Minimal energy cost of entanglement extraction

Hackl, Lucas; Jonsson, Robert H.

doi:10.22331/q-2019-07-15-165

Cited by 22 publications

(26 citation statements)

References 83 publications

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“…with a single variational parameter φ. We have the single tangent vector |V 〉 = |V 1 〉 as defined in (48). From the inner product 〈V |V 〉 = 1 4 , we find g = 1 2 and ω = 0 implying J = 0.…”

Section: General Variational Manifoldmentioning

confidence: 99%

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Geometry of variational methods: dynamics of closed quantum systems

et al. 2020

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We present a systematic geometric framework to study closed quantum systems based on suitably chosen variational families. For the purpose of (A) real time evolution, (B) excitation spectra, (C) spectral functions and (D) imaginary time evolution, we show how the geometric approach highlights the necessity to distinguish between two classes of manifolds: Kähler and non-Kähler. Traditional variational methods typically require the variational family to be a Kähler manifold, where multiplication by the imaginary unit preserves the tangent spaces. This covers the vast majority of cases studied in the literature. However, recently proposed classes of generalized Gaussian states make it necessary to also include the non-Kähler case, which has already been encountered occasionally. We illustrate our approach in detail with a range of concrete examples where the geometric structures of the considered manifolds are particularly relevant. These go from Gaussian states and group theoretic coherent states to generalized Gaussian states.

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Section: General Variational Manifoldmentioning

confidence: 99%

“…Proposition 1 is also relevant for classifying real subspaces of complex Hilbert spaces. Interestingly, it is linked to the entanglement structure of fermionic Gaussian states, as made explicit in [48].…”

Section: Definition 2 We Classify General Variational Families M ⊂ Pmentioning

confidence: 99%

Geometry of variational methods: dynamics of closed quantum systems

et al. 2020

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“…For a given mode, a mode which purifies the mode is called its partner. A formula to identify the partner mode is proven for the vacuum state [45], for general Gaussian states of a scalar field [46], and it is generalized for fermionic fields in [47]. The partner formulae have been used in the contexts of black hole information loss [48] and entanglement harvesting [47,49].…”

Section: Discussionmentioning

confidence: 99%

“…A formula to identify the partner mode is proven for the vacuum state [45], for general Gaussian states of a scalar field [46], and it is generalized for fermionic fields in [47]. The partner formulae have been used in the contexts of black hole information loss [48] and entanglement harvesting [47,49]. From the viewpoint of QICs, the partner modes correspond to a class of 2-mode QICs.…”

Section: Discussionmentioning

confidence: 99%

Superadditivity of channel capacity through quantum fields

Yamaguchi,

Ahmadzadegan,

Simidzija

et al. 2020

Preprint

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Given that any communication is communication through quantum fields, we here study the scenario where a sender, Alice, causes information-carrying disturbances in a quantum field. We track the exact spread of these disturbances in space and time by using the technique of quantum information capsules (QIC). We find that the channel capacity between Alice and a receiver, Bob, is enhanced by Bob placing detectors not only inside but in addition also outside the causal future of Alice's encoding operation. Intuitively, this type of superadditivity arises because the field outside the causal future of Alice is entangled with the field inside Alice's causal future. Hence, the quantum noise picked up by Bob's detectors outside Alice's causal future is correlated with the noise of Bob's detectors inside Alice's causal future. In effect, this correlation allows Bob to improve the signal-to-noise ratio of those of his detectors which are in the causal future of Alice. Further, we develop the multimode generalization of the QIC technique. This allows us to extend the analysis to the case where Alice operates multiple localized and optionally entangled emitters. We apply the new techniques to the case where Alice enhances the channel capacity by operating multiple emitters that are suitably lined up and pre-timed to generate a quantum shockwave in the field.

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“…This allows us to re-derive existing results (such as the inner product between Gaussian states) in a simplified and often basis-independent way, but also enabled us to find some-to our knowledge-new formulas (such as some of the covariant Baker-Campbell-Hausdorff relations to combine squeezing and displacement). Several results and techniques of this manuscript have been implicitly used in some of our earlier works [16][17][18][19][20][21][22][23][24][25] and we are confident that other researchers can benefit from a thorough exposition of Gaussian states from Kähler structures.…”

Section: Introductionmentioning

confidence: 99%

Bosonic and fermionic Gaussian states from Kähler structures

Hackl

Bianchi

2021

SciPost Phys. Core

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We show that bosonic and fermionic Gaussian states (also known as ``squeezed coherent states’’) can be uniquely characterized by their linear complex structure JJ which is a linear map on the classical phase space. This extends conventional Gaussian methods based on covariance matrices and provides a unified framework to treat bosons and fermions simultaneously. Pure Gaussian states can be identified with the triple (G,\Omega,J)(G,Ω,J) of compatible Kähler structures, consisting of a positive definite metric GG, a symplectic form \OmegaΩ and a linear complex structure JJ with J^2=-\mathbb{1}J2=−1. Mixed Gaussian states can also be identified with such a triple, but with J^2\neq -\mathbb{1}J2≠−1. We apply these methods to show how computations involving Gaussian states can be reduced to algebraic operations of these objects, leading to many known and some unknown identities. We apply these methods to the study of (A) entanglement and complexity, (B) dynamics of stable systems, (C) dynamics of driven systems. From this, we compile a comprehensive list of mathematical structures and formulas to compare bosonic and fermionic Gaussian states side-by-side.

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Minimal energy cost of entanglement extraction

Cited by 22 publications

References 83 publications

Geometry of variational methods: dynamics of closed quantum systems

Geometry of variational methods: dynamics of closed quantum systems

Superadditivity of channel capacity through quantum fields

Bosonic and fermionic Gaussian states from Kähler structures

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