinations of two pure spinors.…”

Section: The Generalized Hitchin Invariant As An Entanglement Measurementioning

confidence: 99%

Hitchin functionals are related to measures of entanglement

Lévay

Sárosi

2012

Phys. Rev. D

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According to the Black Hole/Qubit Correspondence (BHQC) certain black hole entropy formulas in supergravity can be related to multipartite entanglement measures of quantum information.Here we show that the origin of this correspondence is a connection between Hitchin functionals used as action functionals for form theories of gravity related to topological strings, and entanglement measures for systems with a small number of constituents. The basic idea acting as a unifying agent in these seemingly unrelated fields is stability connected to the mathematical notion of special prehomogeneous vector spaces associated to Freudenthal systems coming from simple Jordan algebras. It is shown that the nonlinear function featuring these functionals and defining Calabi-Yau and generalized Calabi-Yau structures is the Freudenthal dual a concept introduced recently in connection with the BHQC. We propose to use the Hitchin invariant for three-forms in 7 dimensions as an entanglement measure playing a basic role in classifying three-fermion systems with seven modes. The representative of the class of maximal tripartite entanglement is the threeform used as a calibration for compactification on manifolds with G 2 holonomy. The idea that entanglement measures are related to action functionals from which the usual correspondence of the BHQC follows at the tree level suggests that one can use the BHQC in a more general context.

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Pairing in fermionic systems: A quantum-information perspective

Cited by 72 publications

References 62 publications

Lindblad model of quantum Brownian motion

Lindblad model of quantum Brownian motion

Fermionic Quantum Many-Body Systems: A Quantum Information Approach

Hitchin functionals are related to measures of entanglement

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